Currently I want to check whether there is a significant difference between the data from two clusters with n1 = n2 = 6.
cluster1 cluster2 av 0 1 cem 3 4 cl 2 4 cm 1 1 md 2 4 mtt 0 3 pf 1 1 pul 0 0 r 1 1 va 1 2 vl 1 5 vm 0 5 vp 0 0
As frequencies aren't bigger than 5 I decided to use Fisher's exact test, but I'm somewhat lost. Something that I noticed is how I put the data into Fisher's exact test.
fisher.test(df$cluster1, df$cluster2) delivers a p-value of 0.1192 for a two-sided Fisher's test while
fisher.test(df) delivers a p-value of 0.7792. What is the correct usage? Secondly, I wonder how to conduct a compromise power analysis for Fisher's test. As my sample size is rather small using alpha = .05 is not a good idea. However, for calculating a power analysis I need the proportions but iirc the proportion is the ratio of the category of interest and the sample size.
Further, I wonder why I get a p-value of 0.7792 if it is the right p-value. As you can see I made a barplot for the distribution of thalamic nuclei in the two clusters. In my eyes, the barplot suggest that there is a significant difference between the two clusters, however, the p-value suggests there isn't.
Am I using the Fisher's test wrong? Is the p-value correct and my interpretation is simply wrong? And are there some other methods to analyse the distribution of my variables?