30.7 Statistical validity conditions

As usual, these results apply under certain conditions, which are the same as those for forming a CI for the difference between two means.

The test above is statistically valid if one of these conditions is true:

1. Both sample sizes are at least 25; or
2. Either sample size is smaller than 25, and both populations have an approximate normal distribution.

The sample size of 25 is a rough figure here, and some books give other values (such as 30). We can explore the histograms of the samples to determine if normality of the populations seems reasonable.

In addition to the statistical validity condition, the test will be

• internally valid if the study was well designed; and
• externally valid if the sample is a simple random sample and is internally valid.

Example 30.1 (Statistical validity) For the reaction-time data, both samples sizes are \(n=32\). This means that the results will be statistically valid.

Explicitly, the data in each group do not need be normally distributed, since both sample sizes are larger than 25.