Testing Differences between p and π (3 of 4)

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The degrees of freedom for chi square is equal to the number of categories minus one. For this section in which there are always just two categories (success and failure for the present example), the degrees of freedom is always one. A chi square table can be used to find that the two-tailed probability value for a chi square of 5.29 with one degree of freedom is 0.0214.

At the beginning of this section it was stated that the chi square test for proportions was equivalent to the one based on the normal distribution. It turns out that chi square will always equal z². For the present example, the value of z was 2.3 and the value of chi square was 5.29. Note that 2.3² = 5.29. The probability values for a z of 2.3 and a chi square of 5.29 are identical (p = 0.0214).

Reporting Results
These results could be reported as follows:

The proportion of subjects choosing the original formulation (0.62) was significantly greater than 0.50, χ²(1, N = 100) = 5.29, p = 0.021. Apparently at least some people are able to distinguish between the original formulation and the new formulation.

The symbol "(1, N = 100)" means that the chi square is based on 1 df and that the total number of subjects is 100.