MathBench > Statistical Tests

Chi-squared Tests

Summary of chi-squared

Here's a summary of the steps needed to do a chi-squared goodness of fit test:

General Steps

In the Dilbert example...

1. Decide on a null hypothesis -- a "model" that the data should fit. Dilbert's null hypothesis was that the sick days were randomly distributed.
2. Note your "expected" and "observed" values. Since 40% of weekdays fall on Monday or Friday, the same should be true of sick days -- or 40 out of 100. The observed value was 42 out of 100.
3. Find the chi-squared statistic [add up (o-e)2 / e ]. We got 0.167.
4. Look up the chi-squared critical value based on your α value and degrees of freedom. With α=0.05 and df=1, chi-squared critical value = 3.84.
5. Determine whether chi-squared statistic < chi-squared critical value-- if so, we say the model fits the data well, so we do not reject the null hypothesis. Chi-squared statistic < chi-squared critical value, so the deviations are small and the data fit the null model of random sick days.