24.8 Statistical validity conditions: Two independent means

As usual, these results apply under certain conditions. The CI computed above is statistically valid if one of these conditions is true:

Both sample sizes are at least 25; or
Either sample size is smaller than 25, and the populations corresponding to both comparison groups 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 CI 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 24.2 (Statistical validity) For the reaction-time data, both samples are larger than \(25\), so the CI will be statisticall valid.

Example 24.3 (Statistical validity) In the whales examples of Example 24.1, the two sample sizes are 26 (for females) and 30 (for males).

Since both samples are larger than 25, the CI will be statistically valid.