PSY 429 Experimental Psychology

Class Exercise #6

 

Homogeneity of Variance Test (Hartley's F_max Test)

One-Way Independent-Measures Analysis of Variance

 

1. What are the assumptions which should be met if you want to use an independent-measures ANOVA?

 1) Samples are independent (between-subject design) and randomly selected from their respective populations.

2) Scores in each population are normally distributed.

3) Scores in each population have homogeneous (equal) variances.

2. What would a relatively large value for F-max indicate?

 That the variances among the groups differs probably more than would be expected by chance. Therefore, there would be a violation of one of the assumptions behind the ANOVA if you were to go ahead and use ANOVA to analyze the data without correcting for unequal variances.

3. Is there a remedy for a large value for F-max?

Scores might have to be transformed before an ANOVA could be used in order to reduce the differences in variances among the groups.

4. If you compare the F-max value that you computed for the sample data with the critical value found in the F-max table and if the F-max you computed is larger than the critical value (in table), what would you conclude?

 I would conclude that the population variances are not homogeneous and differ more than what would be expected from chance alone.

5. If two independent samples each having n = 10 and the sample variances are 12.34 and 9.15 for the two samples, calculate a homogeneity of variance test and determine whether the variances are equal. (Use Hartley's F-max test.)

 F-max = maximum s² / minimum s²

F-max = 12.34 / 9.15 = 1.35

The critical value of F-max at an alpha of .05 is 4.03 and at .01 is 6.54. We conclude that the variances are homogeneous and the assumption has not been violated.

6. Do weather conditions affect people's moods? To examine this question, a researcher randomly selected three samples of college students and administered a mood inventory questionnaire to each student. One group was tested on a dreary, overcast, and drizzly day. The second group was tested during a violent thunderstorm, and the third group was tested on a bright sunny day. Does the following data indicate that weather has an effect on mood?

a. Conduct an F-max homogeneity of variance test to determine whether an ANOVA is appropriate.

b. If the homogeneity of variance test indicates an ANOVA is appropriate, test if the weather has an effect on mood using the .05 level of significance.

c. Put the results into an ANOVA summary table.

Source	df	SS	MS	F	Significance
treatment	2	24.07	12.035	1.895	p > .05
Error	27	171.40	6.35
Total	29	195.47

 

d. Describe the results of this experiment, including any descriptive statistics (mean, standard deviation) which would help the reader to understand the results.

 A one-way independent measures analysis of variance was conducted to determine if the weather affects mood. Scores on a mood inventory were tested for three groups of college students in three different weather conditions: dreary, stormy, and bright. Although the mood scores for those subjects tested in 'bright' conditions was somewhat higher (M = 10.7) than those subjects tested in dreary conditions (M = 8.6), the analysis of variance indicated no significant difference among the three weather conditions, F(2, 27) = 1.895, p > .05.

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