### DEFINITION of Goodness-Of-Fit

The goodness of fit test is a statistical hypothesis test to see how well sample data fit a distribution from a population with a normal distribution. In other words, it tells you if your sample data represents the data you would expect to find in the actual population.

### BREAKING DOWN Goodness-Of-Fit

Goodness-of-fit tests are often used in business decision making. In order to calculate a chi-square goodness-of-fit, it is necessary to first state the null hypothesis and the alternative hypothesis, choose a significance level (such as α = 0.5) and determine the critical value.

For example, a small community gym might be operating under the assumption that it has its highest attendance on Mondays, Tuesdays and Saturdays, average attendance on Wednesdays and Thursdays, and lowest attendance on Fridays and Sundays. Based on these assumptions, the gym employs a certain number of staff members each day to check in members, clean facilities, offer training services and teach classes.

However, the gym is not performing well financially and the owner wants to know if these attendance assumptions and staffing levels are correct. The owner decides to count the number of gym attendees each day for six weeks. He can then compare the gym's assumed attendance with its observed attendance using a chi-square goodness-of-fit test for example. With the new data, he can determine how to best manage the gym and improve profitability.