### 6.0.7. 2 x 2 Tables

Tests for 2 x 2 tables are grouped under the menu items Statistics 1 → Nonparametric Tests (1-2 Samples) → Unpaired Proportions and Paired Proportions. All these tests can also be performed in Contingency Table and Cross-Tabulation procedures (see 6.6.2.3. 2 x 2 Table Statistics).

The Variable Selection Dialogue for these procedures contains the following three data type options.

**1) Two Columns Contain Two Categories Each:** Choose
two columns from the Variables Available list
which contain only two distinct values. The program will not proceed with the
test if this requirement is not met. The selected columns may contain string or
numeric values.

A 2 x 2 table containing four cells (i.e. (1,1), (1,2), (2,1), (2,2)) is formed for each test.

i) For Paired Proportions, the two selected columns should have the same length. The number of cases falling within each cell of the table is counted by the program. The cell (1,1) contains the number of pairs where each member is the smaller of the two values in its own column and the cell (2,2) contains the number of pairs with larger values. In other words, Paired Proportions, forms a 2 x 2 table in a way similar to that in Cross-Tabulation.

ii) For the Unpaired Proportions procedure, the selected columns may have unequal lengths. The program will determine the number of cases in each cell separately for each column, such that the cells (1,1) and (2,1) contain the number of small and large values in the first column respectively, and (1,2) and (2,2) that of small and large values in the second column. Note that this is an entirely different way of forming a 2 x 2 table compared with Paired Proportions and Cross-Tabulation.

**2) Two Columns Contain Continuous Group Data**** (Enter Two Cut-Point****s): **As in the previous data option, two columns
containing string or numeric values can be selected. However, unlike the
previous option, these columns may contain any number of distinct values.

You will be asked to enter a cut-point for each column. These cut-points will separate each column into two groups. For each group, cases less than the cut-point (i.e. excluding it) will be considered as being in group 1 and all those greater than or equal to the cut-point (i.e. including it) will be considered as being in group 2. The string variables are separated according to their lexicographic ordering.

The method of counting frequencies for the Unpaired Proportions procedure is different from that in Paired Proportions and Cross-Tabulation, as explained above in (1).

**3) Cell Frequencies are Given: **Enter the four
elements of the table in row order; i.e. the first column of the first row, the
second column of the first row, the first column of the second row and the
second column of the second row.

i) For Paired Proportions, the cells of the table are entered in the order of (1,1), (1,2), (2,1), (2,2).

When the four frequency values for a 2 x 2 table are already available in the spreadsheet, you do not have to type them again into the Cell Frequencies are Given dialogue. Instead, you can use the Contingency Table procedure (see 6.6.2.3. 2 x 2 Table Statistics).

ii) For the Unpaired Proportions procedure, the cells contain the following frequencies:

(1,1) contains the number of small values in the first column

(1,2) contains the number of small values in the second column

(2,1) contains the number of large values in the first column

(2,2) contains the number of large values in the second column.