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What is Cross Tabulation Statistic?

Cross Tabulation

This a two or three-way cross-tabulation function. If you have two columns of numbers that correspond to different classifications of the same individuals then you can use this function to give a two-way frequency table for cross-classification. This can be stratified by a third classification variable.

 

For two way crosstabs, StatsDirect offers a range of analyses appropriate to the dimensions of the contingency table. For more information see chi-square tests and exact tests.

For three-way crosstabs, StatsDirect offers either odds ratio (for case-control studies) or relative risk (for cohort studies) meta-analyses for 2 by 2 by k tables and generalized Cochran-Mantel-Haenszel tests for r by c by k tables.

Example

A database of test scores contains two fields of interest, sex (M=1, F=0) and grade of skin reaction to an antigen (none = 0, weak + = 1, strong + = 2). Here is a list of those fields for 10 patients:

Sex Reaction
0 0
1 1
1 2
0 2
1 2
0 1
0 0
0 1
1 2
1 0

In order to get a cross-tabulation of these from StatsDirect you should enter these data in two workbook columns. Then choose crosstabs from the analysis menu.

For this example:

Reaction
0 1 2
Sex: 0 2 2 1
1 1 1 3

We could then proceed to an r by c (2 by 3) contingency table analysis to look for an association between sex and reaction to this antigen:

Contingency table analysis

Observed 2 2 1 5
% of row 40% 40% 20%
% of col 66.67% 66.67% 25% 50%
Observed 1 1 3 5
% of row 20% 20% 60%
% of col 33.33% 33.33% 75% 50%
Total 3 3 4 10
% of n 30% 30% 40%

 

TOTAL number of cells = 6

WARNING: 6 out of 6 cells have EXPECTATION < 5

NOMINAL INDEPENDENCE

Chi-square = 1.666667, DF = 2, P = 0.4346

G-square = 1.726092, DF = 2, P = 0.4219

Fisher-Freeman-Halton exact P = 0.5714

 

ANOVA

Chi-square for equality of mean column scores = 1.5

DF = 2, P = 0.4724

 

LINEAR TREND

Sample correlation (r) = 0.361158

Chi-square for linear trend (M²) = 1.173913

DF = 1, P = 0.2786

 

NOMINAL ASSOCIATION

Phi = 0.408248

Pearson’s contingency = 0.377964

Cramér’s V = 0.408248

 

ORDINAL

Goodman-Kruskal gamma = 0.555556

Approximate test of gamma = 0: SE = 0.384107, P = 0.1481, 95% CI = -0.197281 to 1.308392

Approximate test of independence: SE = 0.437445, P = 0.2041, 95% CI = -0.301821 to 1.412932

 

Kendall tau-b = 0.348155

Approximate test of tau-b = 0: SE = 0.275596, P = 0.2065, 95% CI = -0.192002 to 0.888313

Approximate test of independence: SE = 0.274138, P = 0.2041, 95% CI = -0.189145 to 0.885455

 

For more information.