Let's perform a repeated-measures ANOVA: Researchers want to test a new anti-anxiety medication. They measure the anxiety of 7 participants three times: once before taking the medication, once one week after taking the medication, and once two weeks after taking the medication. Anxiety is rated on a scale of 1-10, with 10 being "high anxiety" and 1 being "low anxiety". Are there any differences between the three conditions using alpha = 0.05?

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Steps for Repeated-Measures ANOVA |
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1. Define Null and Alternative Hypotheses 2. State Alpha 3. Calculate Degrees of Freedom 4. State Decision Rule 5. Calculate Test Statistic 6. State Results 7. State Conclusion |

Let's begin.

1. Define Null and Alternative Hypotheses

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2. State Alpha

Alpha = 0.05

3. Calculate Degrees of Freedom

Now we calculate the degrees of freedom using N = 21, s = 7, and a = 3. You should already recognize N. "a" refers to the number of groups ("levels") you're dealing with, and "s" refers to the number of subjects you have in each condition:

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4. State Decision Rule

To look up the critical value, we need to use two different degrees of freedom.

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We now head to the F-table and look up the critical value using (2, 12) and alpha = 0.05. This results in a critical value of 3.8853, so our decision rule is:

If F is greater than 3.8853, reject the null hypothesis.

5. Calculate Test Statistic

To calculate the test statistic, we first need to find three of five values:

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All the values we've found so far can be organized in an ANOVA table:

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We can use the three values we've already found to fill in the two unknown values:

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Now we find each MS by diving each SS by their respective df:

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And finally, we can calculate our F:

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6. State Results

F = 224.27

Result: Reject the null hypothesis.

7. State Conclusion

The three conditions differed significantly on anxiety level, F(2, 12) = 224.27, p < 0.05.