| What Is A Chi-Square Test? | | | | different groups. To accomplish this, it breaks all |
| - The probability density curve of a chi-square | | | | outcomes into groups. |
| distribution is asymmetric curve stretching over the | | | | What the Chi-Squared Test does: |
| positive side of the line and having a long right tail. | | | | - It starts by determining how many defects, for |
| - The form of the curve depends on the value of | | | | example, would be "expected" in each group involved. |
| the degrees of freedom. | | | | - It does this by assuming that all groups have the |
| Types of Chi-Square Analysis: | | | | same defect rate (which Minitab approximates from |
| - Chi-square Test for Association is a | | | | the data provided). |
| (non-parametric, therefore can be used for nominal | | | | - Minitab then compares the expected counts with |
| data) test of statistical significance widely used | | | | what was actually observed. |
| bivariate tabular association analysis. | | | | - If the numbers are different by a large enough |
| - Typically, the hypothesis is whether or not two | | | | amount, Chi-Square determines that the groups do |
| different populations are different enough in some | | | | not have the same proportion. |
| characteristic or aspect of their behavior based on | | | | Chi-Square Requirements: |
| two random samples. | | | | - Data is typically attribute (discrete). At the very |
| - This test procedure is also known as the Pearson | | | | least, all data must be able to be categorized as |
| chi-square test. | | | | being in some category or another). |
| - Chi-square Goodness-of-fit Test is used to test if | | | | - Expected cell counts should not be low (definitely |
| an observed distribution conforms to any particular | | | | not less than 1 and preferable not less than 5) as this |
| distribution. Calculation of this goodness of fit test is | | | | could lead to a false positive indication that there is a |
| by comparison of observed data with data expected | | | | difference when, in fact, none exists. |
| based on the particular distribution. | | | | Chi-Square Hypotheses: |
| When to apply a Chi-Squared Test: | | | | - Ho: The null hypotheses (P-Value > 0.05) means the |
| - Chi-Squared test is used to determine if there is a | | | | populations have the same proportions. |
| statistically significant difference in the proportions for | | | | |