The Pearson chi-square statistic (χ^{2}) involves the squared difference between the observed and the expected frequencies.
The likelihood-ratio chi-square statistic (G^{2}) is based on the ratio of the observed to the expected frequencies.
Use the chi-square statistics to test whether the variables are associated.
In these results, both chi-square statistics are very similar. Use the p-values to evaluate the significance of the chi-square statistics.
Chi-Square | DF | P-Value | |
---|---|---|---|
Pearson | 11.788 | 4 | 0.019 |
Likelihood Ratio | 11.816 | 4 | 0.019 |
When the expected counts are small, your results may be misleading. For more information, see the Data considerations for Cross Tabulation and Chi-Square.
The degrees of freedom (DF) is the number of independent pieces of information on a statistic. The degrees of freedom for a table is (number of rows – 1), multiplied by (number of columns – 1).
Minitab uses the degrees of freedom to determine the p-value associated with the test statistic.
In these results, the degrees of freedom (DF) is 4.
Chi-Square | DF | P-Value | |
---|---|---|---|
Pearson | 11.788 | 4 | 0.019 |
Likelihood Ratio | 11.816 | 4 | 0.019 |
The p-value is a probability that measures the evidence against the null hypothesis. Lower probabilities provide stronger evidence against the null hypothesis.
Use the p-value to determine whether to reject or fail to reject the null hypothesis, which states that the variables are independent.
Minitab uses the chi-square statistic to determine the p-value.
Minitab does not display the p-value when any expected count is less than 1 because the results can be invalid.
In these results, the p-value is 0.019. Because the p-value is less than α, you reject the null hypothesis. You can conclude that the variables are associated.
Chi-Square | DF | P-Value | |
---|---|---|---|
Pearson | 11.788 | 4 | 0.019 |
Likelihood Ratio | 11.816 | 4 | 0.019 |