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.

A value is significant if its distance from the mean exceeds the standard of error.

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.

This is a preview of Lesson 13. To access the full book, please purchase a hard copy or a digital version. If you opt for the digital version, you will receive a link via email within 1 business day.

Continue to Lesson 14, or select a lesson below.

Lesson 1: Introduction to Statistical Research Methods
Lesson 2: Visualizing Data
Lesson 3: Central Tendency
Lesson 4: Variability
Lesson 5: Standardizing
Lesson 6: Normal Distribution
Lesson 7: Sampling Distributions
Lesson 8: Estimation
Lesson 9: Hypothesis Testing
Lesson 10: t-Tests for Dependent Samples
Lesson 11: t-Tests for Independent Samples
Lesson 12: Intro to One-Way ANOVA
Lesson 13: One-Way ANOVA: Test significance of differences
Lesson 14: Correlation
Lesson 15: Linear Regression
Lesson 16: Chi-Squared Tests

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