Goodness-of-fit test

Definition

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.

5 Must Know Facts For Your Next Test

1. A common goodness-of-fit test is the Chi-Square ($\chi^2$) test.
2. The null hypothesis ($H_0$) typically states that there is no significant difference between observed and expected frequencies.
3. Degrees of freedom for the Chi-Square goodness-of-fit test are calculated as $df = k - 1$, where $k$ is the number of categories.
4. 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.
5. 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?

Related terms

Chi-Square Statistic: A measure used in statistics to assess how much observed counts deviate from expected counts based on categorical data.

Null Hypothesis: A general statement or default position that there is no relationship between two measured phenomena or no association among groups.

P-Value: The probability of obtaining results at least as extreme as the observed results, assuming that the null hypothesis is true.