Statistical test to use for ranked data among 3 different groups - ANOVA or Kruskal-Wallis or other?

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Statistical test to use for ranked data among 3 different groups - ANOVA or Kruskal-Wallis or other?

Postby marcoj » Tue Aug 15, 2017 3:15 pm

I conducted a survey among three independent groups (managers N=110, analysts N=105 and investors N=80) and in one question I asked them to rank the 5 out of 14 available financial metrics used when analyzing a company based on their importance (with 1 being the most important down to 5 and leaving the other metrics blank). I then constructed scores for the responses (a rank 1 will get 5, the rank 2 will get 4 etc. and no rank 0) to establish/order which metrics are on average more important overall and for each group of respondents. Now I would like to compare the three groups for each of the 14 metrics and I am not sure which test (I use SPSS) to use and these are my thoughts.

1) I tried to use an ANOVA but since a rank could be considered an ordinal variable I am not sure it is still appropriate? As only for 4 metrics out of 14 the Levene's test was not significant, I applied the Welch Test in case of heterogeneous variances. The ANOVA showed that there were statistical differences at the p<0.001 level among the three groups (for about 6 out of the 14 financial metrics under study). Post-hoc (both Scheffe and Games-Howell given the unequal sample sizes and unequal variances instances) analysis indicated that there was a significant difference in means between some groups for some metrics. Would this approach be correct?

2) Given the issues mentioned in point 1, I also ran the Kruskal-Wallis tests with Dunns-Bonferroni Post-hoc the pairwise comparisons (in the SPSS model viewer) led me to essentially the same results. However, I am not sure that this is the right test either given the heterogeneous variances.

Many thanks in advance for any help.

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