Test data for differences

Question

I am trying to figure out the best way to test my data for differences in R. The data I have look like this:

domain               variable    lifecycle
162                      CSP1         5
162               old Species        10
162                        BD        16
162                       DBH        14
162                    Height        16
162           Height comments        16
162            Other comments         4
162                      Year         5
123                   species        12
123                  den bran        14
123                  den core        14
191                      CSP2         4
191                   C kg ha         5
185                  location         5
185                   biomass         6            
 82                   CSP num         6 
 82                  depth lb         8
 82                       C t         7
190                     Layer         8     
190                Dry weight         9
204                 item plot         5
204               item volume         7
204 within central plot small         7
205                      plot         3
205        successional stage         3
205            rarefy hundred         3

Now I want to use the "variable" column as factorial group and the "lifecycle" as the characteristiom to compare. Because the data is not normally distributed and I have more than two groups to compare I chose a Kruskal-Wallis test, which shows no significant differences.

Kruskal-Wallis rank sum test  

data:  lifecycle by variable
Kruskal-Wallis chi-squared = 25, df = 25, p-value = 0.4624

My question is now if I can use the Kruskal-Wallis in this case to find differences in "lifecycle" for the "variable" groups, or is the sample size to small with only one value per group?

And if it is not usable here in this case what would be a better solution?

EDIT:

I did the Kruskal-Wallis now with the domain as grouping factor. Which gives me a significant difference. The interpretation would be that there are domains with significant more or less impact than other.

After that I performed a post-hoc test to see between which of the domains the differences occur. But supprisingly the paired wilcoxon test with bonferroni correction showed up no significant grup differences. How could this be?

Answer 1

Damian is correct that you need to look much more closely at what your question is conceptually before we can address this. If the table you have displayed represents the entirety of your data, applying statistics makes no sense because there is no variability present within your categories. Each category is entirely described by one score. The Kruskal-Wallis test asks whether groups differ in their median values. With only one score this question is meaningless.

Answer 2

non parametric procedures are quite robust. It is not a suprise that KW test detects a significant difference but later a a pairwise comparision yields non signficant results. The bonferroni correction also makes the test more conservative (and some authors may say that also increases the chances of making a type II error if you have many comparisons). Another issue that prevents you to find differences in the multiple comparison is the low sample size. There are other procedures to protect for type I error (Sidak, sequencial bonferroni, Hochberg procedure). Why did you choose a Wilcoxon test por multiple comparison? do you have paired data?, Looking at your data it doesnt look like that. Other option could be to test it using U Mann Whitney test. please excuse my english