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I have a table of counts with 4 columns and 25 rows. What statistical test should be used to asses significance for values within each row? In other words I want to perform significance testing on individual rows to see if there is homogeneity. I was thinking of something similar to rowwise ANOVA, except I have counts instead of means. Can chi squared be performed on individual rows? I am using R to perform this analysis.

Edit: Mainly, I want to do a significance test of each row, so 25 tests. However, I'm not sure whether a chi-squared test for just 4 values would make statistical sense.

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  • $\begingroup$ What do you mean by 'homogeneity'? Check if each row is consistent with probability 1/4 in each cell? Or see if rows are consistent with each other? // It would help if you could tell us what you are doing, what is being counted, typical sizes of counts, and what you want to know. $\endgroup$
    – BruceET
    Apr 17, 2022 at 3:49
  • $\begingroup$ By homogeneity I just mean making sure there is no significant variance between cells of each row. Each row corresponds to a different biological process. Each cell represents the count of proteins that are associated with that biological process. Each column represents a different sample. I want to test each row individually because row 1 might have a range of 130-150 while row 2 might have a range of 3–10. $\endgroup$
    – Rebecca Forbes
    Apr 17, 2022 at 3:57
  • $\begingroup$ This will likely go better with a more informative question. Please edit. // If you want 25 tests, one on each row, then in R, code r = c(23,15,25,40); chisq.test(r) rejects probability 1/4 in each cell with P-value near $0$ for that one row. // Do you want no comparisons among the 25 rows? If not, why mention them? What if half the rows had proportions $(.2, .2, .2, .4)?$ Would that be interesting? $\endgroup$
    – BruceET
    Apr 17, 2022 at 4:35
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    $\begingroup$ Yes I want to do a significance test of each row, so 25 tests. I wasn’t sure if a chi squared test for just 4 values would make statistical sense $\endgroup$
    – Rebecca Forbes
    Apr 17, 2022 at 4:40
  • $\begingroup$ Edited your Q. Reversed vote to close. Please do more editing as appropriate. // If you do 25 individual tests on the rows---all at the 5% level---do not be surprised if one of them happens to show inconsistency with 1/4 in each cell. $\endgroup$
    – BruceET
    Apr 17, 2022 at 5:05

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Assuming the counts are large enough, a chisquare test for just 4 values makes statistical sense. You must just be prepared for the multiplicity problems of making many tests, so the p-values cannot be taken at face value, some multiple testing correction must be done.

With simulated data, 25 rows so 25 pvalues, we cam make a qqplot against the uniform distribution:

qqplot of 25 pvalues

which seems consistent with the null hypothesis, which is true in this simulation. The R code used:

set.seed(7*11*13)  # My public seed
tab <- matrix(as.integer(NA), nrow=25, ncol=4) 
for (i in 1:25) tab[i, ] <- 
   table(factor(sample(1:4, 100, replace=TRUE, prob=rep(1/4, 4)),
                levels=1:4)) 

pvals <- rep(0, 25)
for (i in 1:25) pvals[i] <- chisq.test(tab[i, ])$p.value 

qqplot(ppoints(25), pvals) 
qqline(pvals, distribution=qunif, col="red")

You could of course equally well have done a qqplot of the 25 observed chisquare test statistics against the chisquared distribution with 1 df.

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