Solved – Chi-square/G-test/Fisher exact with replicates

chi-squared-testfishers-exact-testhypothesis testing

I want to use Fisher exact or G-test/Chi-squared (the choice depends on the numbers of observations in a particular case) to test difference in species frequencies between and within replicated groups of observations. Here are some toy-data

    1.1 1.2 1.3 2.1 2.2 2.3
spec1   1   2   1   3   5   4
spec2   4   4   6   0   1   1
spec3   10  12  9   9   10  10

The first row denotes samples. The first digit of a sample ID represents a replicated group and the second one represents a replicate. Here is an example of the dataset collapsed for the first species.

spec1   1   2   1   3   5   4
others  14  16  15  9   11  11

It's easy to compare replicates within groups, because we can simply perform a bunch of pair-wise tests and apply some multiple-comparison p-value adjustment, but how do we treat replicates when we compare different groups? Can we just combine them into one sample?

I'm aware of this post, but it has no answers.

Best Answer

Testing species frequencies

I understand the OP's first question to be "Are the proportions of species 1, 2, and 3 identical across all six columns?" I think a chi-square test of independence of rows and columns would be applicable if the cell counts are sufficiently high (that's a whole other topic).

When can count data be combined?

My reading on this topic suggests that one can combine count data if one can show that the data (replicates) are homogeneous. Zar [1] describes combining multiple tests of goodness of fit (section 22.6) or multiple 2x2 contingency tables (section 23.4) through a heterogeneity chi-square. This test is performed by calculating the chi-square statistics for each replicate separately, and then comparing the sum of those chi-square statistics to the chi-square statistic one derives from pooling the data. Zar describes the steps in detail and this page does so as well.

[1]: Jerold H. Zar. 1999. Biostatistical Analysis, 4th edition.

Related Solutions

Solved – Fisher’s exact test or chi-square test

It takes more time to post the question than to try it out. Here is Stata:

. tabi  7  13 \ 15 5 \ 15 5 \ 19 1 , exact

Enumerating sample-space combinations:
stage 4:  enumerations = 1
stage 3:  enumerations = 14
stage 2:  enumerations = 65
stage 1:  enumerations = 0

            |          col
        row |         1          2 |     Total
 -----------+----------------------+----------
          1 |         7         13 |        20 
          2 |        15          5 |        20 
          3 |        15          5 |        20 
          4 |        19          1 |        20 
 -----------+----------------------+----------
      Total |        56         24 |        80 

       Fisher's exact =                 0.000

. ret li

scalars:
        r(p_exact) =  .000426720882576
              r(c) =  2
              r(r) =  4
              r(N) =  80

You could report the P-value as 0.0004 or 0.00043, say. So, Fisher's test can be done for tables this size. A standard chi-square test (not shown here) gives a P-value of 0.00042, which every statistical person I know would regard as essentially identical. The tests support the interpretation that is evident from eyeballing the table of an association between row and column variables.

Solved – Fisher exact test (9×2) vs pearson chi-square (SPSS)

I would simply use the Fisher exact p-value for in call cases. You already have the values. This is a well accepted test that will be reliable in all cases. Unless the counts are small, Fisher's exact test and Pearson chi-square will give similar results anyway.

I work in the biomedical genomic research and one hardly never sees a Pearson chi-square test in that literature. Fisher's exact test is standard.