The Tukey Honestly Significant Difference (HSD) test is a post-hoc analysis used to determine which specific group means are statistically different after an ANOVA test finds a significant difference among the means of three or more groups. It calculates a critical value that represents the minimum difference between two means required for the difference to be considered statistically significant. For example, if an ANOVA reveals significant differences in average crop yields across four fertilizer treatments, the HSD test can pinpoint which fertilizer treatments yielded statistically different results from one another. The output typically includes a table displaying the differences between each pair of means and an indication of whether those differences exceed the calculated critical value.
This method offers a rigorous approach to multiple comparisons, controlling the family-wise error rate, unlike pairwise t-tests which inflate the probability of Type I errors (false positives) when comparing multiple groups. This control is vital for drawing reliable conclusions from complex datasets. Developed by statistician John Tukey, the HSD test has become a standard procedure in various research fields, from agriculture to medicine, enhancing the interpretability and validity of experimental findings. Its widespread adoption reflects its robustness and practical utility in identifying true effects amidst variations in data.
