Goodness-of-fit test

Definition

A goodness-of-fit test determines if a sample data matches a population with a specific distribution. It assesses the discrepancy between observed and expected frequencies.

5 Must Know Facts For Your Next Test

1. It is typically used with categorical data.
2. The most common goodness-of-fit test is the Chi-Square test.
3. The null hypothesis states that there is no difference between observed and expected frequencies.
4. The test statistic for the Chi-Square goodness-of-fit test is calculated as $\sum \frac{(O_i - E_i)^2}{E_i}$, where $O_i$ are the observed frequencies and $E_i$ are the expected frequencies.
5. A significant result indicates that the observed data does not fit the expected distribution.

Review Questions

• What does the null hypothesis state in a goodness-of-fit test?
• How is the test statistic for a Chi-Square goodness-of-fit test calculated?
• What type of data is typically analyzed using a goodness-of-fit test?

Related terms

Chi-Square Distribution: A probability distribution used in tests of independence and goodness-of-fit for categorical data.

Null Hypothesis: A statement that there is no effect or no difference, often denoted as $H_0$.

Expected Frequency: The frequency of occurrences predicted by a theoretical model, assuming the null hypothesis is true.