A chi-square goodness-of-fit test is used to test the hypothesis that an observed frequency distribution fits (or conforms to) some claimed distribution.

This test compares the observed frequencies of a categorical dataset with the expected frequencies under a specific theoretical distribution, such as a uniform distribution or a normal distribution. The test uses the following formula:

$\chi^2 = \sum \frac{(O_i - E_i)^2}{E_i}$

Where:

• $O_i$: Observed frequency for the $i$-th category.
• $E_i$: Expected frequency for the $i$-th category.

The resulting chi-square statistic is then compared to a critical value from the chi-square distribution with $k-1$ degrees of freedom ($k$ is the number of categories).

Would you like further explanation or help setting up such a test?

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Related Questions:

1. What are the assumptions required for the chi-square goodness-of-fit test?
2. How is the expected frequency calculated for a given distribution?
3. How do you interpret the p-value obtained from a chi-square test?
4. What are some common applications of the chi-square goodness-of-fit test in real-world scenarios?
5. How does the chi-square test differ from a t-test or ANOVA?

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Tip:

For a chi-square test, ensure all expected frequencies are sufficiently large (typically $\geq 5$) to ensure the validity of the test.