Tests of Differences between Means, Independent Groups, Standard Deviation Estimated (1 of 8)

This section explains how to test the difference between group means for significance. The formulas are slightly simpler when the sample sizes are equal. These formulas are given first.

Equal Sample Sizes
An experiment was conducted comparing the memory of expert and novice chess players. The mean number of pieces correctly placed across several chess positions was computed for each subject. (These data are from the novices and tournament players in the dataset "Chess.") The question is whether the difference between the means of these two groups of subjects is statistically significant.

The first step is to specify the null hypothesis and an alternative hypothesis. For experiments testing differences between means, the null hypothesis is that the difference between means is some specified value. Usually the null hypothesis is that the difference is zero.

For this example, the null and alternative hypotheses are:

H_o: µ₁ - µ₂ = 0
H₁: µ₁ - µ₂ ≠ 0