14.7 Apply a correction for multiple comparisons

14.7.1 Bonferroni corrections

The corrected p-value is the result of multiply all your raw p-values by m, where m is the number of separate tests. Such as in the previous case we had to compare placebo vs drug1, placebo vs drug2, drug1 vs drug2; so we had 3 tests.

\[{p}'=p*m\] \({p}'< \alpha = 0.05\)

posthocPairwiseT( my.anova, 
                  p.adjust.method = "bonferroni")

## 
##  Pairwise comparisons using t tests with pooled SD 
## 
## data:  mood.gain and drug 
## 
##          placebo anxifree
## anxifree 0.4506  -       
## joyzepam 9.1e-05 0.0017  
## 
## P value adjustment method: bonferroni

14.7.2 Holm corrections

Another method, pretending the tests are done sequentially.

\[{p}'_j=j*p_j\]

posthocPairwiseT( my.anova )

## 
##  Pairwise comparisons using t tests with pooled SD 
## 
## data:  mood.gain and drug 
## 
##          placebo anxifree
## anxifree 0.1502  -       
## joyzepam 9.1e-05 0.0011  
## 
## P value adjustment method: holm

14.7.3 Normality, Homogeneity of variance and Independence

14.7.3.1 Welch one-way test

F(2,)

oneway.test(mood.gain ~ drug, data = clin.trial)

## 
##  One-way analysis of means (not assuming equal variances)
## 
## data:  mood.gain and drug
## F = 26.322, num df = 2.0000, denom df = 9.4932, p-value = 0.000134

oneway.test(mood.gain ~ drug, data = clin.trial, var.equal = TRUE)

## 
##  One-way analysis of means
## 
## data:  mood.gain and drug
## F = 18.611, num df = 2, denom df = 15, p-value = 8.646e-05