Illuminating Statistical Analysis Using Scenarios and Simulations

ERepeated Measures

Statistical Scenario—Weight Change

Let's say you want to test the effectiveness of a new diet. First, you get 30 random people to participate. You weigh them before they start the diet and then after 12 weeks on the diet.

The average weight change across all 30 participants is a loss of about 2 lbs.

Is this average weight loss statistically significant?

For this scenario, we cannot use the approach covered in Part II because the weights would just be lumped together into two groups: 30 before weights and 30 after weights. Instead, we need to assess the 30 pairs of before and after weights. For each pair, the weight before dieting is subtracted from the weight after dieting to give the difference in weight for each of the 30 individuals. Then, we can assess whether the mean of the differences is sufficiently far from zero. Table E.1 shows some of the dieting data along with the after-minus-before differences.

Table E.1 Example sample data.

Before	After	Difference
228	222	−6
228	230	2
223	219	−4
177	178	1
etc.	etc.	etc.

The Paired -test performs such an assessment. In a nutshell, after it calculates the individual differences and the mean and variance of the differences, it uses the variance of the differences and the number of differences to determine the standard error of the differences. Then, it determines how many standard errors separate ...