To explain in an abstract way what I am trying to investigate, please imagine that you are interested in seeing if certain letters are enriched in the words of a sentence compared to the words another sentence. The alphabet in both cases is the same, however, the length of the words as well as the number of words per sentence might differ.

To make things comparable, I have calculated the occurrence of each letter per word as a percentage:

letter word1  word2  word3  word4
A      25     27     10     8
B      15     20     10     12
C      25     33     10     5
D      35     20     70     75
sum    100    100    100    100
sent.  1      1      2      2

Here, word 1 + 2 form one sentence and word 3 + 4 for another. Now, as you can see by eye, the second sentence has on average more Ds compared to the first, which in turn is more uniformly distributed.

Note: the real data stems from an alphabet of 64 letters with percentages being floating point numbers, i.e. 0.2546 vs. 0.1268 etc.

My question is: how can I assess this enrichment statistically given that I have a couple of thousand words per sentence and several sentences to compare? In the end, what I want to know is which letter(s) is/are significantly enriched in one sentence compared to the others.

For two words, a chi-square test should be appropriate, however, given the large number of words + several sentences to compare, I was thinking that a GLM could work with sentence being the dependent variable. Unfortunately, this type of analysis is not my specialty and I am uncertain whether this is indeed OK to use, and if it is, which model distribution would be appropriate.

Any help is greatly appreciated!


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