Stata presents chi-square statistics in several contexts, primarily related to:
1. Tests of Independence:
* Hypotheses:
* Null: The two categorical variables are independent.
* Alternative: The two categorical variables are dependent.
* Interpretation:
* Large p-value (> 0.05): We fail to reject the null hypothesis. There is not enough evidence to conclude that the variables are dependent.
* Small p-value (< 0.05): We reject the null hypothesis. There is enough evidence to suggest that the variables are dependent.
* Additional Information:
* Stata provides a Pearson chi-square statistic and its corresponding p-value.
* Stata also presents degrees of freedom (df), which helps determine the critical chi-square value for the test.
* You can also look at the expected frequencies and observed frequencies in the table to visually assess the relationship.
2. Goodness-of-Fit Tests:
* Hypotheses:
* Null: The observed frequencies follow a specified theoretical distribution.
* Alternative: The observed frequencies do not follow the specified theoretical distribution.
* Interpretation:
* Large p-value (> 0.05): We fail to reject the null hypothesis. The data does not provide enough evidence to conclude that the observed frequencies deviate from the specified distribution.
* Small p-value (< 0.05): We reject the null hypothesis. The data suggests that the observed frequencies do not follow the specified distribution.
* Additional Information:
* You need to specify the expected distribution (e.g., uniform, binomial, Poisson) when conducting the goodness-of-fit test.
* Stata provides the chi-square statistic and its corresponding p-value.
3. Other Tests:
* Stata also uses chi-square statistics in other contexts, such as testing the equality of proportions. The interpretation follows the same general principles as above.
Important Points:
* The chi-square test is sensitive to sample size. With large samples, even small deviations from independence can lead to a significant p-value.
* The chi-square test assumes that the expected frequencies are not too small (usually at least 5). If this assumption is violated, you might consider using Fisher's exact test instead.
* The p-value only tells you whether there is evidence of association between the variables. It does not tell you the strength or direction of the association.
Example:
Suppose you want to test the independence of gender and opinion on a certain policy. Stata outputs the following:
```
| Opinion
| Agree Disagree | Total
-------------+------------------------+-------
Gender | |
Male | 120 80 | 200
Female | 150 100 | 250
-------------+------------------------+-------
Total | 270 180 | 450
Pearson chi2(1) = 10.00 P = 0.0016
```
* Interpretation: The p-value is less than 0.05, suggesting that there is a statistically significant association between gender and opinion.
* Conclusion: We reject the null hypothesis of independence. There is evidence to suggest that gender and opinion are dependent.
Remember: Always consider the context of your research question and the limitations of the chi-square test when interpreting the results.