Track 10 · Comparing Groups and Categorical Data · Lesson 3 of 11
Chi-square goodness of fit
Test whether the counts of one categorical variable are consistent with a claimed distribution, including a fitted model whose parameters are estimated from the data.
A retail chain plans staffing on the assumption that 20% of baskets come from new customers, 50% from returning customers and 30% from loyalty-card members. A month of till data has arrived. Is the planning mix still credible, or have the shares moved?
The goodness-of-fit (GOF) test uses one categorical variable with categories. A hypothesis specifies the probability of each category, (summing to 1). We compare the observed counts with the counts that hypothesis predicts.
- : the population proportions are .
- : at least one proportion differs.
Included with a Formula Quest membership
It has 7 graded exercises with feedback, hints and worked solutions. After it you will be able to:
- Compute expected counts $N p_i$ and the goodness-of-fit statistic
- Choose df = k − 1 − (number of estimated parameters)
- Group sparse categories so expected counts are large enough
- Read a non-significant fit as “compatible with”, never as proof