I conducted a Survey to find reasons why firms invest in a specific asset. I asked them in a Likert-question if different aspects are a reason to invest in [asset]. The Response for each aspect can be:

  • strongly agree (sa)
  • agree (a)
  • neutral
  • disagree (d)
  • strongly disagree (sd)

Now my question is: Is it appropriate to use a Chi-Square test for each aspect to investigate if this aspect is in favor or against the firm investing? I.e. testing if the distribution of Responses (sa + a) and (sd + d) is significant different than the total number of non-neutral answers / 2.

Thank you!

(If this matters: For some aspects I have an expected tendency from Theory, for other aspects I do not know what to expect)

My data looks somewhat like in the image.

My collected data looks like this (values are numbers of respondents):


For Aspect 1 I would calculate the positive answers: 6+7=13 and the negative answers 3+1=4 and then do a Chi-Square test against the expected equal distribution of all non-neutral answers: (6+7+3+1)/2=8.5


1 Answer 1


The Chi-Square / Fisher's exact test is not the right choice here, since it doesn't acknowledge the ordinality of the Likert scale.

Instead you should do a Kruskal-Wallis test (Friedmann test if data are paired) where your Aspects are the factors and the Likert scale is the outcome (you cannot do ANOVA since normality/interval scale assumptions don't hold for Likert scale). This test assesses if there is ANY Aspect that's significantly different from the others. This KW test should be significant. Afterwards you can do a multiple testing procedure, more precisely the Dunn test (with Bonferroni correction), where you test pairwise Aspects for significance. This should show which aspects are in agreement/disagreement.

  • $\begingroup$ Thank you very much! $\endgroup$
    – dbucher
    Jun 16, 2019 at 15:36
  • $\begingroup$ These procedures should be available in common statistics software. Which one are you using? $\endgroup$
    – Edgar
    Jun 16, 2019 at 15:37
  • $\begingroup$ I am using R (PMCMR package). Reading into it at the moment. $\endgroup$
    – dbucher
    Jun 17, 2019 at 10:34
  • 1
    $\begingroup$ May I ask a follow up question: Did I understand this right: The significant Kruskal Wallis test shows me that there are differences between the items. And the post-hoc Dunn test shows me which aspects are significantly different from each other. I think this is a bit Overkill, since I just need to prove if single items (aspects) are perceived positive or negative. I do not need to make a link between items. $\endgroup$
    – dbucher
    Jun 18, 2019 at 13:41
  • 1
    $\begingroup$ I know one shouldn't write comments to say "thanks" but you really helped me a lot! I appreciate it! thank you! $\endgroup$
    – dbucher
    Jun 18, 2019 at 19:41

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