Goodness-of-Fit Test

The goodness-of-fit test establishes whether an observed frequency distribution mirrors a claimed distribution.

Consider the dataset of people visiting the gym on weekdays. One can perform a goodness-of-fit test to determine whether the observed client attendance agrees with the expected frequency of client attendance.

To perform a goodness-of-fit test, the dataset values must be randomly selected and have a frequency value for each category, with the expected frequency of each category being at least 5.

The chi-square test statistic for the goodness-of-fit test can be computed using the shown formula. Here, O and E represent the observed and expected attendances, k is the number of weekdays, and n is the number of sample values or attendance counts recorded. The number of degrees of freedom is k minus one.

Goodness-of-fit hypothesis tests are always right-tailed, implying that the critical region and critical values are located at the extreme right of the distribution curve.

The critical values and P-values help determine if there is a good fit between the observed and expected values.