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Power and Sample Size

Blog posts and articles about statistical power and sample size, especially in quality improvement projects.

You often hear the data being blamed when an analysis is not delivering the answers you wanted or expected. I was recently reminded that the data chosen or collected for a specific analysis is determined by the analyst, so there is no such thing as bad data—only bad analysis.  This made me think about the steps an analyst can take to minimise the risk of producing analysis that fails to answer... Continue Reading
In statistics, t-tests are a type of hypothesis test that allows you to compare means. They are called t-tests because each t-test boils your sample data down to one number, the t-value. If you understand how t-tests calculate t-values, you’re well on your way to understanding how these tests work. In this series of posts, I'm focusing on concepts rather than equations to show how t-tests work.... Continue Reading

7 Deadly Statistical Sins Even the Experts Make

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When it comes to statistical analyses, collecting a large enough sample size is essential to obtaining quality results. If your sample size is too small, confidence intervals may be too wide to be useful, linear models may lack necessary precision, and control charts may get so out of control that they become self-aware and rise up against humankind. Okay,that last point may have been... Continue Reading
Five-point Likert scales are commonly associated with surveys and are used in a wide variety of settings. You’ve run into the Likert scale if you’ve ever been asked whether you strongly agree, agree, neither agree or disagree, disagree, or strongly disagree about something. The worksheet to the right shows what five-point Likert data look like when you have two groups. Because Likert item data are... Continue Reading
P values have been around for nearly a century and they’ve been the subject of criticism since their origins. In recent years, the debate over P values has risen to a fever pitch. In particular, there are serious fears that P values are misused to such an extent that it has actually damaged science. In March 2016, spurred on by the growing concerns, the American Statistical Association (ASA) did... Continue Reading
I am a bit of an Oscar fanatic. Every year after the ceremony, I religiously go online to find out who won the awards and listen to their acceptance speeches. This year, I was so chuffed to learn that Leonardo Di Caprio won his first Oscar for his performance in The Revenant in the 88thAcademy Awards—after five nominations in  previous ceremonies. As a longtime Di Caprio fan, I still remember... Continue Reading
There are many reasons why a distribution might not be normal/Gaussian. A non-normal pattern might be caused by several distributions being mixed together, or by a drift in time, or by one or several outliers, or by an asymmetrical behavior, some out-of-control points, etc. I recently collected the scores of three different teams (the Blue team, the Yellow team and the Pink team) after a laser... Continue Reading
Did you ever wonder why statistical analyses and concepts often have such weird, cryptic names? One conspiracy theory points to the workings of a secret committee called the ICSSNN. The International Committee for Sadistic Statistical Nomenclature and Numerophobia was formed solely to befuddle and subjugate the masses. Its mission: To select the most awkward, obscure, and confusing name possible... Continue Reading
As Halloween approaches, you are probably taking the necessary steps to protect yourself from the various ghosts, goblins, and witches that are prowling around. Monsters of all sorts are out to get you, unless they’re sufficiently bribed with candy offerings! I’m here to warn you about a ghoul that all statisticians and data scientists need to be aware of: phantom degrees of freedom. These phantoms... Continue Reading
Step 3 in our DOE problem solving methodology is to determine how many times to replicate the base experiment plan. The discussion in Part 3 ended with the conclusion that our 4 factors could best be studied using all 16 combinations of the high and low settings for each factor, a full factorial. Each golfer will perform half of the sixteen possible combinations and each golfer’s data could stand as... Continue Reading
Step 1 in our DOE problem-solving methodology is to use process experts, literature, or past experiments to characterize the process and define the problem. Since I had little experience with golf myself, this was an important step for me. This is not an uncommon situation. Experiment designers often find themselves working on processes that they have little or no experience with. For example, a... Continue Reading
Repeated measures designs don’t fit our impression of a typical experiment in several key ways. When we think of an experiment, we often think of a design that has a clear distinction between the treatment and control groups. Each subject is in one, and only one, of these non-overlapping groups. Subjects who are in a treatment group are exposed to only one type of treatment. This is the... Continue Reading
By Matthew Barsalou, guest blogger.   Many statistical tests assume the data being tested came from a normal distribution. Violating the assumption of normality can result in incorrect conclusions. For example, a Z test may indicate a new process is more efficient than an older process when this is not true. This could result in a capital investment for equipment that actually results in higher... Continue Reading
In my previous post, I wrote about the hypothesis testing ban in the Journal of Basic and Applied Social Psychology. I showed how P values and confidence intervals provide important information that descriptive statistics alone don’t provide. In this post, I'll cover the editors’ concerns about hypothesis testing and how to avoid the problems they describe. The editors describe hypothesis testing... Continue Reading
All processes have some variation. Some variation is natural and nothing to be concerned about. But in other cases, there is unusual variation that may need attention.  By graphing process data against an upper and a lower control limit, control charts help us distinguish natural variation from special cause variation that we need to be concerned about. If a data point falls outside the limits on... Continue Reading
Welcome to the Hypothesis Test Casino! The featured game of the house is roulette. But this is no ordinary game of roulette. This is p-value roulette! Here’s how it works: We have two roulette wheels, the Null wheel and the Alternative wheel. Each wheel has 20 slots (instead of the usual 37 or 38). You get to bet on one slot. What happens if the ball lands in the slot you bet on? Well, that depends... Continue Reading
It’s safe to say that most people who use statistics are more familiar with parametric analyses than nonparametric analyses. Nonparametric tests are also called distribution-free tests because they don’t assume that your data follow a specific distribution. You may have heard that you should use nonparametric tests when your data don’t meet the assumptions of the parametric test, especially the... Continue Reading
If you wanted to figure out the probability that your favorite football team will win their next game, how would you do it?  My colleague Eduardo Santiago and I recently looked at this question, and in this post we'll share how we approached the solution. Let’s start by breaking down this problem: There are only two possible outcomes: your favorite team wins, or they lose. Ties are a possibility,... Continue Reading
  In my experience, one of the hardest concepts for users to wrap their head around revolves around the Power and Sample Size menu in Minitab's statistical software, and more specifically, the field that asks for the "difference" or "difference to detect."  Let’s start with power. In statistics, the definition of power is the probability that you will correctly reject the null hypothesis when it is... Continue Reading
Stepwise regression and best subsets regression are both automatic tools that help you identify useful predictors during the exploratory stages of model building for linear regression. These two procedures use different methods and present you with different output. An obvious question arises. Does one procedure pick the true model more often than the other? I’ll tackle that question in this post. Fi... Continue Reading