I have applied an R chi square test on a dataset with two nominal variables, namely subject category(SC) and Research Institution(RI). The table looks like this
RI1 RI2 RI3 RI4 RI5 RI6 RI7 RI8 RI9 RI10
sc1 4.95 2.97 2.97 5.94 3.96 7.92 25.74 44.55 0.99 0.00
sc2 6.53 3.01 11.55 5.52 5.02 6.03 23.61 38.19 0.00 0.50
sc3 6.12 4.08 10.20 6.12 0.00 2.04 24.48 44.89 0.00 2.04
sc4 10.00 0.00 2.00 8.00 0.00 4.00 32.00 42.00 0.00 2.00
sc5 10.93 3.12 6.25 3.12 1.56 6.25 23.43 42.18 1.56 1.56
sc6 6.10 4.58 12.21 6.87 3.05 4.58 24.42 35.87 1.52 0.76
sc7 11.90 7.14 11.90 7.14 2.38 2.38 33.33 19.04 0.00 4.76
sc8 8.60 3.22 6.98 5.37 3.76 3.76 20.96 43.01 1.61 2.68
sc9 7.27 4.84 13.93 6.06 4.24 2.42 19.39 40.00 1.21 0.60
sc10 3.75 0.00 8.75 7.50 1.25 1.25 33.75 40.00 2.50 1.25
The chi-square results are as follows:
chisq.test(mydata)
Pearson's Chi-squared test
data: mydata
X-squared = 102.51, df = 81, p-value = 0.05357
Warning message:
In chisq.test(mydata) : Chi-squared approximation may be incorrect
I would like to apply a Bonferroni correction on the p-value. My hypothesis is that subject category does not influence the number of publications in a research institute. My question is, since i have 10 subject categories, should i divide the p-value by 10?...
P.S. I have not yet reached 15 points therefore cannot create a new tag "Bonferroni correction"
If you are going to do multiple pairwise comparisons after your overall Chi Sq test, your Bonferroni correction would be .05/(number of tests). See helpful references here and here
You probably need to test all possible pairs, meaning that you'd be doing a lot more than 10 tests. However, before going ahead, you might want to think about other ways to tackle this.
The first step might be to re-assess your hypothesis. E.g. if your Research Institutions have different numbers of researchers, your analysis would need to take that into account (more researchers can be expected to produce more publications, regardless of subject). When you have clarified your research question, you might want to use another statistical method rather than Chi Sq. Helpful to search questions/answers at Cross Validated.