Goodness of Fit

These work on the principle of distribution shape rather than on actual series.
To compare overall patterns you need to put the series into a frequency form.
We use the frequencies of the scores rather than the actual scores.
There are several tests based on the distribution of statistics and all of these fall under the term Chi-Square measure of association or Tests of Association.

These tests include the following:

  • Simple Chi-Square

  • One Sample Chi-Square

  • Complex Chi-Square

In tests of goodness of fit, the categories into which the frequencies of scores fall are called cells.
The cells contain counted items
There are a few rules for Ch-square measure of association tests:
1 - items in cells must be independent.
2 - they cannot appear more than once
3 - each item must be an isolated event
4 - the number of items appearing in the "expected" category must be at least 5 (although some tests don't insist on this)
5 - the tests must be carried out on the actual numbers of items which appear in the cells (not derived proportions or percentages)

CHI Square Test - this is a test that can be used to determine if two groups of numbers have come from the same population
Instead of using the actual numbers this test uses the distribution of the numbers
This measures the goodness of fit

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