GLM and proportions

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GLM and proportions
Message posted by Mark Waters (via 128.243.220.45) on November 13, 2001 at 1:32 PM (ET)

I work with chloroplasts in plant cells. Say I want to count the number of chloroplasts in a cell, and determine the proportion of those that are in the process of dividing. I also want to know whether this proportion changes with cell type, size etc. So I have many proportions, between 1 and zero, one for each of my cells. I have been taught how to use GLM in Minitab. Now, I could do an ANOVA to see if the proportions are significantly different between two cell types. But I think this undermines the assumptions of the GLM. If I apply an angular transformation, will this help? Will a non-parametric (Mann-Whitney) test on the raw proportions be a valid test?

Many thanks for your advice.

READERS RESPOND:
(In chronological order. Most recent at the bottom.)

Re: GLM and proportions
Message posted by bd (via 172.170.48.163) on November 24, 2001 at 2:00 PM (ET)

The arc sin sqrt transformation is used to equalize the variation associated with nonnormatility of distributions of proportions.

Re: GLM and proportions
Message posted by Mark Waters (via 128.243.220.25) on November 25, 2001 at 10:14 AM (ET)

Thanks - I need more data really but for the minute I am making do with Mann-Whitneys until I am happy that my distributions are more normal.

Re: GLM and proportions
Message posted by Jack Tomsky (via 208.249.113.130) on November 26, 2001 at 12:54 PM (ET)

To test equality of proportions, you can do a chi-square test on contingency tables. For the n cells, the table would consist of 2 rows (# of dividers and # of nondividers)and n columns.

Provided the sample sizes are sufficiently large, the chi-square statistic would be approximately distributed as a chi-square with n-1 degrees of freedom. If the null hypothesis is rejected, you can do multiple comparisons on contrasts of the proportions.

Re: GLM and proportions
Message posted by Mark Waters (via 128.243.220.45) on November 28, 2001 at 9:19 AM (ET)

The trouble with this is that I get a lot of expecteds less than 5. The P value is tiny (less than 0.001) but I am suspicious. Besides, all this tests is whether individual cells vary in the number of dividing chloroplasts. [In fact, it is not dividing chloroplasts I am interested in, but it is a useful analogy]. What I really want to know is:

Do the number of dividing chloroplasts vary with chloroplast density (i.e. number of chloroplasts per unit cell area)?

Ditto with chloroplast size?

Ditto with cell type?

So really I need a GLM in which I can control for all these factors. It is looking increasingly like I need LOTS of datapoints because of how much the proportion appears to vary. Do you have any input/advice on my approach?

Thanks again for your help.

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