What are the two requirements that must be satisfied to perform a goodness-of-fit test?

Verified step by step guidance

1. Understand that a goodness-of-fit test is used to determine if observed categorical data matches an expected distribution.
2. The first requirement is that the data must be in the form of counts or frequencies for each category, not percentages or means.
3. The second requirement is that the expected frequency for each category should be sufficiently large, typically at least 5, to ensure the validity of the chi-square approximation.
4. Verify that the observations are independent of each other, meaning the occurrence of one observation does not affect another.
5. Confirm that the categories are mutually exclusive and collectively exhaustive, so each observation fits into exactly one category.

Key Concepts

Goodness-of-Fit Test

A goodness-of-fit test evaluates whether observed categorical data match an expected distribution. It compares observed frequencies to expected frequencies under a specific hypothesis, typically using the chi-square statistic to determine if deviations are due to chance.

Expected Frequency Requirement

For a goodness-of-fit test to be valid, each expected frequency should be sufficiently large, usually at least 5. This ensures the chi-square approximation to the sampling distribution is accurate, allowing reliable inference from the test results.

Independence of Observations

The observations must be independent, meaning the outcome of one observation does not influence another. This assumption is crucial because dependence can distort the test statistic and lead to incorrect conclusions about the fit.