Hartley's H Critical Values for Alpha of .05
Number of Groups Contrasted Variance
2 | 3 | 4 | 5 | 6 | 7 | 8 | ||
Number | 3 | 39 | 87.5 | 142 | 202 | 266 | 333 | 403 |
of | 4 | 15.4 | 27.8 | 39.2 | 50.7 | 62 | 72.9 | 83.5 |
Events | 5 | 9.6 | 15.5 | 20.6 | 25.2 | 29.5 | 33.6 | 37.5 |
6 | 7.15 | 10.8 | 13.7 | 16.3 | 18.7 | 20.8 | 22.9 | |
7 | 5.82 | 8.32 | 10.4 | 12.1 | 13.7 | 15 | 16.3 | |
8 | 4.99 | 6.94 | 8.44 | 9.7 | 10.8 | 11.8 | 12.7 | |
9 | 4.43 | 6 | 7.18 | 8.12 | 9.03 | 9.78 | 10.5 | |
10 | 4.03 | 5.34 | 6.31 | 7.11 | 7.8 | 8.41 | 8.95 | |
11 | 3.72 | 4.85 | 5.67 | 6.34 | 6.92 | 7.42 | 7.87 | |
12 | 3.5 | 4.51 | 5.23 | 5.82 | 6.32 | 6.76 | 7.15 | |
13 | 3.28 | 4.16 | 4.79 | 5.3 | 5.72 | 6.09 | 6.42 | |
16 | 2.86 | 3.54 | 4.01 | 4.37 | 4.68 | 4.95 | 5.19 | |
21 | 2.46 | 2.95 | 3.29 | 3.54 | 3.76 | 3.94 | 4.1 | |
31 | 2.07 | 2.4 | 2.61 | 2.78 | 2.91 | 3.02 | 3.12 | |
61 | 1 .67 | 1.85 | 1.96 | 2.04 | 2.11 | 2.17 | 2.22 | |
infinity | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
To use the table to find the critical value required to reject the assumption of equal (homogeneous) sample variances, look at how many groups are compared. In this case, there are three groups. Thus, look at the third column on the chart to find the appropriate sets of values. To find the appropriate row, look at the number of events within each group. In this case there are five events in each group (corresponding to five viewing days). Thus, go to the row corresponding to five. The intersection of these columns and rows reveals the critical value. If the test statistic is more than this amount, we will reject the null hypothesis of equal variances among groups.
The data for analysis are found on the Web page Inferential Statistics II.
b. What is the observed H statistic?____________________
The formula takes the largest variance and divides it by the smallest variance. Specifically, to compute the Hartley's H test, one takes the largest variance and divides by the smallest variance, such as this formula shows:
In our case, you need to compute the sample variances (remember the formula from page 308 in the textbook) for the three sample groups.
c. Are the variances among these groups equal or unequal?___________
d. If the variances were unequal, what would be the
implications for
your research?