Power and Sample Size

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

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
Using a sample to estimate the properties of an entire population is common practice in statistics. For example, the mean from a random sample estimates that parameter for an entire population. In linear regression analysis, we’re used to the idea that the regression coefficients are estimates of the true parameters. However, it’s easy to forget that R-squared (R2) is also an estimate.... Continue Reading
Do you suffer from PAAA (Post-Analysis Assumption Angst)? You’re not alone. Checking the required assumptions for a statistical  analysis is critical. But if you don’t have a Ph.D. in statistics, it can feel more complicated and confusing than the primary analysis itself. How does the cuckoo egg data, a common sample data set often used to teach analysis of variance, satisfy the following formal... Continue Reading
A few weeks ago I looked at the number of goals that were being scored in the World Cup. At the time there were 2.9 goals per game, which was the highest since 1970. Unfortunately for spectators who enjoyed the higher scoring goals, this did not last. By the end, the average had fallen to 2.7 goals per game, the same amount scored in the 1998 World Cup. After such a high-scoring start, the goals... Continue Reading
Remember "The Little Engine That Could," the children's story about self-confidence in the face of huge challenges? In it, a train engine keeps telling itself "I think I can" while carrying a very heavy load up a big mountain. Next thing you know, the little engine has done it...but until that moment, the outcome was uncertain. It's a wonderful story for teaching kids about self-confidence. But... Continue Reading
Minitab graphs are powerful tools for investigating your process further and removing any doubt about the steps you should take to improve it. With that in mind, you’ll want to know every feature about Minitab graphs that can help you share and communicate your results effectively. While many ways to modify your graph are on the Editor menu, some of the best features become available when you... Continue Reading
It's all too easy to make mistakes involving statistics. Powerful statistical software can remove a lot of the difficulty surrounding statistical calculation, reducing the risk of mathematical errors—but  correctly interpreting the results of an analysis can be even more challenging.  No one knows that better than Minitab's technical trainers. All of our trainers are seasoned statisticians with... Continue Reading
We’re in the thick of the Stanley Cup playoffs, which means hockey fans are doing what seems to be every sports fan's favorite hobby...complaining about the refs! While most complaints, such as “We’re not getting any of the close calls!” are subjective and hard to get data for, there's one question that we should be able to answer objectively with a statistical analysis: Are hockey penalties... Continue Reading