﻿ Bowker's Chi-Square Test of Symmetry

# Bowker's Chi-Square Test of Symmetry

Statistics > Basic Statistics > Chi-Square > Bowker's Test

Bowker's chi-square test on a two-dimensional contingency table.

This procedure computes Bowker's test of symmetry for square two-way tables that are larger than 2×2. For 2×2 tables, Bowker's test is identical to McNemar's test. For Bowker's test of symmetry, the null hypothesis is that the probabilities in the square table satisfy symmetry, or that pij=pji for all pairs of table cells. When there are more than two categories for each variable, Bowker's test of symmetry is calculated as

For large samples, QB has an asymptotic chi-square distribution with r(r-1)/2 degrees of freedom under the null hypothesis of symmetry of the expected counts. For two categories, this test of symmetry is identical to McNemar's test.

### Dialog box items

Rows:
Select the variables displayed in rows in the crosstabulation. Selected variables should be factors with at least two levels. A crosstabulation is produced for each combination of row and column variables.

Columns:
Select the variables displayed in columns in the crosstabulation. Selected variables should be factors with at least two levels. A crosstabulation is produced for each combination of row and column variables.

DataSet is a Contingency Table:
Select if the data set specified is a contingency table.

Report:
The display of outputs of VisualStat.

### Data

To use Cross Tabulation, your data should be categorical. To define the categories of each table variable, use values of a numeric or short string (eight or fewer characters) variable. For example, for gender, you could code the data as 1 and 2 or as male and female.

### Statistics

Measures of Association
Describes the association between the two variables of the contingency table

oCramer's V: Check to display Cramer's V coefficient.

oPhi Coefficient: Check to display Phi Coefficient.

oContingency Coefficient: Check to display Contingency Coefficient.

oKappa Coefficient: Check to display Kappa Coefficient.

oObserved values: Check to display each cell's observed count.

### Options

Apply Continuity Correction: Check to apply Yates’ correction for continuity.

Confidence Level: Enter the level of confidence desired. Enter any number between 0 and 100. Entering 90 will result in a 90% confidence interval. The default is 95%.

### Example

The data show test scores for 34 children in two class (1 or 2). The child's gender ("male" or "female") and grade (4, 5, or 6) is also recorded.

1.Open the DataBook summary.vstz

2.Select the sheet crosstab

3.Choose the tab Statistics, the group Basic Statistics and the command Bowker's Test

4.In Rows, select Gender. In Columns, select Class

5.Click OK

Report window output

Bowker's Chi-Square Test of Symmetry

without continuity correction

Null hypothesis under test >>>  Independence of the rows and columns

data:  Gender and Class from data sheet summary.vstz

NB                 34

Bowker's Chi2      0.0435

Degree of freedom  1

p-value            0.8348

alpha-level        0.05

Critical Value     3.8415

Conclusion         Accept the Null Hypothesis

Interpreting the results

No evidence exists for association (p = 0.8348) between gender and class attachment.