Statistics – Exact Test on small or skewed data

 In Statistics & methods

Hi, sometimes it happens that you have too small or too skewed data to be allowed doing traditional statistical tests. For example chi2-test has some rules that has to be fulfilled (I will show you), otherwise it’s many times not allowed to use the test.

In such case “Exact Test” is possible to use, it’s an extra module but it will give you extra subcommands within chi2 and the nonparametric tests.

Look at this crosstable, where I want to test if male and female differs in the distribution of job categories:

You use Chi2-test for testing the frequencies, and the command is under the menu: Analyze – Descriptive Statistics – Crosstabs . Then click on the button: “Statistics” and then “Chi-Square”:

But if I have a look on the chi2-test result, I have got some footnotes under the table that indicate that I have too small expected frequencies. If more than 20% of the cells has expected frequencies under 5 then it will be a problem. Here I have 40%, so I would rather use Exact test. Another rule that has to be fulfilled is that the minimum expected  Count should not be under 1 (here it’s 2.25 so that’s ok):

We can see in the cross table that it’s not so many people in my study, and the distribution is skewed in some places (very few  people in some categories) so that’s why this problem come up:

So if I go back to the chi2-test dialog box you can see that I have an extra button (subcommand) that I click on. You cannot see this button if you haven’t the add on module “Exact Test”:

I then choose the following:

Now I got this result instead, where I changed the decimal-format of the p-value, so you can see the exakt value from both results:   

The left p-value (significance value) you find in the column: “Asymptotig Significance” is the one I got when I made the traditional chi2-test that was not allowed to use. The right p-value (“Exact Sig”) is the exakt p-value I am allowed to report. I can see that the value is far under 0.05. So the conclusion is that it’s 95% sure that male and female differ in job category distribution (p<0.05, Exact chi2 test).

Gunilla Rudander


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