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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

                         

  1. What is the critical H value for the data from the second "Acitivites to Probe Further" exercise for Chapter 14 in the textbook (page 379)?___________________

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:

wpe2.jpg (3706 bytes)

 

 

 

 

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?