The ANOVA Post Hoc Analyses article discusses the liberality of the variety of t
ID: 3228275 • Letter: T
Question
The ANOVA Post Hoc Analyses article discusses the liberality of the variety of the post hoc tests once a significant difference has been found after conducting an ANOVA. What does being a "liberal" test mean? a. Likely to result in a Type II error b. Lower power is adequate to conduct the post hoc c. Likely to result in a Type I error d. Smaller sample size is adequate to conduct the post hoc What post hoc analysis mentioned in the paper is the most liberal? a. Tukey-Kramer HSD b. Fisher PLSD c. Scheffe d. SNKExplanation / Answer
answer c) likely to result in a type 1 error
b) Fisher PLSD is the most liberal
When we compare say 3 groups using ANOVA and find the means are different. We want to find out which pair of means are different? Is it A vs B or B vs C or A vs C. Let us say alpha = 0.05, meaning the type1 error probability is 5%.
If we want to know where the difference comes from, we have to do 3 tests as stated above ( k * (k-1)/2). Then the error rate multiplies to 0.05*0.05*0.05
family wise error rate = 1 - (1-0.05) *(1-0.05)*(1-0.05) = 0.1426
type1 error rate increases to 14.26%.
So post ANOVA tests tries to reduce this type1 error, but some of the tests are "liberal" and they worry about type2 increasing the type1 error. Hence answer for first part is c)
Fisher's LSD sets alpha at 0.05 for every pairwise t-test among the groups. Hence chances of type1 error increases and is liberal among all the post hoc ANOVA. It is ideally suited for comparison of 3 groups
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