How to Find Chi Square

The Chi Square test can be used to test whether observed results follow an expected pattern.

The Chi Square test is one of the most important and commonly used test in statistics. The Chi Square test is used to find how close a series of observations follow the observations that are expected, either from previous observations or from what would be expected by chance. The Chi Square test is generally used to test whether a hypothesis is true within a certain allowable error bound. Finding the Chi Square test statistic is possible in a few short steps.

Instructions

1. Collect data for your experiment or statistical test. As an example, assume you have measured three data points: 8, 8 and 14, where the expected data points are 10, 10 and 10.

2. Find the difference between the observed data point and the expected data point for each data point. In the example above, there are three data points for this calculation: 8 - 10, 8 - 10 and 14 - 10. These produce -2, -2 and 4.

3. Square the difference between the observed and expected data points (that is, multiply the numbers by themselves). Doing this for the data points -2, -2 and 4 renders 4, 4 and 16.

4. Divide the square of the difference between the observed and expected data points by the expected data points of that particular measurement. For example, you would divide the number 4 by the expected measurement of that sample, which was 10. This produces 0.4, 0.4 and 1.6 for each data point. Call these numbers A, B and C.

5. Find the sum of the numbers from the previous step. In the example used here, summing the numbers A, B and C together equals 2.4. This is the Chi Square statistic.

Tips & Warnings

• If there are a large number of data points in your sample, you may want to consider using a spreadsheet or calculator to make the Chi Square calculation easier.

References

• Engineering Statistics Handbook: Chi-Square Goodness-of-Fit Test
• Oklahoma State University: Chi Square