Final answer:
Bonferroni, Fisher's LSD, and Tukey's HSD are post hoc tests used to identify which group means are significantly different following a one-way ANOVA. They adjust for multiple comparisons to control Type I error and require that the populations are normally distributed with equal variances.
Step-by-step explanation:
The three main post hoc tests used for pairwise comparisons in statistics are the Bonferroni, Fisher's LSD (Least Significant Difference), and Tukey's HSD (Honestly Significant Difference) tests. These tests are employed following a one-way Analysis of Variance (ANOVA) when the null hypothesis has been rejected, to determine exactly which means are significantly different from one another. ANOVA is used to compare the means of three or more independent groups to see if at least one group mean is statistically different from the others.
The Bonferroni test is a conservative method that controls for Type I error across multiple comparisons by adjusting the significance level. Fisher's LSD is less conservative and may be used when conducting a small number of comparisons. Tukey's HSD is preferred when all pairwise comparisons are to be made and is particularly powerful when the sample sizes are equal.
It's important to note that all three methods require the assumption of normally distributed populations with equal variances, and that the samples are independently and randomly selected from each population.