1 question. 6 factors. Each with a Likert scale from 1 to 5. How can I analyze the results to answer my hypothesis?

Question

I hope you're all doing well. I find myself in need of some statistical guidance for my research project, and I'd greatly appreciate your expertise.I'm working on a project exploring a certain country's preferences for different aspects (taste, health, sustainability, price) and their impact on the acceptance of meat alternatives.

Hypotheses:

H0: The main motivational factor for consumers when choosing meat substitutes is not taste, and other factors such as health, sustainability, and price are equally or more influential.

H1: The main motivational factor for consumers when choosing meat substitutes is taste, and it holds greater importance compared to other factors such as health, sustainability, and price.I used a Likert scale to ask respondents to rate the importance of six factors (Taste being the first one). The Likert scale went from 1 to 5.

1 = Not important at all

3 = Neutral

5 = Very important

Each row in my survey data represents one respondent. For each respondent, there is a rating (from 1 to 5) given for each of the six factors. In the survey, Taste emerged as the highest-rated factor, with 85% of respondents giving it a rating of 4 or 5 on the Likert scale. Despite this clear preference for Taste, my assessors believe that this information is not sufficient, and they expect me to find "statistical significant differences".

I have zero knowledge about statistics, and unfortunately, none of my supervisors are willing to provide guidance. Given my lack of statistical expertise, could you recommend a straightforward way to test this hypothesis using the Likert scale data? I asked ChatGPT and it suggested to me to use ANOVA or the Kruskal-Wallis test to compare the means or medians of the factors. I tried doing the Kruskal-Wallis test, but the results are questionable. Do you think that could work? I am looking for an approach that's simple to understand, as my assessors do not have a deep understanding of statistics.

I appreciate any help or advice you can offer. Thank you in advance!

Answer 1

Your hypothesis can be tested by comparing the responses to the taste Likert item against those to each of the other 5 Likert items. It doesn't require a preliminary omnibus test like Kruskal-Wallis over all 6 items.

The tests that you mention don't take into account the fact that each individual (presumably) responded to all the Likert items. That would pose problems if individuals differed in their overall rankings (e.g., some with all responses tending high, others tending low). If your hypothesis related to taste was developed before you looked at the data, the following can work.

Do the 5 comparisons of taste against each of the other items with a paired Wilcoxon test. Make sure that you use the paired version of the test. That will help minimize systematic differences in rankings among individuals, with each respondent as its own control.

You then have to correct for multiple comparisons.* The classic Bonferroni correction, which would require p < 0.01 for each of 5 comparisons, is too stringent. The Holm correction (default in the R p.adjust() function) is a good choice. That will still require at least 1 p-value less than 0.01 in this situation, but higher p-values are tested against less strict criteria.

Be aware that rank tests like Wilcoxon or Kruskal-Wallis don't strictly compare medians, unless the response distributions meet specific criteria.

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*An omnibus test only documents that there are some differences among the responses to the 6 Likert items. You then face the same multiple comparisons problem in evaluating pairwise differences between taste and the other items.