## INTRODUCTION

Some tools of Lean Six Sigma aren't graphical; they're simply analytical. Sometimes you want to be able to compare two processes or products and learn something about their quality using statistics alone. Healthcare research often uses these tools to compare the effects of two or more medications or protocols. Six Sigma practitioners can use these tools to compare performance before and after an improvement to verify its effectiveness. This falls under the category of something known as hypothesis testing.

When doing research or clinical trials, these statistical tools help to evaluate the efficacy of various medications or protocols. When using Lean Six Sigma to solve problems, these tools can help to compare the before and after performance to determine whether the results are statistically significant.

## HYPOTHESIS TESTING

I've come to suspect that hypothesis testing is where statistics got the nickname "sadistics." I found it confusing because it seems to use negative logic to describe everything. But it's really not that hard once you understand how it works.

Let's say that you have two medications or protocols and you want to prove that they are (1) the same (i.e., equal) or (2) different (i.e., not equal) at a certain level of confidence. You might want to compare a control group with a test group to determine whether a medication is effective. Because Lean Six Sigma is obsessed with variation and central tendencies, you might want to prove that the average or variation is the same or different. Hypothesis testing helps you to evaluate these two hypotheses.

The English geneticist who dreamed this up decided that the same or equal result would be called the null hypothesis. Different results are known as the alternate hypothesis. Then, based on the analysis, you want to accept the null hypothesis (i.e., that the two medications or protocols are the same) or reject the null hypothesis (i.e., that the two medications or protocols are different). There are several tools that can help you to do this depending on whether you are most interested in the average or the variation.

## HYPOTHESIS TESTING FOR VARIATION

Because variation can affect results, it's useful to determine whether variation in two or more samples is the same or different. To evaluate variation statistically, use the F-test or Levene's test.

### F-Test for Variation

If you have a single factor measured at two levels (e.g., calcium levels) and you want to know whether they have the same or different variability, use the F-test. An F-test using two samples compares two independent sets of test data. It helps to determine whether the variances are the same or different from each other. Consider the following example.

If you're ...

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