Overview
Tukey’s LSD (Least Significant Difference) is another post-hoc test that can be used following an ANOVA with a significant result. It is similar to Tukey’s HSD test, except that a t-test is used instead of a q-test. This means that it has higher power but is more susceptible to an inflated type I error.
The test statistic is
and the confidence interval is
where tcrit = T.INV.2T(α, df).
Example
For Example 1 of Tukey HSD, the LSD analysis is as shown in Figure 1.
Figure 1 – LSD Test
The formulas used are the same as those used in Figure 3 of Tukey HSD with the exception that cell K9 contains the formula =T.INV.2T(J3,J9), cell I12 contains the formula =SQRT(2*I9/J9/HARMEAN(H5,H6)), cell M12 contains the formula =T.DIST.2T(J12,J$9), cell N12 contains the formula =I12*K$9, and similarly for the formulas in I13:I17, M13:M17, and N13:N17.
Note that the LSD post-hoc test is similar to pairwise t tests except that a pooled standard error is used.
Examples Workbook
Click here to download the Excel workbook with the examples described on this webpage.
Reference
Howell, D. C. (2010) Statistical methods for psychology (7th ed.). Wadsworth, Cengage Learning.
https://labs.la.utexas.edu/gilden/files/2016/05/Statistics-Text.pdf