# GLM with binomial errors: underestimating interactions?

#### mango_man

##### New Member
I have problems with analyzing survival data, from experiments in a 2x2 factorial setting - the statistical approach which I am using seems to greatly underestimate interaction between factors, which interaction is the most interesting thing about the data. For analyzing my two datasets, both in SPSS and in R, I was using generalised linear modelling assuming a binomial error function.

In the first experiment, I conducted 99 independent trials in a 2x2 factorial setting, recording successes or failures. The data is as follows:

FactorA FactorB No_successes No_failures
0 0 25 0
0 1 25 0
1 0 16 8
1 1 24 1

When looking at the data, it seems clear that the major drop in success rate occurs only when FactorA=1 and FactorB=0. However, according to GLM with binomial errors, p for interaction is 1, but for both main effects p<0.01. It doesn't seem to make much sense!

In the second, larger data set (in the same 2x2 factorial design) the general picture is similar, but the differences in proportions between cells are even larger (for A=1 and B=0 the success rate is 0.37, in three other cases 0.79-0.95). When I analyze the data assuming binomial errors (as I should), p for interaction is 0.45. When I analyze the same data assuming its normal distribution (which is obviously wrong, but...), the significance of the main effects doesn't change dramatically, but p for interaction becomes less than 0.001!

It seems quite apparent that GLM assuming binomial error function seriously underestimates the effects of interactions between factors. Is there any procedure improving chances of detecting interactions in such data?

#### Masteras

##### TS Contributor
did you plot the data to get an idea? The normal is wrong, you were right.

#### mango_man

##### New Member
did you plot the data to get an idea? The normal is wrong, you were right.
I did, and in both data sets the effect of interaction seems to be much greater than the sum of the main effects (and as I wrote, GLM incorrectly assuming normal distribution of data detects such significant interaction in both data sets). I just need to find a way of confirming the effect statistically before resubmitting a research article preliminarily accepted by a good journal...

#### Masteras

##### TS Contributor
i say stick with it, the fact that GLM finds other things is reasonable. If the logistic found nothing then go ahead. Also use poisson regression or even a chi-square test to check for independency.