Fisher's LSD and Sidak Pairwise Comparisons

Fisher's LSD and Sidak pairwise comparisons test every pair of group means with t tests that use the pooled ANOVA mean square error and its error degrees of freedom.

Fisher LSD 와 Sidak 짝비교는 일원분산분석의 합동 평균제곱오차와 오차 자유도를 써서 모든 집단 평균 쌍을 t 검정으로 비교하는 사후검정입니다.

After a significant one-way ANOVA, how do I run Fisher's LSD or Sidak comparisons and get letter groupings?

일원분산분석이 유의하게 나온 뒤 Fisher LSD 나 Sidak 으로 사후검정하고 문자 표시까지 받으려면 어떻게 하나요?

Each pair of means is compared with t = (mean difference) / sqrt(MSE(1/n_i + 1/n_j)) on N - k degrees of freedom, where MSE comes from the one-way ANOVA. Fisher's LSD leaves the per-comparison p values unadjusted and is protected only when the overall F test is significant, while the Sidak version adjusts each p value to 1 - (1 - p)^m for m comparisons.

When to use Fisher's LSD and Sidak Pairwise Comparisons

• A one-way ANOVA with three groups was significant and you want the least conservative valid follow-up (protected LSD).
• You need pairwise comparisons with familywise error control that is slightly less conservative than Bonferroni (Sidak).
• You want a compact letter display for a table or bar chart of group means.

When to use something else

• You compare four or more groups and need strong familywise control; use Tukey HSD.
• Group variances clearly differ; use Games-Howell.

Assumptions and requirements

• Observations are independent.
• Residuals are approximately normally distributed.
• Group variances are equal, since all comparisons share the pooled MSE.

What the analysis reports

• Omnibus F, its p value, MSE and error degrees of freedom
• Mean difference, standard error, t, raw and adjusted p for each pair
• Critical difference and confidence interval for each pair (Sidak-adjusted level when method = sidak)
• Compact letter display and Cohen's d per pair

How to report it

A one-way ANOVA was significant, F([df1], [df2]) = [value], p = [value]; Fisher's LSD comparisons (MSE = [value]) showed that [group 2] scored higher than [group 1], mean difference = [value], 95% CI [[lower], [upper]], p = [value].

Related methods

• Tukey HSD Post Hoc Test
• Bonferroni Correction
• One-way ANOVA

Run Fisher's LSD and Sidak Pairwise Comparisons on Quorant