# Chi Square Analysis Example in Six Sigma

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Use this Chi Square Analysis Template to do the following:

- Chi Square Test for Association is a (non-parametric, therefore can be used for nominal data) test of statistical significance widely used bivariate tabular association analysis. Typically, the hypothesis is whether or not two different populations are different enough in some characteristic or aspect of their behavior based on two random samples. This test procedure is also known as the Pearson chi-square test.
- Chi Square Goodness-of-fit Test is used to test if an observed distribution conforms to any particular distribution. Calculation of this goodness of fit test is by comparison of observed data with data expected based on the particular distribution.

In Six Sigma, a Chi Squared test is used to determine if there is a statistically significant difference in the proportions for different groups. To accomplish this, it breaks all outcomes into groups.

The test looks for differences in proportions by doing the following:

- It starts by determining how many defects, for example, would be “expected” in each group involved.
- It does this by assuming that all groups have the same defect rate.
- The Chi Square Calculator then calculates the expected counts with what was actually observed.
- If the numbers are different by a large enough amount, Chi-Square determines that the groups do not have the same proportion.

Requirements for a Chi Square Test:

- Data is typically attribute (discrete). All data must be able to be categorized as being in some category or another.
- Expected cell counts should not be low (definitely not less than 1 and preferable not less than 5) as this could lead to a false positive indication that there is a difference when, in fact, none exists.