Let's perform a one-way ANOVA: Researchers want to test a new anti-anxiety medication. They split participants into three conditions (0mg, 50mg, and 100mg), then ask them to rate their anxiety level on a scale of 1-10. Are there any differences between the three conditions using alpha = 0.05?

Steps for One-Way ANOVA

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

2. State Alpha

Alpha = 0.05

3. Calculate Degrees of Freedom

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

4. State Decision Rule

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

We now head to the F-table and look up the critical value using (2, 18) and alpha = 0.05. This results in a critical value of 3.5546, so our decision rule is:

If F is greater than 3.5546, reject the null hypothesis.

5. Calculate Test Statistic

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

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

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

And finally, we can calculate our F:

6. State Results

F = 86.56

Result: Reject the null hypothesis.

7. State Conclusion

The three conditions differed significantly on anxiety level, F(2, 18) = 86.56, p < 0.05.