A goodness-of-fit test is a statistical hypothesis test used to determine if a sample data matches a population with a specific distribution. It assesses how well the observed frequencies fit the expected frequencies under the null hypothesis.
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A common goodness-of-fit test is the Chi-Square ($\chi^2$) test.
The null hypothesis ($H_0$) typically states that there is no significant difference between observed and expected frequencies.
Degrees of freedom for the Chi-Square goodness-of-fit test are calculated as $df = k - 1$, where $k$ is the number of categories.
The Chi-Square statistic formula is $\chi^2 = \sum \frac{(O_i - E_i)^2}{E_i}$, where $O_i$ are observed frequencies and $E_i$ are expected frequencies.
A high Chi-Square value indicates that the observed data does not fit the expected distribution well.
Review Questions
What does a goodness-of-fit test assess in statistical analysis?
How do you calculate degrees of freedom for a Chi-Square goodness-of-fit test?
What would a high Chi-Square statistic indicate about your sample data?