Question

Which post-hoc test should be used if sample sizes were 20, 4 and 15?

a) Tukey's HSD
b) Bonferroni correction
c) Dun's test
d) Scheffé's method

Answer 1

The most appropriate post-hoc test for unequal sample sizes (20, 4, 15) from the given options is Scheffe's method, as it is robust to such conditions.

Step-by-step explanation:

The appropriate post-hoc test to use when the sample sizes are unequal (20, 4, 15) would likely be Dunnett's C or the Games-Howell test, which are not listed in the provided options. However, if we are to choose from the given options and considering that the sample sizes are quite different, Scheffe's method might be the most appropriate because it is robust to unequal sample sizes. Tukey's honestly significant difference (HSD) assumes equal sample sizes so it may not be ideal in this case. The Bonferroni correction could be used but it is conservative and would require a separate calculation for each comparison. With unequal sample sizes and the absence of additional context or restrictions, Scheffe's method would usually be most suitable among the listed choices.