## Monday, April 12, 2010

### Sample Size Statements

One of our readers, Gary Kelly, who is carefully reading our book Analyzing and Interpreting Continuous Data Using JMP: A Step-by-Step Guide, had, what he called, a curious question:

I am wondering how you typically report out the sample size and power in a statement, given that it is a function of both alpha and beta.

He pointed out that in our book we don't explicitly state it, which is true. He wanted to know

Using your example in chapter 5, starting on page 244, how would you write a statement about the sample size output?

The example in Section 5.3.5, pages 243-248, describes the sample size calculations for comparing two sample means. Figure 5.12, page 247, shows the JMP output from the Sample Size and Power calculator

In my previous post, How Many Do I Need?, I went over the required four "ingredients" for the calculations. We use JMP's default value of Alpha= 0.05 (5%), as the significance level for the test, we state that the noise in the system Std Dev=1 unit, or 1 sigma, that we want to detect a difference of at least 1.5 standard deviations (Difference to detect), and that we want the test to have Power of 0.9 (90%). The calculator indicates that we need a total of 21 samples, or 21/2 = 11 (rounding up) per group, for our study.

So how do we frame our statement about this sample size calculation? We can say that

A total sample size of 22 experimental units, 11 per group, provides a 90% chance of detecting a difference ≥ 1.5 standard deviations between the two populations means with 95% confidence.

Thanks Gary for bringing this up.