One way to €˜€˜automate€ pairwise comparisons that works particularly well when the sample sizes are balanced is to compute a single value that can serve as a threshold for when a pair of sample means are far enough apart to suggest that the population means differ between those two groups. One such value is called Fisher€™s Least Significant Difference or LSD for short.

You may recognize this as the margin of error for a confidence interval for a difference in two means after doing an ANOVA. That is exactly how we compute it. Recall that the test for a pair of means will show a significant difference exactly when the confidence interval fails to include zero. The confidence level should be matched to the significance level of the test (for example, a 95% confidence interval corresponds to a 5% significance level). If the difference in two group means (in absolute value) is smaller than the LSD margin of error, the confidence interval will have one positive and one negative endpoint. Otherwise, the interval will stay either all positive or all negative and we conclude 

Reject H0 and conclude
the two means differ ‡‡’ |xÌ…_i ˆ’ xÌ…_j| > LSD

Compute LSD using a 5% significance level for the ANOVA data comparing textbook costs in Example 8.10 on page 516. Use the value to determine which academic fields appear to show evidence of a difference in mean textbook costs.

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LSD = t*,| MSE \Ni пj