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Determine Equality of Variance for two groups
These tutorials briefly explain the use and interpretation of standard statistical analysis techniques. The examples include how-to instructions for Excel. Although there are different version of Excel in use, these should work about the same for most recent versions. They also assume that you have installed the Excel Analysis Pak which is free and comes with Excel (Go to Tools, Addins... if it is not already installed in your version of Excel.)
See www.stattutorials.com/EXCELDATA for files mentioned in this tutorial, © TexaSoft, 2008
Equality of Variance using Excel
In several statistical analyses, in particular an independent group t-test, and assumption is that the groups have equal variances. This example illustrates how you can test that assumption.
The hypotheses for this test are
Ho: σ1 = σ2 (null hypothesis, variances are equal)
Ho: σ1 ≠ σ2 (alternative hypothesis, variances are not equal)
For example, suppose we are interested in comparing SCORES across GROUPS, where there are two groups. The purpose is to determine if the mean SCORE on a test is different for the two groups tested (i.e., control and treatment groups). The example data is shown here:
Group
Scores
1
20
1
23
1
32
1
24
1
25
1
28
1
27.5
2
25
2
46
2
56
2
45
2
46
2
51
2
34
2
47.5
In this example, the GROUP variable contains two group indicators, group "1" or "2", indicating which group each subject was in.
To decide if the variances are equal in both groups, (which can determine the type of t-test to perform) you can perform a statistical test to determine equality.
To do a statistical test to determine equality of variance, follow these instructions. (The test for equality of variances is an F-test.)
- In Excel, select Tools/ Data Analysis / F-Test Two Sample for Variance.
- In the F-Test Two Sample for Variance dialog box: For the Input Range for Variable 1, highlight the seven values of Score in group 1 (values from 20 to 27.5). For the input range for Variable 2, highlight the eight values of Score in group 2 (values from 25 to 47.5). Leave the other items at their default selections. This dialog box is shown below. Click OK.
The following results are produced by Excel:
F-Test Two-Sample for Variances
Variable 1
Variable 2
Mean
25.64285714
43.8125
Variance
15.22619048
96.42410714
Observations
7
8
df
6
7
F
0.157908545
P(F<=f) one-tail
0.019378053
F Critical one-tail
0.23771837
Notice the highlighted probability p=0.01937. This is a one-tail p-value associated with the test for equality of variance. Generally, if this value is less than 0.05 you assume that the variances are NOT equal.
How to use this information when doing an independent group t-test:
- If the variances are assumed to NOT be equal, proceed with the t-test that assumes non-equal variances.
- If the variances are assumed to be equal, proceed with the t-test that assumes equal variances.
End of tutorial
See http://www.stattutorials.com/EXCEL
For Excel data files click here
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