2x2 Tables - Quick Tab

The Quick tab of the 2 x 2 Tables dialog box contains the options described here.

Frequencies. Enter the frequencies for the 2 x 2 table in the four boxes on the Quick tab. The four boxes appear in the same "shape" as the 2 x 2 table. That is, put the frequency for the first cell in the table (Row One, Column One) in the first box. The frequency for Row One, Column Two would go in the box adjacent to the first box.

Summary: 2X2 Table. Click the Summary: 2x2 Table button after you enter the frequencies. In addition to the standard Pearson Chi-square statistic and the corrected Chi-square statistic (V-square), Yates corrected Chi-square, Phi-square, Fisher exact test, and McNemar Chi-square test will be computed:

Corrected Chi-square (V-square). This statistic has a sample-size correction applied to the Chi-square statistic. It is asymptotically equivalent to the Pearson Chi-square statistic. However, for small sample sizes, it is more conservative than the Pearson Chi-square for small sample sizes. The V-square statistic is calculated as follows:

Where nij is the frequency in the ijth cell of the 2x2 table. V2 follows a chi-square distribution with 1 degree of freedom (Rhoades & Overall, 1982).

Yates corrected Chi-square. The approximation of the Chi-square statistic in small 2 x 2 tables can be improved by reducing the absolute value of differences between expected and observed frequencies by 0.5 before squaring (Yates' correction). This correction, which makes the estimation more conservative, is usually applied when the table contains only small observed frequencies, so that some expected frequencies become less than 10 (for further discussion of this correction, see Conover, 1974; Everitt, 1977; Hays, 1988; Kendall & Stuart, 1979; and Mantel, 1974).

Phi-square. The Phi-square is a measure of correlation between the two categorical variables in the table.

Fisher exact test. Given the marginal frequencies in the table, and assuming that in the population the two factors in the table are not related, how likely is it to obtain cell frequencies as uneven or worse than the ones that were observed? For small n, this probability can be computed exactly by counting all possible tables that can be constructed based on the marginal frequencies. This is the underlying rationale for the Fisher exact test. It computes the exact probability under the null hypothesis of obtaining the current distribution of frequencies across cells, or one that is more uneven.

McNemar Chi-square (A/D, B/C). This test is applicable in situations where the frequencies in the 2 x 2 table represent dependent samples. For example, in a before-after design study, we may count the number of students who fail a test of minimal math skills at the beginning of the semester and at the end of the semester. Two Chi-square values are reported: A/D and B/C. The Chi-square A/D tests the hypothesis that the frequencies in cells A and D (upper left, lower right) are identical. The Chi-square B/C tests the hypothesis that the frequencies in cells B and C (upper right, lower left) are identical.