ABSTRACT

The χ2 for comparing the 63:37 ratio above is calculated in Table 1. The expected numbers are calculated by multiplying the total by the predicted frequency (e.g. 100 × 1/4 white). The deviation, or difference, between the observed and expected number is squared to remove negative numbers, and divided by the expected value to undo the squaring and standardize the numbers. This is repeated for each class (the red class and the white class in this example) and the values are added (summed) to give the overall value of χ2. Notice that the value of χ2 increases when the deviations from expected are large, so large values of χ2 lead us to reject the null hypothesis. The data does not fit if χ2 is large. A perfect fit gives a χ2 of zero. We are not interested in identifying unusually close fits, so we use a one tailed test which tells us the probability of getting a large deviation from the expected. The example (Table 1) gives a χ2 value of 7.68. What does this mean? We need another piece of information before we can look this up in statistical tables. We need to know the degrees of freedom.