The formula to calculate the Honestly Significant Difference (HSD) is:
\[ HSD = q \times \sqrt{\left(\frac{MSW}{n}\right) \times \left(\frac{1}{a}\right)} \]
Where:
The Honestly Significant Difference (HSD) is a statistical test that is used to determine whether there are significant differences between two or more groups of data. It is often used in conjunction with an ANOVA (Analysis of Variance) test, which determines whether there are any significant differences between groups, but does not specify which groups are significantly different from each other. The HSD test is used to make pairwise comparisons between groups to determine exactly which groups differ from each other. It calculates a range of values, and if the difference between the means of two groups falls within this range, then the difference is considered to be statistically significant. The HSD test is particularly useful when dealing with large data sets, as it controls for the increased probability of making a Type I error (false positive) that occurs when making multiple comparisons.
Let's assume the following values:
Using the formula:
\[ HSD = 3.5 \times \sqrt{\left(\frac{4.2}{30}\right) \times \left(\frac{1}{5}\right)} = 0.59 \]
The Honestly Significant Difference (HSD) is 0.59.
