# is Kruskal- Wallis test appropriate in this case?

Does this make sense, is this test appropriate in order to see how responses differ among more then 2 different groups? I have no experience working with SPSS. Is there any chance someone can help me to find appropriate tests for what I need (I can explain better) to do and to interpret the results?

• 0. Welcome to the CV community. 1. Can you please describe the targe of your analysis and your data so there is context to your question? 2. KW is an extension of the Wilcoxon rank sum test to more than two groups. Is the null hypothesis that data in $s_A$ and $s_B$ are samples from continuous distributions with equal medians relevant to this application? We cannot tell based on the information provided. – usεr11852 says Reinstate Monic Jul 13 at 12:09
• docs.google.com/forms/d/e/…, so I have coded the answers to this questionnaire into numeric, nominal values, and now I am trying to analyse it looking at how do the answers differ across different groups (nationality, gender, year of study); I want to check the validity of hypothesis (last 3 questions) - to see if there is any link between housing conditions and mental, physical health and academic success. I apologise for my mediocre question. – Ilinca Jul 13 at 14:10
• No need to apologise. – usεr11852 says Reinstate Monic Jul 13 at 14:41
• If you have different variable types then you should probably use different tests for numeric, nominal, ... Easy place to start is ANOVA, you can then find a modification of this based on the variable types. – user2974951 Jul 15 at 11:32
• Thank you for these clarification (+1 to your question). You are having the correct idea but you need to be slightly careful when you compare multiple group against each other. Please see my post for more details. – usεr11852 says Reinstate Monic Jul 18 at 1:05

Krustal-Wallis is appropriate for this use-case if we "simply" want to identify if at least one of the groups in our overall sample is different from at least one other group. i.e. we will get the $$p$$-value for the null hypothesis that the data in each group comes from the same distribution. In that sense, KW is fine first step.
Now, as we potentially care to identify which group comes from a different distribution we need to have a principled way to perform multiple group $$A$$ vs group $$B$$ comparisons. They are many different procedures to perform these multiple comparisons in theoretically coherent way, e.g. Scheffe's procedure, Bonferroni correction, Tukey's Honestly Significant Difference procedure, Dunn-Šidák's cor, Holm-Bonferroni correction, etc. Ultimately all procedures try to control for what is called Family Wise Error Rate (the probability of making at least one type I error (False positive) in our family of tests - see this (in)-famous XKCD "green jelly beans" cartoon for a nice cartoonish description). As a starting point, I would suggest you try Holm-Bonferroni (sometimes called simply Holm or Holm step-down) correction. It is available in most statistical packages and it can be easily explained as directly controlling FWER while being more powerful than the "ordinary" Bonferroni procedure.