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Is there any anova-like approach for calculating contingency tables across multiple levels within a factor

Cross Validated Asked by Brad Davis on January 1, 2022

I want to compare success rates across a large number of different levels within a third factor to detect if there are statistically significant differences for at least one of the groups. I’m not specifically interested in the post-hoc question of which groups are different from each other, if any.

For example, I have 3 groups, and total failures and total attempts for each of those groups, lke

group A 15 200
group B 6  100
group C 4  50
group D 45 90

In this particular example, the P value would be (presumably) less than 0.05 because group D 45% compared to between 15 and 20% for the other groups.

The equivalent for continuous variables, like the measured heights of 11 year old children, would be to use a ANOVA.

Does anyone know of a method for doing this?

One possibility would be to create all pairwise combinations, but the number of levels within that variable are too large for it to be practical or useful, let alone having enough data to account for the multiple comparisons for each level.

Another possibility I’ve thought of: take one group, say group A, and compare it against the sum of all other groups and do a standard goodness of fit test, then you only have to do N-1 comparisons for N_group groups AND it tells you if a specific group is an outlier relative to the rest. e.g. group 1 = 15, 200, group 2 = 55, 240? The question then would be how to calculate the correct degrees of freedom for comparison. The normal df = k-c, where k= filled cells and c= estimated parameters, so in this case c = N_group?

Thanks,
Brad

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