Solved – Cross tabulation of two categorical variables: recommended techniques

association-measurecategorical datacontingency tables

I'm aware that this one is far from yes or no question, but I'd like to know which techniques do you prefer in categorical data analysis – i.e. cross tabulation with two categorical variables.

I've come up with:

χ² test – well, this is quite self-explanatory
- Fisher's exact test – when n < 40,
- Yates' continuity correction – when n > 40,
Cramer's V – measure of association for tables which have more than 2 x 2 cells,
Φ coefficient – measure of association for 2 x 2 tables,
contingency coefficient (C) – measure of association for n x n tables,
odds ratio – independence of two categorical variables,
McNemar marginal homogeniety test,

And my question here is: Which statistical techniques for cross-tabulated data (two categorical variables) do you consider relevant (and why)?

Best Answer

I think you need to rework this question. It all depends on the problem/data which has generated the cross-tab.

Related Solutions

Solved – n alternative to Cramer’s V for computing effect size when chi-squared is inappropriate

The effect sizes I assume you are considering --- Cramer's V, (phi), Contingency coefficient C, and Cohen's w --- can all be calculated with the chi-square value. But the chi-square is simply calculated from the difference of observed values from expected values. This is way Cohen defines his w in Cohen (1988).

I assume that because there's no inference with these statistics, that it is fine to report them even if some test using the chi-square statistic would not be appropriate. It's like saying the difference between two means is some value, without addressing whether or not you could use a t-test or not in this case.

Solved – Chi squared test result and Cramer’s V value

Because your sample size is large, the Chi-square test is likely to return a low p-value even for a table with small differences from the expected proportions.

To get a sense of the effect size being reported by Cramer's v, it is helpful to look at the proportions in the table. For example, for column 1, you can see that there is not much difference in the proportions for each grade within the rows. Row 0 is about one-half to 1 percent of the observations in each grade. Row 2 is, say, 93 to 97 percent of observations in each grade. And so on.

Whether these kind of differences in proportions are meaningful in your context is up to you. The p-value and Cramer's v give you certain information. The practical importance of your results is something you will have decide.

The following is code for R.

I am getting a slightly different Cramer's v than you, so that's something that you might want to look into.

Input =("
Col1               Grade1  Grade2   Grade3   Grade4   Grade5
0                   290      392      932     1812     2854
1                   522      421      574      917     1247
2                 56789    81296   117971   147811   204480
3                  3719     2975     2811     1704     2244
")

Matrix = as.matrix(read.table(textConnection(Input),
                   header=TRUE,
                   row.names=1))

Matrix

chisq.test(Matrix)

   ### Pearson's Chi-squared test
   ###
   ### X-squared =  8113.9, df = 12, p-value < 2.2e-16

library(vcd)

assocstats(Matrix)

   ### Cramer's V        : 0.065 

prop.table(Matrix, margin=2)

   ###        Grade1      Grade2      Grade3      Grade4      Grade5
   ### 0 0.004729289 0.004607212 0.007621353 0.011901947 0.013537294
   ### 1 0.008512720 0.004948051 0.004693837 0.006023226 0.005914858
   ### 2 0.926108937 0.955479291 0.964698090 0.970882268 0.969903949
   ### 3 0.060649054 0.034965446 0.022986720 0.011192559 0.010643899

Best Answer

Related Solutions

Solved – n alternative to Cramer’s V for computing effect size when chi-squared is inappropriate

Solved – Chi squared test result and Cramer’s V value

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