Enter all but one of the critical value, Mean Square Within, total number of observations, and number of groups being compared into the calculator to determine the Honestly Significant Difference (HSD), and this calculator can also evaluate any of the variables given the others are known.

Hsd (Honestly Significant Difference) Formula

The following formula is used to calculate the Honestly Significant Difference (HSD) in a statistical analysis:

HSD = q * sqrt((MSW / n) * (1 / a))


  • HSD is the Honestly Significant Difference
  • q is the critical value from the Studentized Range Distribution table
  • MSW is the Mean Square Within (error variance)
  • n is the total number of observations
  • a is the number of groups being compared

To calculate the HSD, multiply the critical value (q) by the square root of the product of the Mean Square Within (MSW) divided by the total number of observations (n) and the reciprocal of the number of groups being compared (a).

What is a Hsd (Honestly Significant Difference)?

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.

How to Calculate Hsd (Honestly Significant Difference)?

The following steps outline how to calculate the Honestly Significant Difference (HSD).

  1. First, determine the mean difference between the groups.
  2. Next, calculate the standard deviation within each group.
  3. Next, determine the number of observations in each group.
  4. Next, calculate the critical value for the desired level of significance (alpha).
  5. Finally, calculate the HSD using the formula: HSD = critical value * (standard deviation / square root of the number of observations).
  6. After inserting the variables and calculating the result, check your answer with the calculator above.

Example Problem:

Use the following variables as an example problem to test your knowledge.

Mean difference = 5

Standard deviation = 2

Number of observations = 20

Desired level of significance (alpha) = 0.05