Minitab  Minitab
Blog posts and articles about using Minitab software in quality improvement projects, research, and more.
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Thu, 28 Jul 2016 22:12:59 +0000
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OneSample ttest: Calculating the tstatistic is not really a bear
http://blog.minitab.com/blog/marilynwheatleysblog/onesamplettestcalculatingthetstatisticisnotreallyabear
<p>While some posts in our Minitab blog focus on <a href="http://blog.minitab.com/blog/adventuresinstatistics/understandingtteststvaluesandtdistributions">understanding ttests and tdistributions</a> this post will focus more simply on how to handcalculate the tvalue for a onesample ttest (and how to replicate the pvalue that Minitab gives us). </p>
<p>The formulas used in this post are available within <a href="http://www.minitab.com/enus/products/minitab/">Minitab Statistical Software</a> by choosing the following menu path: <strong>Help</strong> > <strong>Methods and Formulas</strong> > <strong>Basic Statistics</strong> > <strong>1sample t</strong>.</p>
<p>The null and three alternative hypotheses for a onesample ttest are shown below:</p>
<p style="marginleft: 40px;"><img border="0" height="184" src="http://cdn.app.compendium.com/uploads/user/458939f4fe084dbcb271efca0f5a2682/f6d0da32ba1d41d4ace1af34dcb51351/File/553bfcce02e2394b13b5175655c99df6/553bfcce02e2394b13b5175655c99df6.png" width="368" /></p>
<p>The default alternative hypothesis is the last one listed: The true population mean is not equal to the mean of the sample, and this is the option used in this example.</p>
<p><img alt="bear" src="http://cdn.app.compendium.com/uploads/user/458939f4fe084dbcb271efca0f5a2682/479b4fbdf8c040119409f4109cc4c745/Image/88db51bd8ccbfcbb306372bb65fa4902/bear.jpg" style="margin: 10px 15px; float: right; width: 400px; height: 290px;" />To understand the calculations, we’ll use a sample data set available within Minitab. The name of the dataset is <strong>Bears.MTW</strong>, because the calculation is not a huge bear to wrestle (plus who can resist a dataset with that name?). The path to access the sample data from within Minitab depends on the version of the software. </p>
<p>For the current version of Minitab, <a href="http://www.minitab.com/enus/products/minitab/whatsnew/">Minitab 17.3.1</a>, the sample data is available by choosing <strong>Help</strong> > <strong>Sample Data</strong>.</p>
<p>For previous versions of Minitab, the data set is available by choosing <strong>File</strong> > <strong>Open Worksheet</strong> and clicking the <strong>Look in Minitab Sample Data folder</strong> button at the bottom of the window.</p>
<p>For this example, we will use column C2, titled Age, in the Bears.MTW data set, and we will test the hypothesis that the average age of bears is 40. First, we’ll use <strong>Stat</strong> > <strong>Basic Statistics</strong> > <strong>1sample t</strong> to test the hypothesis:</p>
<p style="marginleft: 40px;"><img border="0" height="315" src="http://cdn.app.compendium.com/uploads/user/458939f4fe084dbcb271efca0f5a2682/f6d0da32ba1d41d4ace1af34dcb51351/File/d3336e100a9a4a91501ed1206c8e807f/d3336e100a9a4a91501ed1206c8e807f.png" width="400" /></p>
<p>After clicking <strong>OK</strong> above we see the following results in the session window:</p>
<p style="marginleft: 40px;"><img border="0" height="118" src="http://cdn.app.compendium.com/uploads/user/458939f4fe084dbcb271efca0f5a2682/f6d0da32ba1d41d4ace1af34dcb51351/File/e62a2a776614c60eff0dd6383f66e5f5/e62a2a776614c60eff0dd6383f66e5f5.png" width="464" /></p>
<p>With a high pvalue of 0.361, we don’t have enough evidence to conclude that the average age of bears is significantly different from 40. </p>
<p>Now we’ll see how to calculate the T value above by hand.</p>
<p>The formula for the T value (0.92) shown above is calculated using the following formula in Minitab:</p>
<p style="marginleft: 40px;"><img border="0" height="172" src="http://cdn.app.compendium.com/uploads/user/458939f4fe084dbcb271efca0f5a2682/f6d0da32ba1d41d4ace1af34dcb51351/File/701f9c0efa98a38fb397f3c3ec459b66/701f9c0efa98a38fb397f3c3ec459b66.png" width="247" /></p>
<p>The output from the 1sample t test above gives us all the information we need to plug the values into our formula:</p>
<p style="marginleft: 40px;">Sample mean: 43.43</p>
<p style="marginleft: 40px;">Sample standard deviation: 34.02</p>
<p style="marginleft: 40px;">Sample size: 83</p>
<p>We also know that our target or hypothesized value for the mean is 40.</p>
<p>Using the numbers above to calculate the tstatistic we see:</p>
<p style="marginleft: 40px;">t = (43.4340)/34.02/√83) = <strong>0.918542</strong><br />
(which rounds to 0.92, as shown in Minitab’s 1sample ttest output)</p>
<p>Now, we <em>could </em>dust off a statistics textbook and use it to compare our calculated t of 0.918542 to the corresponding critical value in a ttable, but that seems like a pretty big bear to wrestle when we can easily get the pvalue from Minitab instead. To do that, I’ve used <strong>Graph</strong> > <strong>Probability Distribution Plot</strong> > <strong>View Probability</strong>:</p>
<p style="marginleft: 40px;"><img border="0" height="382" src="http://cdn.app.compendium.com/uploads/user/458939f4fe084dbcb271efca0f5a2682/f6d0da32ba1d41d4ace1af34dcb51351/File/e43510dc233e71f22b93f190deb5e523/e43510dc233e71f22b93f190deb5e523.png" width="419" /></p>
<p>In the dialog above, we’re using the t distribution with 82 degrees of freedom (we had an N = 83, so the degrees of freedom for a 1sample ttest is N1). Next, I’ve selected the <strong>Shaded Area</strong> tab:</p>
<p style="marginleft: 40px;"><img border="0" height="383" src="http://cdn.app.compendium.com/uploads/user/458939f4fe084dbcb271efca0f5a2682/f6d0da32ba1d41d4ace1af34dcb51351/File/e36572b6cead5cf393763d880b6f229a/e36572b6cead5cf393763d880b6f229a.png" width="414" /></p>
<p>In the dialog box above, we’re defining the shaded area by the X value (the calculated tstatistic), and I’ve typed in the tvalue we calculated in the <strong>X value</strong> field. This was a 2tailed test, so I’ve selected <strong>Both Tails</strong> in the dialog above.</p>
<p>After clicking <strong>OK</strong> in the window above, we see:</p>
<p style="marginleft: 40px;"><img border="0" height="384" src="http://cdn.app.compendium.com/uploads/user/458939f4fe084dbcb271efca0f5a2682/f6d0da32ba1d41d4ace1af34dcb51351/File/a12abfcbe5ecea6902e4a138e96a53a6/a12abfcbe5ecea6902e4a138e96a53a6.png" width="576" /></p>
<p>We add together the probabilities from both tails, 0.1805 + 0.1805 and that equals 0.361 – the same pvalue that Minitab gave us for the 1sample t test. </p>
<p>That wasn’t so bad—not a difficult bear to wrestle at all!</p>
Data Analysis
Fun Statistics
Hypothesis Testing
Learning
Statistics
Statistics Help
Stats
Wed, 27 Jul 2016 17:57:00 +0000
http://blog.minitab.com/blog/marilynwheatleysblog/onesamplettestcalculatingthetstatisticisnotreallyabear
Marilyn Wheatley

On Paying Bills, Marriage, and Alert Systems
http://blog.minitab.com/blog/meredithgriffith/onpayingbillsmarriageandalertsystems
<p>When I blogged about <a href="http://blog.minitab.com/blog/meredithgriffith/whatatriptothedentisttaughtusaboutautomation">automation</a> back in March, I made my husband out to be an automation guru. Well, he certainly is. But what you don’t know about my husband is that while he loves to automate everything in his life, sometimes he drops the ball. He’s human; even I have to cut him a break every now and then.</p>
<p>On the other hand, instances of hypocrisy in his behavior tend to make for a good story. So here we are again.</p>
<span style="lineheight: 1.2;">On Paying Bills</span>
<p>When we married 5 years ago and began combining our bank accounts, I learned a few things about my husband. Nothing that I haven’t already shared with you. Because he loves automation, it came as no surprise to me that all his accounts resided in a single online repository (mint.com) where he could view his net worth—assets such as his home and car value, and debts including the loan left on his home and bills and credit card expenses that needed to be paid. He’d also made sure to automate the payment of all loans, utility bills, and credit cards—and the respective account would notify him when a payment was made.</p>
<p>This mint.com account served as one dashboard view of all possible accounts he would otherwise have to access independently to see statements and make payments. It was genius! </p>
<p><img alt="mint" src="https://cdn.app.compendium.com/uploads/user/458939f4fe084dbcb271efca0f5a2682/dae6c7b7fc2246169d65f04909c20ab1/Image/299516c1c0685e413532648e7a185d6e/mint.jpg" style="width: 1000px; height: 563px;" /></p>
<p>He could set up savings goals, budgets, email alerts for credit card payment reminders and notification of payment, suspicious account activity, and just about any other miscellaneous charge or activity or change in spending habits. It really did make life easier.</p>
<p>Until I entered the picture.</p>
<span style="lineheight: 1.2;">On Marriage</span>
<p>We married, I synced my bank accounts, and we combined cash. I scoured his historical data to observe spending habits—areas where we could save money (Taco Bell topped the ‘high spending’ for the Food/Dining category). As I began poking around his accounts, I noticed a monthly fee his Chase Freedom Visa credit card was charging him. I asked him about the fee; he pleaded ignorance. When I investigated further, I discovered that he’d been charged this fee for <em>years</em>, since he first got the credit card.</p>
<p>I researched online and discovered that other cardholders had complained of being erroneously enrolled in a protection program when they first got their Chase Freedom card, and were being charged a similar fee of varying amounts monthly. Turns out this monthly fee was a percentage of monthly spending—and the Chase Freedom Visa credit card incentivized a cardholder to make all his purchases with that card, given its offer of 5% cash back on all purchases at the time.</p>
<p>Needless to say, I wanted that money back. No less than a few minutes later, we were on the phone with Chase disputing the program enrollment and monthly charges. They acknowledged their error and refunded us the money lost over a span of several years.</p>
<p>The lesson in all of this? Marry someone who’s not afraid to dig through your historical data.</p>
On Alert Systems
<p>More seriously, automating processes or workflows is incredibly helpful, but without the proper attention and alert systems in place, you may still encounter holes in the story. Automation and alerts must go handinhand to be effective—and as a consumer of the information you’re automating, you still must be invested enough to look at the big picture.</p>
<p>For my husband, the beauty in automating his bill payments and aggregating all his accounts on mint.com was to save time he'd otherwise spend paying bills separately and checking cash flows in multiple different accounts. But he failed to set up alerts about important aspects of the process he was automating, and he failed to check in on his process from time to time. Mint.com provides an incredibly useful dashboard to give you the big picture overview of your accounts and your net worth; it also provides a plethora of alert options that save a consumer time from digging for red flags <em>after</em> the undesirable event has become a regular occurrence in the process (like I did). But without checking the status of the system or using its full automation potential, the system is only as good as its inputs until you revisit it or tweak it.</p>
<p>This is just one piece of the puzzle. Alert systems offer so much more!</p>
<ol>
<li><strong>Awareness</strong>—setting alerts through mint.com with regard to miscellaneous fees would have offered insight about the credit card program my husband had been erroneously enrolled in.</li>
<li><strong>Immediate Feedback</strong>—the first time a fee was charged, he would have been able to take immediate action rather than waiting years later for his wife to discover the charge (manually, mind you).</li>
<li><strong>Time Saver</strong>—aside from automating bill pay and combining all accounts into a single repository for a big picture view of one’s financial status (which is certainly a timesaver in reviewing accounts and paying bills in various locations), an alert system would have saved me a lot of time in digging through my husband’s financial data to understand the origin of the fee Chase was charging him.</li>
<li><strong>Money Saver</strong>—while we <em>were </em>refunded all the money charged in monthly fees by Chase, clearly an alert system would have been a more foolproof way to save money in the first place. Alerts are also effective in ensuring bill pay occurs on time, notifying you when a statement has been prepared, when the bill is due, and when the bill has been paid.</li>
</ol>
<p>As process engineers or quality managers in the manufacturing world, you are very close to your process and its inputs. You want to know when something goes wrong, right when it happens. You don’t want a consumer to discover a flaw in a part or product you manufactured and sold years before, only to be faced with product recalls, customer reimbursements, time and money invested to remanufacture and replace the defective product for unhappy customers, and in some cases, lawsuits. The stakes are high.</p>
<p>Minitab offers a solution to this pain point in its RealTime SPC dashboard. The dashboard is completely powered by Minitab Statistical Software, taking the graphs and output you know and love and placing them on customized dashboard views that show the current state of your processes. The dashboard gives you a big picture view of your processes across all your production sites, for instance, and highlights where improvements can be made. You can incorporate any graph or analysis you want—such as histograms, control charts, or process capability analysis. You can automatically generate quality reports about your processes, and set up any alert that will help you respond to defects faster.</p>
<p><img alt="qualityDashboard" src="https://cdn.app.compendium.com/uploads/user/458939f4fe084dbcb271efca0f5a2682/dae6c7b7fc2246169d65f04909c20ab1/Image/c9c6bb0f36670d640bf29072a830b9d5/qualitydashboard.jpg" style="width: 900px; height: 651px;" /></p>
<p><img alt="spcDashboard" src="https://cdn.app.compendium.com/uploads/user/458939f4fe084dbcb271efca0f5a2682/dae6c7b7fc2246169d65f04909c20ab1/Image/27347695ab637e3931fe251860d12079/spcdashboard.jpg" style="lineheight: 1.6; width: 900px; height: 665px;" /></p>
<p><span style="lineheight: 1.6;">In the case of my marriage, alert systems are certainly practical from a financial standpoint. But in the world of manufacturing, ensuring alerts are set up around your automated processes has farreaching implications as the time and moneysaving elements of alert systems greatly impacts a company’s bottom line. To learn more about how Minitab can help you, contact us at </span><a href="mailto:sales@minitab.com" style="lineheight: 1.6;">Sales@minitab.com</a><span style="lineheight: 1.6;">.</span></p>
<p>And if you’ve ever thought twice about whether or not you should marry, let this story be an encouragement to you—you may actually find a spouse who can make you richer.</p>
<p> </p>
Automation
Data Analysis
Quality Improvement
Six Sigma
Mon, 25 Jul 2016 12:00:00 +0000
http://blog.minitab.com/blog/meredithgriffith/onpayingbillsmarriageandalertsystems
Meredith Griffith

Can Regression and Statistical Software Help You Find a Great Deal on a Used Car?
http://blog.minitab.com/blog/understandingstatistics/canregressionandstatisticalsoftwarehelpyoufindagreatdealonausedcar
<p>You need to consider many factors when you’re buying a used car. Once you narrow your choice down to a particular car model, you can get a wealth of information about individual cars on the market through the Internet. How do you navigate through it all to find the best deal? By analyzing the data you have available. </p>
<p><img alt="" src="http://cdn2.content.compendiumblog.com/uploads/user/458939f4fe084dbcb271efca0f5a2682/479b4fbdf8c040119409f4109cc4c745/Image/710ce579b4120727bf67e8b48f5965e8/240_used_car_kovacs.jpg" style="lineheight: 20.7999992370605px; borderwidth: 1px; borderstyle: solid; margin: 10px 15px; float: right; width: 240px; height: 240px;" /></p>
<p>Let's look at how this works using <a href="http://blog.minitab.com/blog/understandingstatistics/wejustgotridoffivereasonstofeardataanalysis">the Assistant</a> in Minitab 17. With the Assistant, you can use regression analysis to calculate the expected price of a vehicle based on variables such as year, mileage, whether or not the technology package is included, and whether or not a free Carfax report is included.</p>
<p>And it's probably a lot easier than you think. </p>
<p>A search of a leading Internet auto sales site yielded data about 988 vehicles of a specific make and model. After putting the data into Minitab, we choose <strong>Assistant > Regression…</strong></p>
<p><img alt="" src="http://cdn2.content.compendiumblog.com/uploads/user/458939f4fe084dbcb271efca0f5a2682/479b4fbdf8c040119409f4109cc4c745/Image/9e87de993a0daa39e6643b8c6d3aed9c/regression_dialog.png" style="width: 395px; height: 247px;" /></p>
<p>At this point, if you aren’t very comfortable with regression, <a href="http://www.minitab.com/products/minitab/assistant/">the Assistant makes it easy to select the right option for your analysis</a>.</p>
A Decision Tree for Selecting the Right Analysis
<p>We want to explore the relationships between the price of the vehicle and four factors, or X variables. Since we have more than one X variable, and since we're not looking to optimize a response, we want to choose Multiple Regression.</p>
<p><img alt="" src="http://cdn2.content.compendiumblog.com/uploads/user/458939f4fe084dbcb271efca0f5a2682/479b4fbdf8c040119409f4109cc4c745/Image/bc802d35bfb57ca3b86e061da4fa4b09/regression_decision_tree_w640.png" style="width: 640px; height: 502px;" /></p>
<p>This <a href="//cdn2.content.compendiumblog.com/uploads/user/458939f4fe084dbcb271efca0f5a2682/479b4fbdf8c040119409f4109cc4c745/File/9ecb2280228deb621ee2db7f6fbe300e/used_cars.MTW">data set</a> includes five columns: mileage, the age of the car in years, whether or not it has a technology package, whether or not it includes a free CARFAX report, and, finally, the price of the car.</p>
<p>We don’t know which of these factors may have significant relationship to the cost of the vehicle, and we don’t know whether there are significant twoway interactions between them, or if there are quadratic (nonlinear) terms we should include—but we don’t need to. Just fill out the dialog box as shown. </p>
<p><img alt="" src="http://cdn2.content.compendiumblog.com/uploads/user/458939f4fe084dbcb271efca0f5a2682/479b4fbdf8c040119409f4109cc4c745/Image/b93a0a755e8e73dc7f681ea4b1965749/regression_dialog_box.png" style="width: 532px; height: 382px;" /></p>
<p>Press OK and the Assistant assesses each potential model and selects the bestfitting one. It also provides a comprehensive set of reports, including a Model Building Report that details how the final model was selected and a Report Card that notifies you to potential problems with the analysis, if there are any.</p>
Interpreting Regression Results in Plain Language
<p>The Summary Report tells us in plain language that there is a significant relationship between the Y and X variables in this analysis, and that the factors in the final model explain 91 percent of the observed variation in price. It confirms that all of the variables we looked at are significant, and that there are significant interactions between them. </p>
<p><img alt="" src="http://cdn2.content.compendiumblog.com/uploads/user/458939f4fe084dbcb271efca0f5a2682/479b4fbdf8c040119409f4109cc4c745/Image/746574a27bba821ffab4f77ae1a2931b/multiple_regression_summary_report_w640.png" style="width: 640px; height: 480px;" /></p>
<p>The Model Equations Report contains the final regression models, which can be used to predict the price of a used vehicle. The Assistant provides 2 equations, one for vehicles that include a free CARFAX report, and one for vehicles that do not.</p>
<p><img alt="" src="http://cdn2.content.compendiumblog.com/uploads/user/458939f4fe084dbcb271efca0f5a2682/479b4fbdf8c040119409f4109cc4c745/Image/58598060212558634d62d75a7045bf0b/regression_equation_w640.png" style="width: 640px; height: 186px;" /></p>
<p>We can tell several interesting things about the price of this vehicle model by reading the equations. First, the average cost for vehicles with a free CARFAX report is about $200 more than the average for vehicles with a paid report ($30,546 vs. $30,354). This could be because these cars probably have a clean report (if not, the sellers probably wouldn’t provide it for free).</p>
<p>Second, each additional mile added to the car decreases its expected price by roughly 8 cents, while each year added to the cars age decreases the expected price by $2,357.</p>
<p>The technology package adds, on average, $1,105 to the price of vehicles that have a free CARFAX report, but the package adds $2,774 to vehicles with a paid CARFAX report. Perhaps the sellers of these vehicles hope to use the appeal of the technology package to compensate for some other influence on the asking price. </p>
Residuals versus Fitted Values
<p>While these findings are interesting, our goal is to find the car that offers the best value. In other words, we want to find the car that has the largest difference between the asking price and the expected asking price predicted by the regression analysis.</p>
<p>For that, we can look at the Assistant’s Diagnostic Report. The report presents a chart of Residuals vs. Fitted Values. If we see obvious patterns in this chart, it can indicate problems with the analysis. In that respect, this chart of Residuals vs. Fitted Values looks fine, but now we’re going to use the chart to identify the best value on the market.</p>
<p><img alt="" src="http://cdn2.content.compendiumblog.com/uploads/user/458939f4fe084dbcb271efca0f5a2682/479b4fbdf8c040119409f4109cc4c745/Image/d55ae8720ba281bf37135b68b2069434/multiple_regression_diagnostic_report_w640.png" style="width: 640px; height: 480px;" /></p>
<p>In this analysis, the “Fitted Values” are the prices predicted by the regression model. “Residuals” are what you get when you subtract the actual asking price from the predicted asking price—exactly the information you’re looking for! The Assistant marks large residuals in red, making them very easy to find. And three of those residuals—which appear in light blue above because we’ve selected them—appear to be very far below the asking price predicted by the regression analysis.</p>
<p>Selecting these data points on the graph reveals that these are vehicles whose data appears in rows 357, 359, and 934 of the data sheet. Now we can revisit those vehicles online to see if one of them is the right vehicle to purchase, or if there’s something undesirable that explains the low asking price. </p>
<p>Sure enough, the records for those vehicles reveal that two of them have severe collision damage.</p>
<p><img alt="" src="http://cdn2.content.compendiumblog.com/uploads/user/458939f4fe084dbcb271efca0f5a2682/479b4fbdf8c040119409f4109cc4c745/Image/5dbbf5aa405d4b2d53ec720657a09556/vehicles.jpg" style="width: 320px; height: 356px;" /></p>
<p>But the remaining vehicle appears to be in pristine condition, and is several thousand dollars less than the price you’d expect to pay, based on this analysis!</p>
<p><img alt="" src="http://cdn2.content.compendiumblog.com/uploads/user/458939f4fe084dbcb271efca0f5a2682/479b4fbdf8c040119409f4109cc4c745/Image/640bd720a3d1f8b04713aa0ec321a570/nice_car.png" style="width: 254px; height: 189px;" /></p>
<p>With the power of regression analysis and the Assistant, we’ve found a great used car—at a price you know is a real bargain.</p>
<p> </p>
Data Analysis
Fun Statistics
Regression Analysis
Statistics
Statistics Help
Fri, 22 Jul 2016 10:00:00 +0000
http://blog.minitab.com/blog/understandingstatistics/canregressionandstatisticalsoftwarehelpyoufindagreatdealonausedcar
Eston Martz

High Cpk and a FunnyLooking Histogram: Is My Process Really that Amazing?
http://blog.minitab.com/blog/marilynwheatleysblog/highcpkandafunnylookinghistogramismyprocessreallythatamazing
<p>Here is a scenario involving process capability that we’ve seen from time to time in Minitab's technical support department. I’m sharing the details in this post so that you’ll know where to look if you encounter a similar situation.</p>
<p>You need to run a capability analysis. You generate the output using <a href="http://www.minitab.com/enus/products/minitab/">Minitab Statistical Software</a>. When you look at the results, the Cpk is huge and the histogram in the output looks strange:</p>
<p style="marginleft: 40px;"><img border="0" height="468" src="https://cdn.app.compendium.com/uploads/user/458939f4fe084dbcb271efca0f5a2682/f6d0da32ba1d41d4ace1af34dcb51351/File/9549037dc2e0a30a77ab36737edeeb09/9549037dc2e0a30a77ab36737edeeb09.png" width="624" /></p>
<p>What’s going on here? The Cpk seems unrealistic at 42.68, the "within" fit line is tall and narrow, and the bars on the histogram are all smashed down. Yet if we use the exact same data to make a histogram using the Graph menu, we see that things don’t look so bad:</p>
<p style="marginleft: 40px;"><img border="0" height="384" src="https://cdn.app.compendium.com/uploads/user/458939f4fe084dbcb271efca0f5a2682/f6d0da32ba1d41d4ace1af34dcb51351/File/d111d612a239ac72e49fe7d3fccab0f5/d111d612a239ac72e49fe7d3fccab0f5.png" width="576" /></p>
<p><span style="lineheight: 1.6;">So what explains the odd </span><span style="lineheight: 20.8px;">output for the </span><span style="lineheight: 1.6;">capability analysis?</span></p>
<p>Notice that the ‘within subgroup’ variation in the capability output is represented by the tall dashed line in the middle of the histogram. This is the StDev (Within) shown on the left side of the graph. The within subgroup variation of 0.0777 is very small relative to the overall standard deviation. </p>
<p>So what is causing the within subgroup variation to be so small? Another graph in Minitab can give us the answer: The Capability Sixpack. In the case above, the subgroup size was 1 and Minitab’s Capability Sixpack in <strong>Stat</strong> > <strong>Quality Tools</strong> > <strong>Capability Sixpack</strong> > <strong>Normal</strong> will plot the data on a control chart for individual observations, an Ichart:</p>
<p style="marginleft: 40px;"><img border="0" height="468" src="https://cdn.app.compendium.com/uploads/user/458939f4fe084dbcb271efca0f5a2682/f6d0da32ba1d41d4ace1af34dcb51351/File/46352209a7f75bbfba20794c925fc897/46352209a7f75bbfba20794c925fc897.png" width="624" /></p>
<p>Hmmm...this could be why, in <a href="http://www.minitab.com/enus/services/training/">Minitab training</a>, our instructors recommend using the Capability Sixpack first.</p>
<p>In the Capability Sixpack above, we can see that the individually plotted values on the Ichart show an upward trend, and it appears that the process is <em>not </em>stable and in control (as <span><a href="http://blog.minitab.com/blog/understandingstatistics/ithinkicaniknowicanahighleveloverviewofprocesscapabilityanalysis">it should be for data used in a capability analysis</a></span>). A closer look at the data in the worksheet clearly reveals that the data was sorted in ascending order:</p>
<p style="marginleft: 40px;"><img border="0" height="265" src="https://cdn.app.compendium.com/uploads/user/458939f4fe084dbcb271efca0f5a2682/f6d0da32ba1d41d4ace1af34dcb51351/File/44945e3490bf95cfc2c796618195b75e/44945e3490bf95cfc2c796618195b75e.png" width="103" /></p>
<p>Because the withinsubgroup variation for data not collected in subgroups is estimated based on the <a href="http://blog.minitab.com/blog/marilynwheatleysblog/whatsamovingrangeandhowisitcalculated">moving ranges</a> (average of the distance between consecutive points), sorting the data causes the withinsubgroup variation to be very small. With very little withinsubgroup variation we see a very tall, narrow fit line that represents the within subgroup variation, and that is ‘smashing down’ the bars on the histogram. We can see this by creating a histogram in the Graph menu and forcing Minitab to use a very small standard deviation (by default this graph uses the overall standard deviation that is used when calculating Ppk): <strong>Graph</strong> > <strong>Histogram </strong>> <strong>Simple</strong>, enter the data, click <strong>Data View</strong>, choose the <strong>Distribution </strong>tab, check <strong>Fit distribution</strong> and for the Historical StDev enter 0.0777, then click <strong>OK</strong> and now we get:</p>
<p style="marginleft: 40px;"><img src="https://cdn.app.compendium.com/uploads/user/458939f4fe084dbcb271efca0f5a2682/f6d0da32ba1d41d4ace1af34dcb51351/File/a20807e5892fdb0823bccf0828b5f585/a20807e5892fdb0823bccf0828b5f585.png" /></p>
<p style="marginleft: 40px;"><img src="https://cdn.app.compendium.com/uploads/user/458939f4fe084dbcb271efca0f5a2682/f6d0da32ba1d41d4ace1af34dcb51351/File/421afe5e10ba17256da42ac98bf11192/421afe5e10ba17256da42ac98bf11192.png" /></p>
<p>Mystery solved! And if you still don’t believe me, we can get a better looking capability histogram by randomizing the data first (<strong>Calc</strong> > <strong>Random Data</strong> > <strong>Sample From Columns</strong>):</p>
<p style="marginleft: 40px;"><img border="0" height="312" src="https://cdn.app.compendium.com/uploads/user/458939f4fe084dbcb271efca0f5a2682/f6d0da32ba1d41d4ace1af34dcb51351/File/7f92652636a67fd8f17396bcb52e960c/7f92652636a67fd8f17396bcb52e960c.png" width="397" /></p>
<p>Now if we run the capability analysis using the randomized data in C2 we see:</p>
<p style="marginleft: 40px;"><img border="0" height="468" src="https://cdn.app.compendium.com/uploads/user/458939f4fe084dbcb271efca0f5a2682/f6d0da32ba1d41d4ace1af34dcb51351/File/5c4c93d603abfb79a1f49b4c412c689b/5c4c93d603abfb79a1f49b4c412c689b.png" width="624" /></p>
<p>A note of caution: I’m <strong><em>not </em></strong>suggesting that the data for a capability analysis should be randomized. The moral of the story is that the data in the worksheet should be entered in the order it was collected so that it is representative of the normal variation in the process (i.e., the data should not be <em>sorted</em>). </p>
<p>Too bad our Cpk doesn’t look as amazing as it did before…now it's time to get to <a href="http://blog.minitab.com/blog/michelleparet/howtoimprovecpk">work with Minitab to improve our Cpk</a>!</p>
Capability Analysis
Data Analysis
Lean Six Sigma
Quality Improvement
Reliability Analysis
Wed, 20 Jul 2016 12:00:00 +0000
http://blog.minitab.com/blog/marilynwheatleysblog/highcpkandafunnylookinghistogramismyprocessreallythatamazing
Marilyn Wheatley

Conditional Formatting of Large Residuals and Unusual Combinations of Predictors
http://blog.minitab.com/blog/statisticsandqualityimprovement/conditionalformattingoflargeresidualsandunusualcombinationsofpredictors
<p>If you've used our software, you’re probably used to <a href="http://support.minitab.com/enus/minitab/17/topiclibrary/modelingstatistics/usingfittedmodels/basics/storedmodeloverview/">many of the things you can do in Minitab</a> once you’ve fit a model. For example, after you fit a response to a given model for some predictors with <strong>Stat > DOE > Response Surface > Analyze Response Surface Design</strong>, you can do the following:</p>
<ul>
<li>Predict the mean value of the response variable for new combinations of settings of the predictors.</li>
<li>Draw factorial plots, surface plots, contour plots, and overlaid contour plots.</li>
<li>Use the model to find combinations of predictor settings that optimize the predicted mean of the response variable.</li>
</ul>
<p style="marginleft: 40px;"><img alt="In the Response Surface Menu, you can see tools that you can use with a fitte model: Predict, Factorial Plots, Contour Plot, Surface Plot, Overlaid Contour Plot, Response Optimizer" src="https://cdn.app.compendium.com/uploads/user/458939f4fe084dbcb271efca0f5a2682/22791f44517c42aa9f28864c95cb4e27/Image/7bdafa3c9c81fdc2493d9656f7eaaeb0/path_that_shows_model_tools.png" style="width: 639px; height: 364px;" /></p>
<p>But once your response has that little green check box that says you have a valid model, there’s even <em>more</em> that you can do. For example, you can also use <a href="http://blog.minitab.com/blog/statisticsandqualityimprovement/3newthingsyoucandobyrightclickinginminitab172">conditional formatting</a> to highlight two kinds of rows:</p>
<ul>
<li>Unusual combinations of predictor values</li>
<li>Values of the response variable that the model does not explain well</li>
</ul>
<p>Want to try it out? You can follow along using <a href="https://cdn.app.compendium.com/uploads/user/458939f4fe084dbcb271efca0f5a2682/22791f44517c42aa9f28864c95cb4e27/File/96adbf05648e5835dc93916b93c93f75/stream_blog_post.MTW">this data set about how deep a stream is and how fast the water flows</a>. Open the data set in Minitab, then:</p>
<ol>
<li>Choose <strong>Stat > Regression > Regression > Fit Regression Model</strong>.</li>
<li>In <strong>Response</strong>, enter <em>Flow</em>.</li>
<li>In <strong>Continuous Predictors</strong>, enter <em>Depth</em>.</li>
<li>In <strong>Categorical Predictors</strong>, enter <em>Location</em>. Click <strong>OK</strong>.</li>
</ol>
<p>Once you’ve clicked OK, the green checkbox will appear in your worksheet to show that you have a valid model.</p>
<p style="marginleft: 40px;"><img alt="The green square with a white checkmark shows that the column is a response variable for a current model." src="https://cdn.app.compendium.com/uploads/user/458939f4fe084dbcb271efca0f5a2682/22791f44517c42aa9f28864c95cb4e27/Image/3e19e56f2f7af5c34e442315827d2b93/highlight_current_model_indicator.png" style="width: 254px; height: 186px;" /></p>
<p>To show unusual combinations of predictors, follow these steps:</p>
<ol>
<li>Choose <strong>Data > Conditional Formatting > Statistical > Unusual X</strong>.</li>
<li>In <strong>Response</strong>, enter <em>Flow</em>. Click <strong>OK</strong>.</li>
</ol>
<p>The text and background color for the response value in row 7 changes so that you can see that it’s unusual to have a depth of 0.76 in the first stream.</p>
<p style="marginleft: 40px;"><img alt="The value of the response in the row with the unusual X value has red shading and red letters." src="https://cdn.app.compendium.com/uploads/user/458939f4fe084dbcb271efca0f5a2682/22791f44517c42aa9f28864c95cb4e27/Image/bc2fbce0aed179d52767cfe21821e760/leverage_point_in_red.png" style="width: 259px; height: 238px;" /></p>
<p>You can indicate values that aren’t fit well by the model in a similar fashion.</p>
<ol>
<li>Choose <strong>Data > Conditional Formatting > Statistical > Large Residual</strong>.</li>
<li>In <strong>Response</strong>, enter <em>Flow</em>.</li>
<li>In <strong>Style</strong>, select <strong>Yellow</strong>. Click <strong>OK</strong>.</li>
</ol>
<p>Now, in the worksheet, the unusual combinations of predictors are red and the values that aren’t fit well by the model are yellow:</p>
<p style="marginleft: 40px;"><img alt="The unusual cell with the response value for the row with an unusual X value has a red theme. The cell with the response value for a row that the model does not fit well has a yellow theme." src="https://cdn.app.compendium.com/uploads/user/458939f4fe084dbcb271efca0f5a2682/22791f44517c42aa9f28864c95cb4e27/Image/6dc6958185e62d60519edb659f9d74ce/leverage_point_in_red__outlier_in_yellow.png" style="width: 251px; height: 265px;" /></p>
<p>Not all of the ways that Minitab can conditionally format depend on the model. If you’re ready for more, take a look at the online support center to see examples of these other uses of conditional formats:</p>
<ul>
<li><a href="http://support.minitab.com/minitab/17/topiclibrary/minitabenvironment/dataanddatamanipulation/conditionalformatting/exampleofformattingcellsthatcontainmissingobservations/">Example of formatting cells that contain missing observations</a></li>
<li><a href="http://support.minitab.com/minitab/17/topiclibrary/minitabenvironment/dataanddatamanipulation/conditionalformatting/exampleofformattingcellsthatcontainvaluesgreaterthanthespecifiedvalue/">Example of formatting cells that contain values greater than the specified value</a></li>
<li><a href="http://support.minitab.com/minitab/17/topiclibrary/minitabenvironment/dataanddatamanipulation/conditionalformatting/exampleofformattingcellsthatcontainthelowestvalues/">Example of formatting cells that contain the lowest values</a></li>
<li><a href="http://support.minitab.com/minitab/17/topiclibrary/minitabenvironment/dataanddatamanipulation/conditionalformatting/exampleofformattingcellsthatcontaintheleastfrequentvalues/">Example of formatting cells that contain the least frequent values</a></li>
<li><a href="http://support.minitab.com/minitab/17/topiclibrary/minitabenvironment/dataanddatamanipulation/conditionalformatting/exampleofformattingcellsthatcontainoutliers/">Example of formatting cells that contain outliers</a></li>
<li><a href="http://support.minitab.com/minitab/17/topiclibrary/minitabenvironment/dataanddatamanipulation/conditionalformatting/exampleofformattingcellsthatcontainoutofcontrolvalues/">Example of formatting cells that contain outofcontrol values</a></li>
</ul>
Data Analysis
Project Tools
Statistics
Stats
Mon, 18 Jul 2016 12:06:00 +0000
http://blog.minitab.com/blog/statisticsandqualityimprovement/conditionalformattingoflargeresidualsandunusualcombinationsofpredictors
Cody Steele

DOE Center Points: What They Are & Why They're Useful
http://blog.minitab.com/blog/michelleparet/doecenterpointswhattheyarewhytheyreuseful
<p><a href="http://blog.minitab.com/blog/statisticsandqualitydataanalysis/designofexperimentdoe:searchingforaselfiefountainofyouth">Design of Experiments</a> (DOE) is the perfect tool to efficiently determine if key inputs are related to key outputs. Behind the scenes, DOE is simply a regression analysis. What’s not simple, however, is all of the choices you have to make when planning your experiment. What X’s should you test? What ranges should you select for your X’s? How many replicates should you use? Do you need center points? Etc. <span style="lineheight: 1.6;">So let’s talk about center points.</span></p>
What Are Center Points?
<p>Center points are simply experimental runs where your X’s are set halfway between (i.e., in the center of) the low and high settings. For example, suppose your DOE includes these X’s:</p>
<p><img alt="TimeAndTemp" src="https://cdn.app.compendium.com/uploads/user/458939f4fe084dbcb271efca0f5a2682/6060c2dbf5d9449babe268eade74814a/Image/a353ac7271581a7dadcf8dac48e33d3f/timeandtemp.jpg" style="width: 300px; height: 80px;" /></p>
<p>The center point would then be set midway at a Temperature of <strong>150 °C</strong> and a Time of <strong>20 seconds</strong>.</p>
<p>And your data collection plan in <a href="http://www.minitab.com/products/minitab/">Minitab Statistical Software</a> might look something like this, with the center points shown in blue:</p>
<p><img alt="Minitab Worksheet" src="https://cdn.app.compendium.com/uploads/user/458939f4fe084dbcb271efca0f5a2682/6060c2dbf5d9449babe268eade74814a/Image/32105497dbf355948fd66f57cde703bf/minitabworksheet.jpg" style="width: 361px; height: 320px;" /></p>
<p>You can have just 1 center point, or you can collect data at the center point multiple times. This particular design includes 2 experimental runs at the center point. Why pick 2, you may be asking? We’ll talk about that in just a moment.</p>
Why Should You Use Center Points in Your Designed Experiment?
<p>Including center points in a DOE offers many advantages:</p>
<strong><em>1. Is Y versus X linear?</em></strong>
<p>Factorial designs assume there’s a linear relationship between each X and Y. Therefore, if the relationship between any X and Y exhibits curvature, you shouldn’t use a factorial design because the results may mislead you.</p>
<p>So how do you statistically determine if the relationship is linear or not? With center points! If the center point pvalue is significant (i.e., less than alpha), then you can conclude that curvature exists and use response surface DOE—such as a central composite design—to analyze your data. While factorial designs can <em>detect </em>curvature, you have to use a response surface design to <em>model</em> (build an equation for) the curvature.</p>
<p><img alt="Bad Fit Factorial Design" src="https://cdn.app.compendium.com/uploads/user/458939f4fe084dbcb271efca0f5a2682/6060c2dbf5d9449babe268eade74814a/Image/53c32bd3909d45e8354cb646226163c8/bad_fit.jpg" style="width: 300px; height: 200px; marginleft: 5px; marginright: 5px;" /><img alt="Good Fit Response Surface Design" src="https://cdn.app.compendium.com/uploads/user/458939f4fe084dbcb271efca0f5a2682/6060c2dbf5d9449babe268eade74814a/Image/253453eaca36868d557cc80e23c8e4de/good_fit.jpg" style="width: 300px; height: 200px;" /></p>
<p>And the good news is that curvature often indicates that your X settings are near an optimum Y, and you've discovered insightful results!</p>
<strong><em>2. Did you collect enough data?</em></strong>
<p>If you don’t collect enough data, you aren’t going to detect significant X’s even if they truly exist. One way to increase the number of data points in a DOE is to use replicates. However, replicating an entire DOE can be expensive and timeconsuming. For example, if you have 3 X’s and want to replicate the design, then you have to increase the number of experimental runs from 8 to 16!</p>
<p>Fortunately, using replicates is just one way to increase power. An alternative way to increase power is to use center points. By adding just a few center points to your design, you can increase the probability of detecting significant X’s, and estimate the variability (or pure error, statistically speaking).</p>
Learn More about DOE
<p><span style="lineheight: 1.6;">DOE is a great tool. It tells you a lot about your inputs and outputs and can help you optimize process settings. But it’s only a great tool if you use it the right way. If you want to learn more about DOE, check out our elearning course <a href="http://www.minitab.com/products/qualitytrainer/">Quality Trainer</a> for $30 US. Or, you can participate in a fullday Factorial Designs course at one of our <a href="http://www.minitab.com/services/training/schedule/">instructorled training sessions</a>.</span></p>
Data Analysis
Design of Experiments
Lean Six Sigma
Quality Improvement
Six Sigma
Statistics
Fri, 15 Jul 2016 12:00:00 +0000
http://blog.minitab.com/blog/michelleparet/doecenterpointswhattheyarewhytheyreuseful
Michelle Paret

What Were the Odds of Getting into Willy Wonka's Chocolate Factory?
http://blog.minitab.com/blog/funwithstatistics/whatweretheoddsofgettingintowillywonkaschocolatefactory
<p>In the great 1971 movie <em>Willy Wonka and the Chocolate Factory</em>, the reclusive owner of the Wonka Chocolate Factory decides to place golden tickets in five of his famous chocolate bars, and allow the winners of each to visit his factory with a guest. Since restarting production after three years of silence, no one has come in or gone out of the factory. Needless to say, there is enormous interest in finding a golden ticket!</p>
<p>Through a series of news reports we get an understanding that all over the world, kids are desperately purchasing and opening Wonka bars in an attempt to win. But just what were the odds? Unfortunately young Charlie Bucket's teacher is not particularly good at percentages and doesn't offer much help:</p>
<p style="textalign: center;"></p>
<p>I hope I can be at least a little more useful. While <a href="https://en.wikipedia.org/wiki/Willy_Wonka_%26_the_Chocolate_Factory" target="_blank">the movie</a> only vaguely suggests how many bars were actually being opened, we are provided with two data points. First, the spoiled, bratty, unlikable Veruca Salt's factoryowning father states that he's had his workers open 760,000 Wonka bars just before one of them finds a golden ticket:</p>
<p style="textalign: center;"></p>
<p>Meanwhile the polite, likable Charlie Bucket—who is very poor—has received one Wonka Bar for his birthday and another from his Grandpa Joe. Neither bar was a winner, but Charlie finds some money on the street to buy a third:</p>
<p style="textalign: center;"></p>
<p>In the movie, you can't help but feel that Charlie's odds must have been much, much higher than the nasty Veruca Salt's (or any of the other winners). But is there statistical evidence of that?</p>
<p>In <a href="http://www.minitab.com/products/minitab">Minitab Statistical Software</a>, I set up a basic 2x2 table like this:</p>
<p><img alt="2x2 table" src="http://cdn.app.compendium.com/uploads/user/458939f4fe084dbcb271efca0f5a2682/46889f0ef0a54b4a8a192d2b8dce6087/Image/d76afbe1db44e097b81b1cece8c00f58/data.PNG" style="width: 381px; height: 136px;" /></p>
<p>Often when practitioners have a 2x2 table the <span><a href="http://blog.minitab.com/blog/understandingstatistics/chisquareanalysisofhalloweenandfridaythe13thisthereaslashermoviegendergap">ChiSquare test</a></span> immediately comes to mind. but the ChiSquare test is not accurate when any of the cell counts or expected cell counts are small, which is clearly the case here. But we can use Fisher's exact test without such a restriction, which is available in the "Other Stats" subdialog of<strong> Stat > Tables > Cross Tabulation and ChiSquare</strong>. The output looks like this:</p>
<p style="marginleft: 40px;"><img alt="Fishers output" src="http://cdn.app.compendium.com/uploads/user/458939f4fe084dbcb271efca0f5a2682/46889f0ef0a54b4a8a192d2b8dce6087/Image/64619150a8da9274129704a539767930/fishers.PNG" style="width: 384px; height: 388px;" /></p>
<p>For the ChiSquare portion of the output, Minitab not only refuses to provide a pvalue but gives two warnings and a note. The Fisher's exact test <em>can </em>be performed, however, and tests whether the likelihood of a winning tickets was the same for both Charlie and Veruca. The pvalue of 0.0000079 confirms what we all knew—karma was working for Charlie and against Veruca!</p>
<p>For fun, let's ignore this evidence that the odds were not equal for each child. Let's pretend that the odds are the same, and a really unlikely thing happened anyway because that's what makes the movie great. Aside from our two data points, we have reports from two children in the classroom that they have opened 100 and 150 bars, respectively, and neither won. So we have two golden tickets among 3 + 760,000 + 100 + 150 = 760,253 Wonka bars. This would be a proportion of 3/760,253 = 0.00000395 or 0.0000395%. Think those odds are low? That represents an inflated estimate! That is because rather than randomly sampling many children, our sample includes two known winners. Selecting four children at random would almost certainly produce four nonwinners and the estimate would be 0%.</p>
<p>There is one additional data point that doesn't really make logical sense, but let's use it to come up with a lowend estimate by accepting that it is likely not a real number. At one point, a news reporter indicates that five tickets are hidden among the "countless billions of Wonka bars." Were there actually "countless billions" of unopened Wonka bars in the world? Consider that the most popular chocolate bar in the world—the famous Hershey bar—has annual sales of about 250 million units. And that's <em>per year</em>! It is very, very unlikely that there were countless billions of unopened Wonka bars from that single factory at any one time. Further, that news report is about the contest being announced, so the Wonka factory had not yet delivered the bars with the golden tickets inside. Suffice to say, this is not an accurate number.</p>
<p>But let's suppose that even 1 billion Wonka bars were produced in the run that contained the golden tickets. Then the odds of a single bar containing one would be 5/1,000,000,000 = 0.000000005 or 0.0000005%.</p>
<p>Either way, the chances of finding one were incredibly low...confirming again what grandpa Joe told Charlie:</p>
<p><strong>CHARLIE: "I've got the same chance as anybody else, haven't I?"</strong></p>
<p><strong>GRANDPA JOE: "You've got more, Charlie, because you want it more! Go on, open it!"</strong></p>
Data Analysis
Fun Statistics
Statistics
Wed, 13 Jul 2016 12:00:00 +0000
http://blog.minitab.com/blog/funwithstatistics/whatweretheoddsofgettingintowillywonkaschocolatefactory
Joel Smith

A Visual Look at Baseball's AllStar Teams
http://blog.minitab.com/blog/startingoutwithstatisticalsoftware/avisuallookatbaseballsallstarteams
<p><img alt="allstar game 2016" src="https://cdn.app.compendium.com/uploads/user/458939f4fe084dbcb271efca0f5a2682/479b4fbdf8c040119409f4109cc4c745/Image/ac206b0fc14f929f89cd52a57fe5a20c/all_star.png" style="width: 250px; height: 247px; margin: 10px 15px; float: right; borderwidth: 1px; borderstyle: solid;" />Last Tuesday Night, Major League Baseball announced the rosters for tomorrow's <a href="http://mlb.com/allstargame/">AllStar game in San Diego</a>. Immediately, as I'm sure was anticipated, people began talking about who made it and who didn't. Who got left out, and who shouldn't have made it.</p>
<p>As a fun little exercise, I decided to take a visual look at the allstar teams, to see what kind of players were selected. I looked at position players only (no pitchers) and made a simple <a href="http://blog.minitab.com/blog/understandingstatistics/usingstatisticssoftwareandgraphstoquicklyexplorerelationshipsbetweenvariables">scatterplot</a>, with the xaxis representing their offensive value so far this season, and the yaxis representing their defensive value. This would allow me to see any extreme outliers in terms of value generated so far this year. In <a href="http://www.minitab.com/products/minitab/">Minitab Statistical Software</a>, this command can be found by going to <strong>Graph > Scatterplot</strong>. I also added data labels through the Editor menu (<strong>Editor > Add > Data Labels</strong>) so that I could see which point on the plot corresponds to which player.</p>
<p>The plot below shows the American League selections:</p>
<p><img alt="scaterrplot" src="https://cdn.app.compendium.com/uploads/user/458939f4fe084dbcb271efca0f5a2682/732ead3410054470b034d7f8b87fabcf/Image/ee1f7d5e288102ac11fa42a4d1a3bd19/al_all_star.jpg" style="width: 600px; height: 400px;" /></p>
<p>Looking at the graph, some groupings become apparent. The most populated quadrant is the upper right, which represents a high offensive and defensive value. For an allstar team, this makes sense: these are the best of the best. Here is where you'll find names like Mike Trout, Josh Donaldson, and Jose Altuve, the American League leaders in Wins Above Replacement, which is a metric that tries to capture all of a player's value into one nice statistic.</p>
<p>Another grouping that becomes apparent is the upper left quadrant. This is where we see our defensive maestros. To fall in the upper left quadrant, you need to have a high defensive value and a (relatively) low offensive output. We have a shortstop and three catchers here, which makes sense given that those are the two most demanding defensive positions. </p>
<p>The lower right corner represents players whose value is mostly on offense. Here we, see Edwin Encarnacion, David Ortiz, and Mark Trumbo. Their defensive value is so low because they don't even play defense—they are designated hitters. </p>
<p>This is a fun way to visualize what kind of allstars we have, and what they excel at. If the manager needs to make a lategame defensive substitution, this graph can show us where they might lean. Additionally, if they need one pinch hitter for a key atbat, we can see whom they might lean on by looking at the other end of the graph.</p>
<p>We looked at the American League in detail up above, and I've also created the same plot for the National League below:</p>
<p><img alt="nl" src="https://cdn.app.compendium.com/uploads/user/458939f4fe084dbcb271efca0f5a2682/732ead3410054470b034d7f8b87fabcf/Image/fbe513318c89e37123e95b6bf1e7677f/nl_all_star.jpg" style="width: 600px; height: 400px;" /></p>
<p>*Note: All statistics from fangraphs.com</p>
Data Analysis
Fun Statistics
Statistics
Statistics in the News
Mon, 11 Jul 2016 12:05:00 +0000
http://blog.minitab.com/blog/startingoutwithstatisticalsoftware/avisuallookatbaseballsallstarteams
Eric Heckman

Does Major League Baseball Really Need the Second Half of the Season?
http://blog.minitab.com/blog/thestatisticsgame/doesmajorleaguebaseballreallyneedthesecondhalfoftheseason
<p><img alt="MLB Logo" src="https://cdn.app.compendium.com/uploads/user/458939f4fe084dbcb271efca0f5a2682/fe2c58f624104b6fb687d378929b1f9b/Image/8fe78a1febf88c009d5cf2943615c4a2/mlb_logo.gif" style="width: 250px; height: 129px; float: right; margin: 10px 15px;" />When you perform a statistical analysis, you want to make sure you collect enough data that your results are reliable. But you also want to avoid wasting time and money collecting more data than you need. So it's important to find an appropriate middle ground when determining your sample size.</p>
<p>Now, technically, the Major League Baseball regular season isn't a statistical analysis. But it does kind of work like one, since the goal of the regular season is to "determine who the best teams are." The National Football League uses a 16game regular season to determine who the best teams are. Hockey and Basketball use 82 games. </p>
<p>Baseball uses 162 games.</p>
<p>So is baseball wasting time collecting more data than it needs? Right now the MLB regular season is about halfway over. So could they just end the regular season now? Will playing another 81 games really have a significant effect on the standings? Let's find out.</p>
How much do MLB standings change in the 2nd half of the season?
<p>I went back through five years of records and recorded where each MLB team ranked in their league (American League and National League) on July 8, and then again at the end of the season. We can use this data to look at concordant and discordant pairs. A pair is concordant if the observations are in the same direction. A pair is discordant if the observations are in opposite directions. This will let us compare teams to each other two at a time.</p>
<p>For example, let's compare the Astros and Angels from 2015. On July 8th, the Astros were ranked 2nd in the AL and the Angels were ranked 3rd. At the end of the season, Houston was ranked 5th and the Angles were ranked 6th. This pair is concordant since in both cases the Astros were ranked higher than the Angels. But if you compare the Astros and the Yankees, you'll see the Astros were ranked higher on July 8th, but the Yankees were ranked higher at the end of the season. That pair is discordant.</p>
<p>When we compare every team, we end up with 11,175 pairs. How many of those are concordant? <a href="http://www.minitab.com/enus/products/minitab/" target="_blank">Minitab Statistical Software</a> has the answer.</p>
<p style="marginleft: 40px;"><img alt="Measures of Concordance" src="https://cdn.app.compendium.com/uploads/user/458939f4fe084dbcb271efca0f5a2682/fe2c58f624104b6fb687d378929b1f9b/Image/29a56ecd2f92d8adf4e17f8dd54c9765/measures_of_concordance.jpg" style="width: 461px; height: 150px;" /></p>
<p>There are 8,307 concordant pairs, which is just over 74% of the data. So most of the time, if a team is higher in the standings as of July 8th, they will finish higher in the final standings too. We can also use Spearman's rho and Pearson's r to asses the association between standings on July 8th and the final standings. These two values give us a coefficient that can range from 1 to +1. The larger the absolute value, the stronger the relationship between the variables. A value of 0 indicates the absence of a relationship. </p>
<p style="marginleft: 40px;"><img alt="Pearsons r and Spearmans rho" src="https://cdn.app.compendium.com/uploads/user/458939f4fe084dbcb271efca0f5a2682/fe2c58f624104b6fb687d378929b1f9b/Image/24cba34f8af1f68e9a6ef5647d876695/meaures_of_association.jpg" style="width: 180px; height: 52px;" /></p>
<p>Both values are high and positive, once again indicating that teams ranked higher than other teams on July 8th usually stay that way by the end of the season. So did we do it? Did we show that baseball doesn't really need the 2nd half of their season?</p>
<p>Not quite.</p>
<p>Consider that each league has 15 teams. So a lot of our pairs are comparing teams that aren't that close together, like 1st team to the 15th, the 1st team to the 14th, the 2nd team to the 15th, and so on. It's not very surprising that those pairs are going to be concordant. So let's dig a little deeper and compare each individual team's ranking in July compared to the end of the season. The following <a href="http://blog.minitab.com/blog/michelleparet/3thingsahistogramcantellyou">histogram</a> shows the difference in a team's rank. Positive values mean the team moved up in the standings, negative values mean they fell.</p>
<p style="marginleft: 40px;"><img alt="Histogram" src="https://cdn.app.compendium.com/uploads/user/458939f4fe084dbcb271efca0f5a2682/fe2c58f624104b6fb687d378929b1f9b/Image/1612d472c3a617bfee1098bc29e00f27/histogram_of_difference.jpg" style="width: 576px; height: 384px;" /></p>
<p>The most common outcome is that a team doesn't move up or down in the standings, as 34 of our observations have a difference of 0. However, there are 150 total observations, so most of the time a team does move up or down. In fact, 55 times a team moved up or down in the standings by 3 or more spots. That's over a third of the time! And there are multiple instances of a team moving 6, 7, or even 8 spots! That doesn't seem to imply that the 2nd half of the season doesn't matter. So what if we narrow the scope of our analysis?</p>
Looking at the Playoff Teams
<p>We previously noted that the regular season is supposed to determine the best teams. So let's focus on the top of the MLB standings. I took the top 5 teams in each league (since the top 5 teams make the playoffs) on July 8th, and recorded whether they were still a top 5 team (and in the playoffs) at the end of the season. The following pie chart shows the results.</p>
<p style="marginleft: 40px;"><img alt="Pie Chart" src="https://cdn.app.compendium.com/uploads/user/458939f4fe084dbcb271efca0f5a2682/fe2c58f624104b6fb687d378929b1f9b/Image/be2891f00cde3cab6eadb050a0abeadb/pie_chart_of_playoffs_end.jpg" style="width: 576px; height: 384px;" /></p>
<p>Twenty eight percent of the time, a team that was in the playoffs in July fell far enough in the standings to drop out. So over a quarter of your playoff teams would be different if the season ended around 82 games. That sounds like a significant effect to me. And last, let's return to our concordant and discordant pairs. Except this time, we'll just look at the top half of the standings (top 8 teams). </p>
<p style="marginleft: 40px;"><img alt="Measures of Concordance" src="https://cdn.app.compendium.com/uploads/user/458939f4fe084dbcb271efca0f5a2682/fe2c58f624104b6fb687d378929b1f9b/Image/4ed88280224f9eba7726e54b50450f4c/measures_of_concordance_2.jpg" style="width: 468px; height: 194px;" /></p>
<p>This time our percentage of concordant pairs has dropped to 59%, and the values for Spearman's rho and Pearson's r show a weaker association. Teams ranked higher in the 1st half of the season are usually still ranked higher at the end of the season. But there is clearly enough shuffling among the top teams to warrant the 2nd half of the season. So don't worry baseball fans, your regular season will continue to extend to September.</p>
<p>Because, you know, Major League Baseball <em>totally </em>would have shorten the season if this statistical analysis suggested doing so!</p>
<p>And if you're looking to determine the appropriate sample size for your own analysis, Minitab offers a wide variety of <a href="http://support.minitab.com/enus/minitab/17/topiclibrary/basicstatisticsandgraphs/powerandsamplesize/powerandsamplesizeanalysesinminitab/">power and sample size analyses</a> that can help you out.</p>
<p> </p>
Data Analysis
Fun Statistics
Statistics
Statistics in the News
Fri, 08 Jul 2016 12:00:00 +0000
http://blog.minitab.com/blog/thestatisticsgame/doesmajorleaguebaseballreallyneedthesecondhalfoftheseason
Kevin Rudy

Using Marginal Plots, aka "StuffedCrust Charts"
http://blog.minitab.com/blog/dataanalysisandqualityimprovementandstuff/usingmarginalplotsakastuffedcrustcharts
<p><span style="lineheight: 1.6;">In <a href="http://blog.minitab.com/blog/dataanalysisandqualityimprovementandstuff/thematrixitsacomplexplot" target="_blank">my last post</a>, we took the red pill and dove deep into the unarguably fascinating and uncompromisingly compelling world of the matrix plot. I've stuffed this post with information about a topic of marginal interest...the marginal plot.</span></p>
<p>Margins are important. Back in my English composition days, I recall that margins were particularly prized for the inverse linear relationship they maintained with the number of words that one had to string together to complete an assignment. Mathematically, that relationship looks something like this:</p>
<p style="marginleft: 40px;">Bigger margins = fewer words</p>
<p><img alt="stuffed crust" src="https://cdn.app.compendium.com/uploads/user/458939f4fe084dbcb271efca0f5a2682/479b4fbdf8c040119409f4109cc4c745/Image/62b6ee0d191245cf8e077f414a1e1d2d/stuffed_crust.jpg" style="width: 250px; height: 213px; margin: 10px 15px; float: right;" />In stark contrast to my concept of margins as informationfree zones, the marginal plot actually utilizes the margins of a scatterplot to provide timely and important information about your data. Think of the marginal plot as the stuffedcrust pizza of the graph world. Only, instead of extra cheese, you get to bite into extra data. And instead of filling your stomach with carbs and cholesterol, you're filling your brain with data and knowledge. And instead of arriving late and cold because the delivery driver stopped off to canoodle with his girlfriend on his way to your house (<em>even though he's just not sure if the relationship is <span style="lineheight: 20.8px;">really </span>working out: she seems distant lately and he's not sure if it's the constant cologne of consumables about him, or the everpresent film of pizza <span style="lineheight: 1.6;">grease on his car seats, on his clothes, in his ears?)</span></em></p>
<p><span style="lineheight: 1.6;">...anyway, unlike a cold, late pizza, marginal plots are always fresh and hot, because you bake them yourself, in </span><a href="http://www.minitab.com/enus/products/minitab/" style="lineheight: 1.6;" target="_blank">Minitab Statistical Software</a><span style="lineheight: 1.6;">.</span></p>
<p>I tossed some randomlygenerated data around and came up with this halfbaked example. Like the pepperonis on a hastily prepared pie, the points on this plot are mostly piled in the middle, with only a few slices venturing to the edges. In fact, some of those points might be outliers. </p>
<p style="marginleft: 40px;"><img alt="Scatterplot of C1 vs C2" src="https://cdn.app.compendium.com/uploads/user/458939f4fe084dbcb271efca0f5a2682/8de770baa50a4f6b91449713c3b99f66/Image/1f1e94af3820cd7138eda393fa0b0859/scatterplot_of_c1_vs_c2.jpg" style="width: 360px; height: 240px;" /></p>
<p><span style="lineheight: 20.8px;">If only there were an easy, interesting, and integrated way to assess the data for outliers when we make a scatterplot. </span></p>
<p><span style="lineheight: 20.8px;">Boxplots are a useful way look for outliers. You could make separate boxplots of each variable, like so:</span></p>
<p style="marginleft: 40px;"><img alt="Boxplot of C1" src="https://cdn.app.compendium.com/uploads/user/458939f4fe084dbcb271efca0f5a2682/8de770baa50a4f6b91449713c3b99f66/Image/d542dd348a0c357f5e5dc0476bc5ea9f/boxplot_of_c1.jpg" style="width: 360px; height: 240px;" /> <img alt="Boxplot of C2" src="https://cdn.app.compendium.com/uploads/user/458939f4fe084dbcb271efca0f5a2682/8de770baa50a4f6b91449713c3b99f66/Image/b89d246d7a4e9951d4e0a49be2ad7eaf/boxplot_of_c2.jpg" style="lineheight: 1.6; width: 360px; height: 240px;" /></p>
<p><span style="lineheight: 20.8px;">It's fairly easy to relate the boxplot of C1 to the values plotted on the yaxis of the scatterplot. But it's a little harder to relate the boxplot of C2 to the scatterplot, because the yaxis on the boxplot corresponds to the xaxis on the scatterplot. You can transpose the scales on the boxplot to make the comparison a little easier. Just </span><span style="lineheight: 20.8px;">doubleclick one of the axes and select <strong>Transpose value and category scales</strong>:</span></p>
<p style="marginleft: 40px;"><img alt="Boxplot of C2, Transposed" src="https://cdn.app.compendium.com/uploads/user/458939f4fe084dbcb271efca0f5a2682/8de770baa50a4f6b91449713c3b99f66/Image/6c4db0ef1ee268a3c6f38400fd9e1f1c/boxplot_of_c2__transposed.jpg" style="width: 360px; height: 240px;" /></p>
<p>That's a little better. The only thing that would be <em>even better</em> is if you could put each boxplot right up against the scatterplot...if you could stuff the crust of the scatterplot with boxplots, so to speak. Well, guess what? You can! Just choose <strong>Graph > Marginal Plot > With Boxplots</strong>, enter the variables and click <strong>OK</strong>: </p>
<p style="marginleft: 40px;"><img alt="Marginal Plot of C1 vs C2" src="https://cdn.app.compendium.com/uploads/user/458939f4fe084dbcb271efca0f5a2682/8de770baa50a4f6b91449713c3b99f66/Image/69fdd93c28ebcfd93071ad22af62f407/marginal_plot_of_c1_vs_c2.jpg" style="width: 360px; height: 240px;" /></p>
<p>Not only are the boxplots nestled right up next to the scatterplot, but they also share the same axes as the scatterplot. For example, the outlier (asterisk) on the boxplot of C2 corresponds to the point directly below it on the scatterplot. Looks like that point could be an outlier, so you might want to investigate further. </p>
<p><span style="lineheight: 1.6;">Marginal plots can also help alert you to other important complexities in your data. Here's another halfbaked example. Unlike our pizza delivery guy's relationship with his girlfriend, it looks like the relationship between the fake response and the fake predictor represented in this scatterplot really is working out:</span><span style="lineheight: 20.8px;"> </span></p>
<p style="lineheight: 20.8px; marginleft: 40px;"><img alt="Scatterplot of Fake Response vs Fake Predictor" src="https://cdn.app.compendium.com/uploads/user/458939f4fe084dbcb271efca0f5a2682/8de770baa50a4f6b91449713c3b99f66/Image/a8a2fa08a7a9a917b7130e740c69514d/scatterplot_of_fake_response_vs_fake_predictor.jpg" style="lineheight: 20.8px; width: 360px; height: 240px;" /> </p>
<p style="lineheight: 20.8px;"><span style="lineheight: 1.6;">In fact, i</span><span style="lineheight: 20.8px;">f you use <strong>Stat > Regression > Fitted Line Plot</strong>, the fitted line appears to fit the data nicely. And the regression analysis is highly significant:</span></p>
<p style="lineheight: 20.8px; marginleft: 40px;"><img alt="Fitted Line_ Fake Response versus Fake Predictor" src="https://cdn.app.compendium.com/uploads/user/458939f4fe084dbcb271efca0f5a2682/8de770baa50a4f6b91449713c3b99f66/Image/aea45ae01a9481d7bf2553e1780521c5/fitted_line__fake_response_versus_fake_predictor.jpg" style="width: 360px; height: 240px;" /></p>
<strong>Regression Analysis: Fake Response versus Fake Predictor </strong>
The regression equation is
Fake Response = 2.151 + 0.7723 Fake Predictor
S = 2.12304 RSq = 50.3% RSq(adj) = 49.7%
Analysis of Variance
Source DF SS MS F P
Regression 1 356.402 356.402 79.07 0.000
Error 78 351.568 4.507
Total 79 707.970
<p><span style="lineheight: 1.6;">But wait. If you create a marginal plot instead, you can augment your exploration of these data with histograms and/or dotplots, as I have done below. Looks like there's trouble in </span>paradise:</p>
<p style="marginleft: 40px;"><img alt="Marginal Plot of Fake Response vs Fake Predictor, with Histograms" src="https://cdn.app.compendium.com/uploads/user/458939f4fe084dbcb271efca0f5a2682/8de770baa50a4f6b91449713c3b99f66/Image/107dfda7466c6690e33aee6e7f3918b6/marginal_plot_of_fake_response_vs_fake_predictor__with_histograms.jpg" style="width: 360px; height: 240px;" /> <img alt="Marginal Plot of Fake Response vs Fake Predictor, with Dotplots" src="https://cdn.app.compendium.com/uploads/user/458939f4fe084dbcb271efca0f5a2682/8de770baa50a4f6b91449713c3b99f66/Image/8e3044a69af337cfcc15d4aaacd88f9f/marginal_plot_of_fake_response_vs_fake_predictor__with_dotplots.jpg" style="width: 360px; height: 240px;" /></p>
<p><span style="lineheight: 20.8px;">Like the poorly made pepperoni pizza, the points on our plot are distributed unevenly. There appear to be two clumps of points. The distribution of values for the fake predictor is bimodal: that is, it has two distinct peaks. The distribution of values for the response may also be bimodal.</span></p>
<p>Why is this important? Because the <span style="lineheight: 20.8px;">two </span>clumps of toppings may suggest that you have more than one metaphorical cook in the metaphorical pizza kitchen. For example, it could be that Wendy, who is left handed, started placing the pepperonis carefully on the pie and then got called away, leaving Jimmy, who is right handed, to quickly and carelessly complete the covering of cured meats. In other words, it could be that the <span style="lineheight: 20.8px;">two </span>clumps of points represent <span style="lineheight: 20.8px;">two </span>very different populations. </p>
<p>When I tossed and stretched the data for this example, I took random samples from two different populations. I used 40 random observations from a normal distribution with a mean of 8 and a standard deviation of 1.5, and 40 random observations from a normal distribution with a mean of 13 and a standard deviation of 1.75. The two clumps of data are truly from <span style="lineheight: 20.8px;">two </span>different populations. To illustrate, I separated the <span style="lineheight: 20.8px;">two </span>populations into two different groups in this scatterplot: </p>
<p style="marginleft: 40px;"> <img alt="Scatterplot with Groups" src="https://cdn.app.compendium.com/uploads/user/458939f4fe084dbcb271efca0f5a2682/8de770baa50a4f6b91449713c3b99f66/Image/924cfc845dd807e6e2fd57cbbcc0abcb/scatterplot_of_fake_response_vs_fake_predictor_with_groups.jpg" style="width: 360px; height: 240px;" /></p>
<p>This is a classic conundrum that can occur when you do a <span><a href="http://blog.minitab.com/blog/adventuresinstatistics/regressionanalysishowdoiinterpretrsquaredandassessthegoodnessoffit">regression analysis</a></span>. The regression line tries to pass through the center of the data. And because there are two clumps of data, the line tries to pass through the center of each clump. This <em>looks </em>like a relationship between the response and the predictor, but it's just an illusion. If you separate the clumps and analyze each population separately, you discover that there is no relationship at all: </p>
<p style="marginleft: 40px;"><img alt="Fitted Line_ Fake Response 1 versus Fake Predictor 1" src="https://cdn.app.compendium.com/uploads/user/458939f4fe084dbcb271efca0f5a2682/8de770baa50a4f6b91449713c3b99f66/Image/e5981c9b2604bf841a525926d8282d8f/fitted_line__fake_response_1_versus_fake_predictor_1.jpg" style="width: 360px; height: 240px;" /></p>
<strong>Regression Analysis: Fake Response 1 versus Fake Predictor 1 </strong>
The regression equation is
Fake Response 1 = 9.067  0.1600 Fake Predictor 1
S = 1.64688 RSq = 1.5% RSq(adj) = 0.0%
Analysis of Variance
Source DF SS MS F P
Regression 1 1.609 1.60881 0.59 0.446
Error 38 103.064 2.71221
Total 39 104.673
<p style="marginleft: 40px;"><img alt="Fitted Line_ Fake Response 2 versus Fake Predictor 2" src="https://cdn.app.compendium.com/uploads/user/458939f4fe084dbcb271efca0f5a2682/8de770baa50a4f6b91449713c3b99f66/Image/e7db8af8c22bd83b72ad559ca5aece86/fitted_line__fake_response_2_versus_fake_predictor_2.jpg" style="width: 360px; height: 240px;" /></p>
<strong>Regression Analysis: Fake Response 2 versus Fake Predictor 2</strong>
The regression equation is
Fake Response 2 = 12.09 + 0.0532 Fake Predictor 2
S = 1.62074 RSq = 0.3% RSq(adj) = 0.0%
Analysis of Variance
Source DF SS MS F P
Regression 1 0.291 0.29111 0.11 0.741
Error 38 99.818 2.62679
Total 39 100.109
<p>If only our unfortunate pizza delivery technician could somehow use a marginal plot to help him assess the state of his own relationship. But alas, I don't think a marginal plot is going to help with that particular analysis. Where is that guy anyway? I'm getting hungry. </p>
Fun Statistics
Project Tools
Regression Analysis
Statistics
Wed, 06 Jul 2016 12:27:00 +0000
http://blog.minitab.com/blog/dataanalysisandqualityimprovementandstuff/usingmarginalplotsakastuffedcrustcharts
Greg Fox

Applying DOE for Great Grilling, part 2
http://blog.minitab.com/blog/understandingstatistics/applyingdoeforgreatgrillingpart2
<p><img alt="grill" src="http://cdn.app.compendium.com/uploads/user/458939f4fe084dbcb271efca0f5a2682/479b4fbdf8c040119409f4109cc4c745/Image/111e4a65160cf20662dfb13013408f1f/grill.jpg" style="margin: 10px 15px; width: 202px; height: 202px; lineheight: 18.9px; float: right;" /></p>
<p style="lineheight: 18.9px;"><span style="lineheight: 18.9px;">Design of Experiments is an extremely powerful statistical method, and we added a DOE tool to the Assistant in Minitab 17 to make it more accessible to more people.</span></p>
<p style="lineheight: 18.9px;"><span style="lineheight: 18.9px;">Since it's summer grilling season, I'm applying the Assistant's DOE tool to outdoor cooking.</span><span style="lineheight: 18.9px;"> </span>Earlier, I showed you <a href="http://blog.minitab.com/blog/understandingstatistics/applyingdoeforgreatgrillingpart1">how to set up a designed experiment</a> that will let you optimize how you grill steaks. </p>
<p>If you're not already using it and you want to play along, you can download the <a href="http://it.minitab.com/products/minitab/freetrial.aspx">free 30day trial version</a> of Minitab Statistical Software.</p>
<p style="lineheight: 18.9px;">Perhaps you are following along, and you've already grilled your steaks according to the experimental plan and recorded the results of your experimental runs. Otherwise, feel free to download my data <a href="//cdn.app.compendium.com/uploads/user/458939f4fe084dbcb271efca0f5a2682/479b4fbdf8c040119409f4109cc4c745/File/a0d8f12f27ee5a981619c2c3af59d524/steaks___asst_doe.MTW">here</a> for the next step: analyzing the results of our experiment. </p>
Analyzing the Results of the Steak Grilling Experiment
<p style="lineheight: 18.9px;">After collecting your data and entering it into Minitab, you should have an experimental worksheet that looks like this: </p>
<p style="lineheight: 18.9px;"><img alt="" src="http://cdn.app.compendium.com/uploads/user/458939f4fe084dbcb271efca0f5a2682/479b4fbdf8c040119409f4109cc4c745/Image/ed29e3c1fb41872df6529e91786215f2/grill_doe_worksheet.png" style="width: 500px; height: 320px;" /></p>
<p style="lineheight: 18.9px;">With your results entered in the worksheet, select <strong>Assistant > DOE > Analyze and Interpret</strong>. As you can see below, the only button you can click is "Fit Linear Model." </p>
<p style="lineheight: 18.9px;"><img alt="" src="http://cdn.app.compendium.com/uploads/user/458939f4fe084dbcb271efca0f5a2682/479b4fbdf8c040119409f4109cc4c745/Image/1ce7cb7744e6fb78c4f5cb74d1903cf6/grill_doe_analyze.png" style="width: 500px; height: 375px;" /></p>
<p style="lineheight: 18.9px;">As you might gather from the flowchart, when it analyzes your data, the Assistant first checks to see if the response exhibits curvature. If it does, the Assistant will prompt you to gather more data so you it can fit a quadratic model. Otherwise, the Assistant will fit the linear model and provide the following output. </p>
<p style="lineheight: 18.9px;">When you click the "Fit Linear Model" button, the Assistant automatically identifies your response variable.</p>
<p style="lineheight: 18.9px;"><img alt="" src="http://cdn.app.compendium.com/uploads/user/458939f4fe084dbcb271efca0f5a2682/479b4fbdf8c040119409f4109cc4c745/Image/a851201ceabf727ba38e53ef383d6091/grill_doe_analyze2.png" style="width: 435px; height: 260px;" /></p>
<p style="lineheight: 18.9px;">All you need to do is confirm your response goal—maximizing flavor, in this case—and press OK. The Assistant performs the analysis, and provides you the results in a series of easytointerpret reports. </p>
Understanding the DOE Results
<p style="lineheight: 18.9px;">First, the Assistant offers a summary report that gives you the bottomline results of the analysis. The Pareto Chart of Effects in the top left shows that Turns, Grill type, and Seasoning are all statistically significant, and there's a significant interaction between Turns and Grill type, too. </p>
<p style="lineheight: 18.9px;"><img alt="" src="http://cdn.app.compendium.com/uploads/user/458939f4fe084dbcb271efca0f5a2682/479b4fbdf8c040119409f4109cc4c745/Image/9ac1a8e009efec8b90fdbb32cfebd1df/grill_doe_results_summary.png" style="width: 751px; height: 563px;" /></p>
<p style="lineheight: 18.9px;">The summary report also shows that the model explains very high proportion of the variation in flavor, with an R2 value of 95.75 percent. And the "Comments" window in the lower right corner puts things if plain language: "You can conclude that there is a relationship between Flavor and the factors in the model..."</p>
<p style="lineheight: 18.9px;">The Assistant's Effects report, shown below, tells you more about the nature of the relationship between the factors in the model and Flavor, with both Interaction Plots and Main Effects plots that illustrate how different experimental settings affect the Flavor response. </p>
<p style="lineheight: 18.9px;"><img alt="" src="http://cdn.app.compendium.com/uploads/user/458939f4fe084dbcb271efca0f5a2682/479b4fbdf8c040119409f4109cc4c745/Image/4a9d3a9939ad51a9326bed0fbd061048/grill_doe_results_effects.png" style="width: 751px; height: 563px;" /></p>
<p style="lineheight: 18.9px;">And if we're looking to make some changes as a result of our experimental results—like selecting an optimal method for grilling steaks in the future—the Prediction and Optimization report gives us the optimal solution (1 turn on a charcoal grill, with Montreal seasoning) and its predicted Flavor response (8.425). </p>
<p style="lineheight: 18.9px;"><img alt="" src="http://cdn.app.compendium.com/uploads/user/458939f4fe084dbcb271efca0f5a2682/479b4fbdf8c040119409f4109cc4c745/Image/f9189c39c79160de4b9c5dbf8f4523ab/grill_doe_results_optimization.png" style="width: 751px; height: 563px;" /></p>
<p style="lineheight: 18.9px;"><span style="lineheight: 1.6;">It also gives us the Top 5 alternative solutions, shown in the bottom right corner, so if there's some reason we can't implement the optimal solution—for instance, if we only have a gas grill—we can still choose the best solution that suits our circumstances. </span></p>
<p style="lineheight: 18.9px;">I hope this example illustrates how easy a designed experiment can be when you use the Assistant to create and analyze it, and that designed experiments can be very useful not just in industry or the lab, but also in your everyday life. </p>
<p style="lineheight: 18.9px;">Where could you benefit from analyzing process data to optimize your results? </p>
Design of Experiments
Fun Statistics
Statistics Help
Tue, 05 Jul 2016 12:00:00 +0000
http://blog.minitab.com/blog/understandingstatistics/applyingdoeforgreatgrillingpart2
Eston Martz

Applying DOE for Great Grilling, part 1
http://blog.minitab.com/blog/understandingstatistics/applyingdoeforgreatgrillingpart1
<p>Design of Experiments (DOE) has a reputation for difficulty, and to an extent, this statistical method <em>deserves </em>that reputation. While it's easy to grasp the basic idea—<em>acquire the maximum amount of information from the fewest number of experimental runs</em>—practical application of this tool can quickly become very confusing. </p>
<p><img alt="steaks" src="http://cdn.app.compendium.com/uploads/user/458939f4fe084dbcb271efca0f5a2682/479b4fbdf8c040119409f4109cc4c745/Image/33d85058b493aff4240dfb9d78aff673/steaks.jpg" style="margin: 10px 15px; width: 250px; height: 250px; float: right;" />Even if you're a longtime user of designed experiments, it's still easy to feel uncertain if it's been a while since you last looked at splitplot designs or needed to choose the appropriate resolution for a fractional factorial design.</p>
<p>But DOE <em>is</em> an extremely powerful and useful tool, so when we launched Minitab 17, we added a DOE tool to the Assistant to make designed experiments more accessible to more people.</p>
<p>Since summer is here at Minitab's world headquarters, I'm going to illustrate how you can use the Assistant's DOE tool to optimize your grilling method. </p>
<p>If you're not already using it and you want to play along, you can download the free 30day <a href="http://it.minitab.com/products/minitab/freetrial.aspx">trial version of Minitab Statistical Software</a>.</p>
Two Types of Designed Experiments: Screening and Optimizing
<p>To create a designed experiment using the Assistant, open Minitab and select <strong>Assistant > DOE > Plan and Create</strong>. You'll be presented with a decision tree that helps you take a sequential approach to the experimentation process by offering a choice between a screening design and a modeling design.</p>
<p><img alt="DOE Assistant" src="http://cdn.app.compendium.com/uploads/user/458939f4fe084dbcb271efca0f5a2682/479b4fbdf8c040119409f4109cc4c745/Image/5b585531f6031882fb7880a49700f52c/grill_doe_1.png" style="width: 487px; height: 366px;" /></p>
<p>A <strong>screening design</strong> is important if <span><a href="http://blog.minitab.com/blog/understandingstatistics/whyistheofficecoffeesobadascreeningexperimentnarrowsdownthecriticalfactors">you have a lot of potential factors to consider</a></span> and you want to figure out which ones are important. The Assistant guides you through the process of testing and analyzing the main effects of 6 to 15 factors, and identifies the factors that have greatest influence on the response.</p>
<p>Once you've identified the critical factors, you can use the <strong>modeling design.</strong> Select this option, and the Assistant guides you through testing and analyzing 2 to 5 critical factors and helps you find optimal settings for your process.</p>
<p>Even if you're an old hand at analyzing designed experiments, you may want to use the Assistant to create designs since the Assistant lets you print out easytouse data collection forms for each experimental run. After you've collected and entered your data, the designs created in the Assistant can also be analyzed using <span style="lineheight: 18.9px;">Minitab's </span><span style="lineheight: 1.6;">core DOE tools available through the <strong>Stat > DOE</strong> menu.</span></p>
<span style="lineheight: 1.6;">Creating a DOE to Optimize How We Grill Steaks</span>
<p>For grilling steaks, there aren't that many variables to consider, so we'll use the Assistant to pl<span style="lineheight: 1.6;">an and create a <strong>modeling design</strong> that will optimize our grilling process. Select <strong>Assistant > DOE > Plan and Create</strong>, then click the "Create Modeling Design" button. </span></p>
<p><span style="lineheight: 1.6;">Minitab brings up an easytofollow dialog box; all we need to do is fill it in. </span></p>
<p><span style="lineheight: 1.6;"><img alt="" src="http://cdn.app.compendium.com/uploads/user/458939f4fe084dbcb271efca0f5a2682/479b4fbdf8c040119409f4109cc4c745/Image/eb90fd8499ab96a579aa6dd63fa325d2/grill_doe_dialog_1.png" style="width: 461px; height: 500px;" /></span></p>
<p>First we enter the name of our Response and the goal of the experiment. Our response is "Flavor," and the goal is "Maximize the response." Next, we enter our factors. We'll look at three critical variables:</p>
<ul>
<li>Number of turns, a continuous variable with a low value of 1 and high value of 3.</li>
<li>Type of grill, a categorical variable with Gas or Charcoal as options. </li>
<li>Type of seasoning, a categorical variable with SaltPepper or Montreal steak seasoning as options. </li>
</ul>
<p>If we wanted to, we could select more than 1 replicate of the experiment. A replicate is simply a complete set of experimental runs, so if we did 3 replicates, we would repeat the full experiment three times. But since this experiment has 16 runs, and neither our budget nor our stomachs are limitless, we'll stick with a single replicate. </p>
<p>When we click OK, the Assistant first asks if we want to print out data collection forms for this experiment: </p>
<p><img alt="" src="http://cdn.app.compendium.com/uploads/user/458939f4fe084dbcb271efca0f5a2682/479b4fbdf8c040119409f4109cc4c745/Image/c4c63c4b5af7a4c6e4f3c4caa327f523/grill_doe_collection_form1.png" style="width: 445px; height: 207px;" /></p>
<p>Choose Yes, and you can print a form that lists each run, the variables and settings, and a space to fill in the response:</p>
<p><img alt="" src="http://cdn.app.compendium.com/uploads/user/458939f4fe084dbcb271efca0f5a2682/479b4fbdf8c040119409f4109cc4c745/Image/06ed8ad486f3a243c4aea352c9738b2c/grill_doe_collection_form2.png" style="borderwidth: 1px; borderstyle: solid; width: 500px; height: 313px;" /></p>
<p>Alternatively, you can just record the results of each run in the worksheet the Assistant creates, which you'll need to do anyway. But having the printed data collection forms can make it much easier to keep track of where you are in the experiment, and exactly what your factor settings should be for each run. </p>
<p>If you've used the Assistant in Minitab for other methods, you know that it seeks to demystify your analysis and make it easy to understand. When you create your experiment, the Assistant gives you a Report Card and Summary Report that explain the steps of the DOE and important considerations, and a summary of your goals and what your analysis will show. </p>
<p><img alt="" src="http://cdn.app.compendium.com/uploads/user/458939f4fe084dbcb271efca0f5a2682/479b4fbdf8c040119409f4109cc4c745/Image/a767257b9db465b81d6bd1456e5eb508/grill_doe_2_w1024.png" style="width: 650px; height: 439px;" /></p>
<p>Now it's time to cook some steaks, and rate the flavor of each. If you want to do this for real and collect your own data, please do so! <a href="http://blog.minitab.com/blog/understandingstatistics/applyingdoeforgreatgrillingpart2">Tomorrow's post</a> will show how to analyze your data with the Assistant. </p>
Mon, 04 Jul 2016 12:00:00 +0000
http://blog.minitab.com/blog/understandingstatistics/applyingdoeforgreatgrillingpart1
Eston Martz

QI Trends in Healthcare: What Are the Statistical "Soft Spots"?
http://blog.minitab.com/blog/statisticsandqualitydataanalysis/qitrendsinhealthcare%3Awhatarethestatisticalsoftspots
<p><img alt="big wave" src="https://cdn.app.compendium.com/uploads/user/458939f4fe084dbcb271efca0f5a2682/ba6a552e3bc04eed9c9aeae3ade49498/Image/d14c1c79496ff141809adbe44155263c/256px_big_wave_breaking_in_santa_cruz.jpg" style="lineheight: 20.8px; width: 256px; height: 200px; float: right; borderwidth: 1px; borderstyle: solid; margin: 10px 15px;" />It's been called a "demographic watershed". </p>
<p>In the next 15 years alone, the worldwide population of individuals aged 65 and older is projected to increase more than 60%, from 617 million to about 1 billion.1</p>
<p>Increasingly, countries are asking themselves: How can we ensure a high quality of care for our growing aging population while keeping our healthcare costs under control?</p>
<p>The answer? More efficiency. Less waste. Reduced error. Quicker turnaround. Improved patient outcomes. Which is, of course, where <span><a href="http://blog.minitab.com/blog/understandingstatistics/sixsigmaandleandoingittokeepkidshealthy">lean/six sigma quality improvement</a></span> comes in.</p>
<span style="lineheight: 20.8px;">Another Watershed: Lean/Six Sigma in Healthcare</span>
<p>Faced with the challenge of increased demand and rapidly rising cost, it's no surprise that more and more lean and six sigma studies are being performed and published in the fields of medicine and healthcare. A search for "lean sigma" or "six sigma" in the U.S. National Library of Medicine/National Institutes of Health database pulls up over 470 published studies. The yearbyyear search results are shown in the following Trend Analysis Plot in <a href="http://www.minitab.com/products/minitab">Minitab</a>.</p>
<p><img alt="trend" src="https://cdn.app.compendium.com/uploads/user/458939f4fe084dbcb271efca0f5a2682/ba6a552e3bc04eed9c9aeae3ade49498/Image/b7cfd105b1eee36390d1b56770d7387b/trend_analysis_plot.jpg" style="width: 577px; height: 385px;" /></p>
<p>Note that this trend forecast based on a linear model could be conservative. The database already shows 39 published studies in the first 6 months of this year (2016). In the coming years, these data may require a quadratic (curved) model!</p>
<span style="lineheight: 20.8px;">A Surprising Breadth of Applications</span>
<p><span style="lineheight: 20.8px;">QI studies in healthcare run the gamut. Reducing appointment noshows. Avoiding preventable hospital readmissions. Cutting down on the amount of expired medical drugs and equipment that must be discarded. Reducing the number of falls in nursing care facilities. Even t</span><span style="lineheight: 20.8px;">racking and reducing the number of times the door is opened and closed during surgeries! </span></p>
<p><span style="lineheight: 20.8px;">The one consensus in all these diverse studies? There's no shortage of opportunity for trimming waste and for improving patient outcomes in the healthcare setting. </span></p>
<span style="lineheight: 20.8px;">Improving on Improvement: Statistical "Soft Spots" </span>
<p><span style="lineheight: 1.6;">With the increased number of published studies in lean/six sigma healthcare, comes increased scrutiny. Review studies are beginning to look more closely at the methods used to monitor and measure healthcare quality outcomes. These reviews have identified statistical shortcomings in the published studies.24</span></p>
<ul>
<li>
<p><span style="lineheight: 1.6;"><strong>No testing for statistical significance</strong> <br />
A study might report a reduction in, say, mean waiting times for surgery for patients after an improvement initiative. But no statistical analyses are performed to determine whether that reduction is statistically significant.</span></p>
</li>
<li>
<p><strong>Lack of randomization</strong><br />
The samples examined in a study are not randomly selected, and may not be representative of the population. Therefore, the results are subject to selection bias.</p>
</li>
<li>
<p><strong>Inadequate followup</strong><br />
A study might report a statistically significant change after a lean/six sigma initiative, but there is lack of adequate followup. Therefore, it's unclear whether the improvement "stuck" or whether the initial change was simply a shortterm Hawthorne effect.</p>
</li>
<li>
<p><strong>Missing confidence intervals</strong><br />
Many studies neglect to report associated confidence intervals with their results. As a result, the level of precision is unclear, and the clinical significance of the results cannot be reliably interpreted.</p>
</li>
</ul>
<span style="lineheight: 20.8px;">No Single Study is a Statistical SlamDunk</span>
<p><span style="lineheight: 20.8px;">There's no such thing as a "perfect" study. You do the best you can, with the resources you have and the constraints you face. Progress is made in increments. Conditions change. And results must be reverified and reproduced.</span></p>
<p><span style="lineheight: 20.8px;">Still, it's important to remember that "continuous improvement" can be applied not only to the process itself, but to the methods that we use to monitor and improve a process. To get the most out of <a href="http://www.minitab.com/enus/lp/HealthCareandMinitab/">quality improvement efforts in healthcare</a>, it's critical to be aware of the common statistical soft spots, and how to avoid them.</span></p>
<p><span style="lineheight: 20.8px;">That way, <em>when</em></span><span style="lineheight: 1.6;"><em> </em>the wave breaks, we'll be on sturdier ground.</span></p>
Sources
<p>1 An Aging World: 2015. International Population Reports. US Census Bureau. Available <a href="https://www.census.gov/content/dam/Census/library/publications/2016/demo/p95161.pdf" target="_blank">here</a>.</p>
<p>2 <span style="lineheight: 1.6;">Nicolay </span><span style="lineheight: 20.8px;">CR</span><span style="lineheight: 1.6;">, Purkayastha </span><span style="lineheight: 20.8px;">S</span><span style="lineheight: 1.6;">, Greenhalgh </span><span style="lineheight: 20.8px;">A</span><span style="lineheight: 1.6;">, Benn </span><span style="lineheight: 20.8px;">J</span><span style="lineheight: 1.6;">, Chaturvedi </span><span style="lineheight: 20.8px;">S</span><span style="lineheight: 1.6;">, Phillips </span><span style="lineheight: 20.8px;">N</span><span style="lineheight: 1.6;">, Darzi </span><span style="lineheight: 20.8px;">A </span><span style="lineheight: 1.6;">. Systematic review of the application of quality improvement methodologies from the manufacturing industry to surgical healthcare. </span>Br J Surg. 2012 Mar;99(3):32435. 2011 Nov 18.<span style="lineheight: 1.6;"> </span></p>
<p><span style="lineheight: 1.6;">3 </span>Amaratunga T, Dobranowski J. Systematic review of the application of Lean and Six Sigma quality improvement methodologies in radiology. J Am Coll Radiol. 2016 May 18. </p>
<p>4 Mason SE, Nicolay CR, Darzi A. The use of Lean and Six Sigma methodologies in surgery: a systematic review. Surgeon. 2015 Apr;13(2):91100.</p>
<p>Photo: <em>Big Wave Breaking </em>by Brocken Inaglory. Licensed by Wikimedia Commons. </p>
Health Care Quality Improvement
Lean Six Sigma
Quality Improvement
Six Sigma
Fri, 01 Jul 2016 13:00:00 +0000
http://blog.minitab.com/blog/statisticsandqualitydataanalysis/qitrendsinhealthcare%3Awhatarethestatisticalsoftspots
Patrick Runkel

Those 10 Simple Rules for Using Statistics? They're Not Just for Research
http://blog.minitab.com/blog/understandingstatistics/those10simplerulesforusingstatisticstheyrenotjustforresearch
<p><span style="lineheight: 1.6;">Earlier this month, PLOS.org published an article titled "<a href="http://journals.plos.org/ploscompbiol/article?id=10.1371/journal.pcbi.1004961" target="_blank">Ten Simple Rules for Effective Statistical Practice</a>." </span><span style="lineheight: 20.8px;">The 10 rules are good reading for </span><em style="lineheight: 20.8px;">anyone </em><span style="lineheight: 20.8px;">who draws conclusions and makes decisions based on data</span><span style="lineheight: 20.8px;">, whether you're trying to extend the boundaries of scientific knowledge or make good decisions for your business. </span></p>
<p><span style="lineheight: 20.8px;">Carnegie Mellon University's Robert E. Kass and several coauthors</span><span style="lineheight: 20.8px;"> </span><span style="lineheight: 1.6;">devised the rules in response to the increased pressure on scientists and researchers—many, if not most, of whom are <em>not</em> statisticians—to present accurate findings based on sound statistical methods. </span></p>
<p><span style="lineheight: 20.8px;">Since </span><span style="lineheight: 1.6;">the paper and the discussions it has prompted focus on scientists and researchers, it seems worthwhile to consider how the rules might apply to </span><span style="lineheight: 20.8px;">quality practitioners or business decisionmakers as well</span><span style="lineheight: 1.6;">. </span><span style="lineheight: 1.6;">In this post, I'll share the 10 rules, some with a few modifications to make them more applicable to the wider population of all people who use data to inform their decisions. </span></p>
<img alt="questions" src="http://cdn2.content.compendiumblog.com/uploads/user/458939f4fe084dbcb271efca0f5a2682/d2c0571aacbd48c784f4222276c293fe/Image/36fa08b0c862c669f4e41596fbb76ddd/question_mark_signs.jpg" style="width: 200px; height: 200px; float: right; margin: 10px 15px; borderwidth: 1px; borderstyle: solid;" />1. Statistical Methods Should Enable Data to Answer <span style="color:#FF0000;">Scientific Specific</span> Questions
<p>As the article points out, new or infrequent users of statistics tend to emphasize finding the "right" method to use—often focusing on the structure or format of their data, rather than thinking about how the data might answer an important question. But choosing a method based on the data is putting the cart before the horse. Instead, we should start by clearly identifying the question we're trying to answer. Then we can look for a method that uses the data to answer it. If you haven't already collected your data, so much the better—you have the opportunity to identify and obtain the data you'll need.</p>
2. Signals Always Come With Noise
<p>If you're familiar with <a href="http://blog.minitab.com/blog/understandingstatistics/controlcharttutorialsandexamples">control charts</a> used in statistical process control (SPC) or the Control phase of a Six Sigma DMAIC project, you know that they let you distinguish process variation that matters (specialcause variation) from normal process variation that doesn't need investigation or correction.</p>
<p style="marginleft: 40px;"><img alt="control chart" src="http://cdn2.content.compendiumblog.com/uploads/user/458939f4fe084dbcb271efca0f5a2682/d2c0571aacbd48c784f4222276c293fe/Image/632a05ec67ddca317eb4bc1f4daabe9a/i_chart_of_ph.gif" style="lineheight: 20.8px; width: 573px; height: 172px;" /><br />
<em style="lineheight: 20.8px;">Control charts are one common tool used to distinguish "noise" from "signal." </em></p>
<p>The same concept applies here: whenever we gather and analyze data, some of what we see in the results will be due to inherent variability. Measures of probability for analyses, such as confidence intervals, are important because they help us understand and account for this "noise." </p>
3. Plan Ahead, Really Ahead
<p>Say you're starting a DMAIC project. Carefully considering and developing good questions right at the start of a project—the DEFINE stage—will help you make sure that you're getting the right data in the MEASURE stage. That, in turn, should result in a much smoother and stressfree ANALYZE phase—and probably more successful IMPROVE and CONTROL phases, too. The alternative? You'll have to complete the ANALYZE phase with the data you have, not the data you wish you had. </p>
4. Worry About Data Quality
<p><img alt="gauge" src="http://cdn.app.compendium.com/uploads/user/458939f4fe084dbcb271efca0f5a2682/479b4fbdf8c040119409f4109cc4c745/Image/b82fc879fa26a76f2b00424550aafe9e/gage.jpg" style="width: 250px; height: 173px; float: right; margin: 10px 15px;" />"Can you trust your data?" My Six Sigma instructor asked us that question so many times, it still flashes through my mind every time I open Minitab. That's good, because he was absolutely right: if you can't trust your data, you shouldn't do anything with it. Many people take it for granted that the data they get is precise and accurate, especially when using automated measuring instruments and similar technology. But how do you <em>know </em>they're measuring precisely and accurately? How do you <em>know </em>your instruments are calibrated properly? If you didn't test it, <em>you don't know</em>. And if you don't know, you can't trust your data. Fortunately, with measurement system analysis methods like <span><a href="http://blog.minitab.com/blog/meredithgriffith/fundamentalsofgagerr">gage R&R</a></span> and <a href="http://blog.minitab.com/blog/understandingstatistics/gotgoodjudgmentproveitwithattributeagreementanalysis">attribute agreement analysis</a>, we never have to trust <span style="lineheight: 20.8px;">data</span><span style="lineheight: 20.8px;"> </span><span style="lineheight: 1.6;">quality to blind faith. </span></p>
5. Statistical Analysis Is More Than a Set of Computations
<p>Statistical techniques are often referred to as "tools," and that's a very apt metaphor. A saw, a plane, and a router all cut wood, but they aren't interchangeable—the end product defines which tool is appropriate for a job. Similarly, you might apply ANOVA, regression, or time series analysis to the same data set, but the right tool depends on what you want to understand. To extend the metaphor further, just as we have circular saws, jigsaws, and miter saws for very specific tasks, each family of statistical methods also includes specialized tools designed to handle particular situations. The point is that we select a tool to <em>assist </em>our analysis, not to <em>define </em>it. </p>
6. Keep it Simple
<p>Many processes are inherently messy. If you've got dozens of input variables and multiple outcomes, analyzing them could require many steps, transformations, and some thorny calculations. Sometimes that degree of complexity is required. But a more complicated analysis isn't always better—in fact, overcomplicating it may make your results less clear and less reliable. It also potenitally makes the analysis more difficult than necessary. <span style="lineheight: 20.8px;">You may not </span><em style="lineheight: 20.8px;">need </em><span style="lineheight: 20.8px;">a complex process model that includes 15 factors if you can improve your output by optimizing the three or four most important inputs. </span><span style="lineheight: 1.6;">If you need to improve a process that includes many inputs, </span><a href="http://blog.minitab.com/blog/statisticsandqualityimprovement/createadoescreeningexperimentwiththeassistantinminitab17" style="lineheight: 1.6;">a short screening experiment</a><span style="lineheight: 1.6;"> can help you identify which factors are most critical, and which are not so important. </span></p>
7. Provide Assessments of Variability
<p>No model is perfect. No analysis accounts for all of the observed variation. Every analysis includes a degree of uncertainty. Thus, no statistical finding is 100% certain, and that degree of uncertainty needs to be considered when using statistical results to make decisions. If you're the decisionmaker, be sure that you understand the risks of reaching a wrong conclusion based on the analysis at hand. If you're sharing your results with stakeholders and executives, especially if they aren't statistically inclined, make sure you've communicated that degree of risk to them by offering and explaining confidence intervals, margins of error, or other appropriate measures of uncertainty. </p>
8. Check Your Assumptions
<p>Different statistical methods are based on different assumptions about the data being analyzed. For instance, many common analyses assume that your data follow a normal distribution. You can check most of these assumptions very quickly using functions like a normality test in your statistical software, but it's easy to forget (or ignore) these steps and dive right into your analysis. However, failing to verify those assumptions can yield results that aren't reliable and shouldn't be used to inform decisions, so don't skip that step. <a href="http://www.minitab.com/products/minitab/assistant/">If you're not sure about the assumptions for a statistical analysis, Minitab's Assistant menu explains them</a>, and can even flag violations of the assumptions before you draw the wrong conclusion from an errant analysis. </p>
9. <span style="color:#FF0000;">When Possible, Replicate Verify Success!</span>
<p><span style="lineheight: 1.6;">In science, replication of a study—ideally by another, independent scientist—is crucial. It indicates that the first researcher's findings weren't a fluke, and provides more evidence in support of the given hypothesis. Similarly, when a quality project results in great improvements, we can't take it for granted those benefits are going to be sustained—they need to be verified and confirmed over time. Control charts are probably the most common tool for making sure a project's benefits endure, but depending on the process and the nature of the improvements, hypothesis tests, capability analysis, and other methods also can come into play. </span></p>
10. <span style="color:#FF0000;">Make Your Analysis Reproducible Share How You Did It</span>
<p>In the original 10 Simple Rules article, the authors suggest scientists share their data and explain how they analyzed it so that others can make sure they get the same results. This idea doesn't translate so neatly to the business world, where your data may be proprietary or private for other reasons. But just as science benefits from transparency, the quality profession benefits when we share as much information as we can about our successes. <span style="lineheight: 20.8px;">Of course you can't share your company's secretsauce formulas with competitors</span><span style="lineheight: 20.8px;">—but i</span><span style="lineheight: 1.6;">f you solved a quality challenge in your organization, chances are your experience could help someone facing a similar problem. If a peer in another organization already solved a problem like the one you're struggling with now, wouldn't you like to see if a similar approach might work for you? Organizations like <a href="http://asq.org/index.aspx" target="_blank">ASQ</a> and forums like <a href="https://www.isixsigma.com/" target="_blank">iSixSigma.com</a> help quality practitioners network and share their successes so we can all get better at what we do. And here at Minitab, we love sharing <a href="http://www.minitab.com/company/casestudies/">case studies and examples of how people have solved problems using data analysis</a>, too. </span></p>
<p>How do you think these rules apply to the world of quality and business decisionmaking? What are <em>your </em>guidelines when it comes to analyzing data? </p>
<p> </p>
Data Analysis
Lean Six Sigma
Quality Improvement
Six Sigma
Statistics
Statistics Help
Statistics in the News
Stats
Wed, 29 Jun 2016 12:00:00 +0000
http://blog.minitab.com/blog/understandingstatistics/those10simplerulesforusingstatisticstheyrenotjustforresearch
Eston Martz

Using the Nelson Rules for Control Charts in Minitab
http://blog.minitab.com/blog/statisticsinthefield/usingthenelsonrulesforcontrolchartsinminitab
<p><em style="lineheight: 1.6;">by Matthew Barsalou, guest blogger</em></p>
<p>Control charts plot your process data to identify and distinguish between common cause and special cause variation. This is important, because identifying the different causes of variation lets you take action to make improvements in your process without <em>over</em>controlling it.</p>
<p>When you create a control chart, the software you're using should make it easy to see where you may have variation that requires your attention. For example, Minitab Statistical Software automatically flags any control chart data point that is more than three standard deviations above the centerline, as shown in the I chart below.</p>
<div style="marginleft:40px; width:577; fontsize:11px;"><img alt="I Chart of Data  Nelson Rules" src="http://cdn.app.compendium.com/uploads/user/458939f4fe084dbcb271efca0f5a2682/479b4fbdf8c040119409f4109cc4c745/Image/be7c11b66ec1be76d0ae6cf7ab43f3e4/image002.png" style="lineheight: 20.8px; borderwidth: 0px; borderstyle: solid; width: 576px; height: 384px;" /><br />
I chart example with one outofcontrol point.</div>
<p>A data point that more than three standard deviations from the centerline is one indicator for detecting specialcause variation in a process. There are additional control chart rules introduced by Dr. Lloyd S. Nelson in his April 1984 <em>Journal of Quality Technology </em><a href="http://asq.org/data/subscriptions/jqt_open/1984/oct/jqtv16i4technical.pdf" target="_blank">column</a>. The eight Nelson Rules are shown below, and if you're interested in using them, they can be activated in Minitab.</p>
<div style="marginleft: 40px; width: 550px; fontsize: 11px;"><img alt="Nelson Rules for special cause variation in control charts" src="http://cdn.app.compendium.com/uploads/user/458939f4fe084dbcb271efca0f5a2682/479b4fbdf8c040119409f4109cc4c745/Image/e7bd87833a33a442c6d171932e6e7480/image003.png" style="width: 545px; height: 691px; borderwidth: 1px; borderstyle: solid;" /><br />
The Nelson rules for tests of special causes. Reprinted with permission from <em>Journal of Quality Technology</em> ©<strong><em>1984</em> ASQ</strong>, asq.org.</div>
<p>To activate the Nelson rules, go to <strong>Control Charts > Variables Charts for Individuals > Individuals... </strong>and then click on "I Chart Options." Go to the <strong>Tests </strong>tab and place a check mark next to the test you would like to select—or simply use the dropdown menu and select “Perform all tests for special causes,” as shown below.</p>
<p style="marginleft: 40px;"><img alt="Individual Charts Options in Minitab" src="http://cdn.app.compendium.com/uploads/user/458939f4fe084dbcb271efca0f5a2682/479b4fbdf8c040119409f4109cc4c745/Image/31bbbbe82ef49054f70eb2f474da9a34/image005.png" style="borderwidth: 0px; borderstyle: solid; width: 456px; height: 453px;" /></p>
<p>The resulting session window explains which tests failed.</p>
<p style="marginleft: 40px;"><img alt="session window output" src="http://cdn.app.compendium.com/uploads/user/458939f4fe084dbcb271efca0f5a2682/479b4fbdf8c040119409f4109cc4c745/Image/f0e44dccacaf2851ea8c590d0291cd6e/image006.png" style="borderwidth: 0px; borderstyle: solid; width: 626px; height: 351px;" /></p>
<p>On the chart itself, the data points that failed each test are identified in red as shown below.</p>
<p style="marginleft: 40px;"><img alt="I chart of data" src="http://cdn.app.compendium.com/uploads/user/458939f4fe084dbcb271efca0f5a2682/479b4fbdf8c040119409f4109cc4c745/Image/4832d48fb67f7085cdc38af84e6c2658/image009.png" style="lineheight: 1.6; borderwidth: 0px; borderstyle: solid; width: 576px; height: 384px;" /></p>
<p>Simply activating all of the rules is not recommended—the false positive rate goes up as each additional rule is activated. At some point the control chart will become more sensitive than it needs to be and corrective actions for <a href="http://blog.minitab.com/blog/understandingstatistics/controlchartsshowyouvariationthatmatters">special causes of variation</a> may be implemented when only common cause is variation present.</p>
<p>Fortunately, Nelson provided detailed guidance on the correct application of his namesake rules. Nelson’s guidance on applying his rules for tests of special causes is presented below.</p>
<div style="marginleft:40px; width:685px; fontsize:11px;">
<p><img alt="comments on test for special causes" src="http://cdn.app.compendium.com/uploads/user/458939f4fe084dbcb271efca0f5a2682/479b4fbdf8c040119409f4109cc4c745/Image/f6a2616d41592b9c671ac60cb12c98c1/image010.png" style="lineheight: 1.6; borderwidth: 1px; borderstyle: solid; width: 630px; height: 683px;" /><br />
Comments on tests for special causes. Reprinted with permission from <em>Journal of Quality Technology</em> ©<strong><em>1984</em> ASQ</strong>, asq.org.</p>
</div>
<p>Nelson’s tenth comment is an especially important one, regardless of which tests have been activated. </p>
<p>Minitab, together with the Nelson rules, can be very helpful, but neither can replace or remove the need for the analyst's judgment when assessing a control chart. These rules can, however, assist the analyst in making the proper decision. </p>
<p> </p>
<p><strong>About the Guest Blogger</strong></p>
<p><em><a href="https://www.linkedin.com/pub/matthewbarsalou/5b/539/198" target="_blank">Matthew Barsalou</a> is a statistical problem resolution Master Black Belt at <a href="http://www.3kwarner.de/" target="_blank">BorgWarner</a> Turbo Systems Engineering GmbH. He is a Smarter Solutions certified Lean Six Sigma Master Black Belt, ASQcertified Six Sigma Black Belt, quality engineer, and quality technician, and a TÜVcertified quality manager, quality management representative, and auditor. He has a bachelor of science in industrial sciences, a master of liberal studies with emphasis in international business, and has a master of science in business administration and engineering from the Wilhelm Büchner Hochschule in Darmstadt, Germany. He is author of the books <a href="http://www.amazon.com/RootCauseAnalysisStepStep/dp/148225879X/ref=sr_1_1?ie=UTF8&qid=1416937278&sr=81&keywords=Root+Cause+Analysis%3A+A+StepByStep+Guide+to+Using+the+Right+Tool+at+the+Right+Time" target="_blank">Root Cause Analysis: A StepByStep Guide to Using the Right Tool at the Right Time</a>, <a href="http://asq.org/qualitypress/displayitem/index.html?item=H1472" target="_blank">Statistics for Six Sigma Black Belts</a> and <a href="http://asq.org/qualitypress/displayitem/index.html?item=H1473&xvl=76115763" target="_blank">The ASQ Pocket Guide to Statistics for Six Sigma Black Belts</a>.</em></p>
Data Analysis
Lean Six Sigma
Quality Improvement
Six Sigma
Statistics
Mon, 27 Jun 2016 13:57:00 +0000
http://blog.minitab.com/blog/statisticsinthefield/usingthenelsonrulesforcontrolchartsinminitab
Guest Blogger