1. What Is Tukey's Q Statistic?

Tukey's Q statistic is used in post-hoc analysis following ANOVA to determine which specific group means are significantly different from each other. It's part of Tukey's Honest Significant Difference (HSD) test.

2. How Does the Calculator Work?

The calculator uses Tukey's Q formula:

Where:

• \( X_i, X_j \) — Means of the two groups being compared
• \( MSE \) — Mean square error from ANOVA
• \( n \) — Sample size per group (assuming equal group sizes)

Explanation: The Q statistic measures the standardized difference between two means, accounting for within-group variability.

3. Importance of Tukey's Q

Details: Tukey's Q is crucial for controlling family-wise error rate when making multiple comparisons after ANOVA. It helps identify which specific group differences are statistically significant.

4. Using the Calculator

Tips: Enter the two group means, the MSE from your ANOVA results, and the sample size per group. All values must be valid (MSE > 0, n ≥ 1).

5. Frequently Asked Questions (FAQ)

Q1: When should I use Tukey's test?
A: Use it when you want to compare all possible pairs of means after finding a significant ANOVA result, while controlling the overall Type I error rate.

Q2: What's the difference between Q and HSD?
A: Q is the test statistic, while HSD is the critical value. You compare Q to HSD to determine significance.

Q3: What if my group sizes are unequal?
A: For unequal group sizes, use the harmonic mean of the group sizes in place of n.

Q4: How is MSE obtained?
A: MSE is the within-group mean square from your ANOVA table (SS_error/df_error).

Q5: What's a typical critical Q value?
A: Critical values depend on the number of groups and degrees of freedom, and are found in Tukey's Q tables.