Lesson 13: One-Way ANOVA: Test significance of differences

Now that you know what the F-statistic is and how to find it, we can do a “multiple-comparison test” to determine which populations are significantly different. The most common multiple-comparison test involves computing Tukey’s HSD (honestly significant difference). If the difference between two means are greater than Tukey’s HSD, they are considered honestly significantly different. (Yes, kinda silly.)

Tukey’s HSD is just like the margin of error, which if you remember is the critical value (z* or t*) times the standard error (i.e., the number of standard errors from the mean). Recall that the margin of error is half the length of the confidence interval.

z-test: margin of error = (z*)σ/√n

t-test: margin of error = (t*)s/√n

With CIs, if the distance between a value and the mean is greater than the margin of error, the difference is considered statistically significant. With this multiple-comparison test for ANOVA, if the distance between any two means exceeds Tukey’s HSD, the difference is considered statistically significant.

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