Hey,
I am having trouble with finding the right statistical test for my data. I have a frequency of two types HMA and LMA and their morphologies. First i thought that the chi squared test was the best option. However, many frequency are below 1 and more than 20% in below 5. Therefore the assumptions are not met. I used Chi-square test of independence post hoc using residuals as my post hoc, but i dont think i can use the post hoc test if the chi-square test cannot be used, can i?
Which test could i use with this data (+ post hoc) and how do i have to do it in R?
Thanks in advance!
Hi Jochen Wilhelm. I do not agree with your statement that one should *always* use the Fisher-Irwin test (aka., Fisher's exact test). In the context of 2x2 tables, I agree with Ian Campbell's recommendations that one should use the N-1 Chi-square rather than the Fisher-Irwin test provided that:
For more info, see Campbell's website and his Statistics in Medicine article.
- http://www.iancampbell.co.uk/twobytwo/twobytwo.htm
- Campbell Ian, 2007, Chi-squared and Fisher-Irwin tests of two-by-two tables with small sample recommendations, Statistics in Medicine, 26, 3661 - 3675 http://www3.interscience.wiley.com/cgi-bin/abstract/114125487/ABSTRACT
- https://www.encyclopediaofmath.org/index.php/Irwin,_Joseph_Oscar
HTH.
There exist variants of Fischer's exact test that work on n x m tables.
I did it in R (www.r-project.org) with the function fisher.test(). The two-sided p-value is 0.06535.
PS: you may consider a mean-difference plot instead of a barplot. I find this easier to read and easier to see interesting patterns. I attached a version to clearify what I mean (also produced in R).
Jochen Wilhelm thank you for your response! So if im correct i dont need a post hoc test because there is no significant difference between LMA and HMA (p>0.05). Please correct me if im wrong because im a beginner in statistics.
And another question: i can not add error bars to the bar graph with my data, can i?
What do you want to test? The difference in the frequencies between HMA and LMA for each morphology? These would be binomial tests. The smallest p-value is obtained for "Tubular" (p=0.096), but this is clearly not significant, considering that you are screening over morpologies (the adjusted p-values controlling the family-wise error rate are all 1).
Jochen Wilhelm I would like to know the striking differences between this test in question against the Fischer's test. Because I have read many articles where the expected values are far below 5 and Chi-square was still used. I wonder if my understanding is against the reviewer's for the acceptance of such statistical tool. I would be glad if the main consideration differentiating the two tests are here clarified.
Yes i wanted to test the difference in the frequencies between HMA and LMA for each morphology. what do you mean with: (the adjusted p-values controlling the family-wise error rate are all 1) ? I know you have to correct when doing multiple tests.
Kamoru A. Adedokun, one should *always* use Fisher's exact test. For large tables sometimes the computer hardware is limiting. In this case one get p-values by bootstrapping. The chi-squared test is an approximate test and should only be used when Fisher's test is not available (that was an issue decades back, but not today anymore). However, the approximation is okayish when the expected frequency in the cells exceeds 5.
@Daan van Bendegom, yes that is the correction for multiple testing. Consider "sig" is your level of significance. The probability of a rejection under H0 when p
Hi Jochen Wilhelm. I do not agree with your statement that one should *always* use the Fisher-Irwin test (aka., Fisher's exact test). In the context of 2x2 tables, I agree with Ian Campbell's recommendations that one should use the N-1 Chi-square rather than the Fisher-Irwin test provided that:
For more info, see Campbell's website and his Statistics in Medicine article.
- http://www.iancampbell.co.uk/twobytwo/twobytwo.htm
- Campbell Ian, 2007, Chi-squared and Fisher-Irwin tests of two-by-two tables with small sample recommendations, Statistics in Medicine, 26, 3661 - 3675 http://www3.interscience.wiley.com/cgi-bin/abstract/114125487/ABSTRACT
- https://www.encyclopediaofmath.org/index.php/Irwin,_Joseph_Oscar
HTH.
Bruce Weaver, thank you for bringing this article to our attention. I did not think about the impact of fixed marginal sums. The maximum "type I errors" (actually these were rejection rates under H0, what is loosely related to but the same as "type I" errors), were shown, but I missed pictures of how the "power" behaves. Maybe I have to read it again.
Interestingly, Fishers test is widely used and recommended in over-representation analyses in the omics-field (factor A: gene/protein belongs or does not belong to a particular set [pathway, complex, ontology node...]; factor B: gene/protein is or is not considered differentially expressed. The resulting 2x2 tables are analyzed using Fishers exact test, but here the A-marigin sums may be considered fixed).
Agresti, in Categorical Data Analysis, 3rd., has a discussion of fixed margins for Fisher's exact test and tests not assuming fixed margins. †
It seems the classic unconditional test of association for 2 x 2 tables is Barnard's test. You can find implementations in R, but it doesn't seem like people use this test often. The Wikipedia page has some interesting comments on this test (https://en.wikipedia.org/wiki/Barnard%27s_test). I don't think I've ever seen an implementation for tables larger than 2 x 2. Agresti mentioned a couple of other tests, including Boschloo's test.
______
† Unfortunately the discussion is too long for me to feel okay with posting it all here, and it's too involved for me to try to summarize.
Another resource that I haven't read lately, but remember as being very good was this one by Richardson (1994):
Article The analysis of 2 × 1 and 2 × 2 contingency tables: An histo...
HTH.
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