Extracting genes differentially expressed by Wilcox test I have 2 cell types (NOF and CAF) cultures individually and also have been co-cultured with tumour like this picture.

https://ibb.co/x8Ty1Wz

If this is the log cpm of these 4 samples 

&gt; head(onco[,1:4])
             A10       A11        A12        A2
A2M    11.755100 12.145143 12.9787977 12.407221
ABCB11  2.955457  2.278363  0.1229266  1.493507
ABCC2   6.711643  6.974025  0.1229266  7.628936
ABCC6   6.443439  6.094670  6.1389496  7.483394
ABCF1   9.995098 10.045613  9.6627424 10.314842
ABCG2   7.125483  7.448127  6.8669702  8.492895
&gt; 


I have used log of count per million (cpm) for Kruskal-Wallis rank sum test that says these samples are significantly difference like below;

&gt; NOF1=c(NOF1$`onco$A10`)
&gt; NOF2=c(NOF2$`onco$A11`)
&gt; CAF1=c(CAF1$`onco$A12`)
&gt; CAF2=c(CAF2$`onco$A2`)
&gt; my_data &lt;- data.frame( 
+     group = rep(c("NOF1", "NOF2","CAF1","CAF2"), each = 719),
+     cell_type = c(NOF1,NOF2,  CAF1,CAF2)
+ )

&gt; head((my_data))
  group cell_type
1  NOF1 11.755100
2  NOF1  2.955457
3  NOF1  6.711643
4  NOF1  6.443439
5  NOF1  9.995098
6  NOF1  7.125483
&gt; 

&gt; kruskal.test(cell_type ~ group, data = my_data)

    Kruskal-Wallis rank sum test

data:  cell_type by group
Kruskal-Wallis chi-squared = 22.006, df = 3, p-value = 6.505e-05

&gt; 


I then did Pairwise comparisons using Wilcoxon rank sum test to see which samples are different with each other.

&gt; pairwise.wilcox.test(my_data$cell_type, my_data$group,
+                      p.adjust.method = "BH")

    Pairwise comparisons using Wilcoxon rank sum test 

data:  my_data$cell_type and my_data$group 

     CAF1   CAF2   NOF1  
CAF2 0.0058 -      -     
NOF1 0.2809 4e-05  -     
NOF2 0.6818 0.0016 0.3811

P value adjustment method: BH 
&gt; 


My Question is; how I can extract the genes behind the difference between each pair of samples? I mean something like differential expression by non parametric test. also I am not sure if I am right in using log cpm values for these test

If possible give me a hand to correct myself and get intuition

Thanks
All of the genes are behind the difference, you're doing a rank test comparing all of them against each other at once. Your results have more to do with samples having slightly different outlier genes than any interesting biology. You don't have enough replicates to do a non-parametric test.