CHI-SQUARE (I) TEST

The chi-square (I) test (also known as "goodness-of-fit" test) is used to determine whether a significant difference exists between the expected frequencies and the observed frequencies in one or more categories. Do the number of individuals or objects that fall in each category differ significantly from the number you would expect? Is this difference between the expected and observed due to sampling error, or is it a real difference? The requirements for the chi-square (I) test are:

1. Nominal data

2. One- group test

3. One or more categories

4. Independent observations

5. Adequate sample size

   1. The expected frequencies should be sufficiently large for two categories five or larger.

   2. When more than two categories are present, no more than 20% should be smaller than five.

6. Simple random sample

7. Data in frequency form

8. All observations must be used

9. Two-tailed test only (This test cannot be used as a one-tailed test. If directional testing is necessary, you should use a different test.)

The chi-square formula is:

where O = observed frequencies in each category, E = expected frequencies for the corresponding observed frequencies, & pound ; = sum of, k = number of categories, and df = degrees of freedom (number of categories minus one [k - 1]).