Lesson 9 SPSS

1. Lesson 9SPSS How to conduct a One-Way ANOVA With Independent Samples

2. The Dataset Let’s use our example dataset from the Lesson 9 PowerPoints. In this dataset, we have two variables—grade and score. There are three levels of the treatment grade—3rd, 4th, and 5th. There are five scores in each grade.

3. The Set-Up • The first decision we have to make is whether we have an independent samples or a related samples experiment. Because there has been no matching (we didn’t pair up a 3rd grader with a similar 4th and 5th grader) and we haven’t repeatedly measured the same child as they progressed through the three grades, we need to do an independent measures F-test.

4. The Set-UP Do we want to use a one-tailed or a two-tailed test? UHHHHTT. Trick question. An ANOVA ONLY uses a one-tailed test to determine if the obtained F-statistic is greater than the critical F-value from the table. Let’s state our hypotheses: • Null hypothesis H0: m1 = m2 = m3. • Alternative hypothesis Ha: At least one mean is different.

5. Selecting the Analysis • From the SPSS menu bar, choose • Analyze • Compare means • One-Way ANOVA

6. Select the Variables • The dependent variable goes in the Dependent List box. In this case, we were measuring the variable Score. • The independent variable goes in the Factor box. Here, it’s the Grade level. Next, let’s click on Options and see what else we might want to include in our output.

7. Grouping Variable • Clicking on the Descriptive box will include a variety of descriptive statistics such as the means and standard deviations of each treatment. • The Homogeneity of variance test will conduct a Levene’s test. • Then, click on the Continue button.

8. More to Do • After having picked our options, we are returned to our One-Way ANOVA window. • Since there are three treatment groups, if our F-test proves to be significant we will want to have a post hoc test performed.

9. Choosing Post Hoc Tests • SPSS offers many choices for post hoc tests. Let’s choose three.

10. Post Hoc Test Info • Here’s a little info on the post hoc tests we’ve chosen. • You learned how to do the Tukey’s test by hand. This is the most liberal of the three tests picked. That means that smaller differences between treatment means will be significant than in some other post hoc tests. • The Bonferroni’s is a nice test. Not too liberal; not too conservative. And it takes into account the number of comparisons to be made. It can be used under a wide variety of circumstances. • The Scheffe’s test is the most conservative. It is possible that a Scheffe’s post hoc will indicate no significant differences between pairs of means when the F-test was significant.

11. Ready, Set,… • Click on Continue to go back to the main ANOVA window.

12. Go! • Now we can click on OK to run the analyses.

13. The Output • The first part of the output gives us basic statistics about our three grades. Just as we saw in our hand calculations, the mean for the 3rd graders was 4, the mean for the 4th graders was 6, and the mean for the 5th graders was 8. • We also can see the standard deviation for each group. • Since one of the assumptions of an ANOVA is that the variances for the groups are about equal, we’ll need to do a test to be sure this is the case. • SPSS also gives us a 95% confidence interval for the mean. But we should use this only if we find a significant difference in the means.

14. The Output • And here’s the Levene’s test for equal variances. You might remember from the t-test that equal variances is an assumption of testing differences in means. • The null hypothesis says that the group variances are NOT significantly different from each other. • As you can see here, the significance on this test is .809, which is way bigger than .05, so we fail to reject the null hypothesis and conclude that the group variances are not significantly different. And that’s a GOOD thing!

15. The Output • And here are the results from our ANOVA. Notice that the source table looks exactly as it did when we calculated it by hand. • Notice that there are 2 degrees of freedom Between groups and 12 Within groups. We can see that SPSS has calculated both the Sum of Squares and the Mean Squares. • Our obtained F-value is 5.714. Wow, that’s exactly what we got when we did it by hand! SPSS gives us a specific significance level of .018, which is smaller than .05. Therefore, we can immediately tell we have a significant F-test without having to look anything up in the table.

16. The Output • Now that we know there are significant differences between at least one pair of means, we look at the post hoc table to see where those differences are. Let’s start out looking at the results for the Tukey’s. • Look at the top tier of the table where it says Tukey HSD 3 4. The value of • -2.000 tells you that the means for the 3rd graders and the 4th graders were different by 2.000 (6 – 4). The significance level there is .249, which is not < .05 so these two means are not significantly different.

17. The Output But the difference between 3rd graders and 5th graders was -4.000. See the *? That tells you that SPSS has identified this as a significant difference. The specific significance level here is .014. This is the only significant difference found between pairs of treatment group means. Therefore, the 3rd graders scored significantly lower than the 5th graders, but the 3rd graders were not significantly different from the 4th graders and the 4th graders were not significantly different from the 5th graders.

18. The Output Next, let’s look at the Bonferroni’s. The test results are essentially the same. That is, 3rd graders are significantly different from 5th graders. But notice that the significance level is slightly higher than in the Tukey’s. This is the sign that the Bonferroni’s is a slightly more conservative test than the Tukey’s. Mean’s have to be just a little bit more different to reach the same significance level in a Bonferroni’s than in a Tukeys.

19. The Output • Finally, let’s look at the Scheffe’s. Again, the test results are essentially the same. That is, 3rd graders are significantly different from 5th graders. • But once again, notice that the significance level is slightly higher in the Scheffe’s than in the Bonferroni’s, and a bit higher than in theTukey’s. As I said in the previous slide, is the sign that the Scheffe’s is a slightly more conservative test than the Bonferroni’s, and therefore, a bit more considerative than the Tukey’s.