Cramer's V

[DanielZ]

Hi all

In chapter 17, pg 26, the Cramer's V statistic is defined. Part of the formula for it involves \( e_{ij} \) which is described as "the expected amount of exposure in the ith level of factor one and the jth level of factor two"

The formula for \( e_{ij} \) is given as \( \frac{\sum_i n_{ij} \sum_j n_{ij}}{n} \)
where \( n_{ij} \) is given as "the amount of exposure for the the ith level of factor one and the jth level of factor two"
and n is given as \( \sum_i \sum_j n_{ij} \)

I hope I'm not missing something obvious here, but can anyone explain why the formula for \( e_{ij} \) actually gives the expected value?

Thanks

 

[rans07]

I'm a little confused here too.

Does eij represent the proportion of total exposure represented by Factor one at the ith level and Factor 2 at the jth level?

 

[DanielZ]

ok, I've figured this one out.

The numerator in the Cramer's V statistic is the same as the chi square test statistic.

For a chi square test, when you want to compare actual to expected, you calculate the expected value in the same way as you do here: multiply the total value for the row by the total value for the column and then divide that by the sum total of the whole table.

This should give you the value you expect to have if there is no correlation between the 2 factors.