AS/A2 Stats 1 Stats 2

S3 Topic 4: Goodness of fit and contingency tables
Contingency tables 1
Input observed frequencies into the white cells. You may not need to use all 10 conditions and 10 groups - choose some subset of rows and columns in which to enter your data. For example, if your data table is (2 x 3), then you may choose to enter your data in the 6 cells in the upper left portion of the data table, defined by the first two Conditions and the first three Groups. You can choose any subset of rows and columns for your data. You can also opt to leave cells corresponding to observed frequencies of zero blank. Non-integer observed frequencies are allowed, although it is difficult to imagine how one would obtain these in actual research. In the specific case of 2 x 2 tables, this tool also yields a chi-square incorporating Yates' correction for continuity. This correction is often employed to improve the accuracy of the null-condition sampling distribution of chi-square.

Observed Gp 1 Gp 2 Gp 3 Gp 4 Gp 5 Gp 6 Gp 7 Gp 8 Gp 9 Gp 10 Cond. 1: Cond. 2: Cond. 3: Cond. 4: Cond. 5: Cond. 6: Cond. 7: Cond. 8: Cond. 9: Cond. 10: Output: Chi-square: degrees of freedom: p-value: Yates' chi-square: Status: Yates' p-value:

Summary The degrees of freedom in an n x m contingency table is (n-1)(m-1) Use of the chi-square tests is inappropriate if any expected frequency is below 1 or if the expected frequency is less than 5 in more than 20% of your cells. The status cell at the bottom of the table will let you know if there is a problem. In the 2 x 2 case of the chi-square test of independence, expected frequencies less than 5 are usually considered acceptable if Yates' correction is employed. If you have a graphic calculator, follow this link to find out more about using it to do a Contingency table test: graphic calculator from Practical Stats non-parametrics