BIOL 373 Lecture Notes - Lecture 12: Biostatistics, Multiple Comparisons Problem, John Tukey
Document Summary
Can be used to test all k(k 1)/2 pairwise comparisons: performed after anova or kruskal-wallis test rejects h0, k(k 1)/2: number of combinations of k items drawn 2 at a time. Tukey test etc: sort all sample means in order of increasing size, compare biggest mean with smallest mean, then biggest with next smallest, if two means do not differ: Conclude no difference between pairs of means they enclose. Do not test h0 enclosed by no-difference means: tukey test statistic (q): Where b and a refer to the bigger & smaller means in each pair, and. For the entire experiment, not each comparison: q distribution studentized range distribution. Similar to the t distribution except takes into account the number of means being compared (k: if calculated q critical q , , k ; reject h0. Results can be written down as lines under similar means. X 1 x2 x3 x4 o: overlapping lines indicate type ii errors.
