Hello Pipit,

The fact that one batch has 150 cases and the other 200 is not an issue; it does not violate any assumption of parametric or non-parametric tests. (There are texts that point out some very old work noting that these tests are _slightly_ more robust with respect to violation of the homogeneity assumption when sample sizes are equal, but that's not to say that equal n across groups is necessary.)

The more salient concern is whether scores from a Likert-type scale (whether summated or averaged) are properly treated as interval strength data; they're not. Though with a well-constructed scale, the summated scores will generally perform pretty well, for all practical purposes, which relates to the somewhat tongue-in-cheek suggestion #3, below.

So, you could (and for each, I'm assuming that you're contemplating a single, overall score from the set of 32 items, and not multiple scores):

1. Use polytomous IRT (item response theory) models to generate interval-strength scores from Likert measures (though not for an individual item). Then run t-tests or anova or set up the group comparison as a regression model.

2, Use a rank-based test (such as Mann-Whitney or Kruskal-Wallis). These do require homogeneity.

3. Use the parametric test and hope that nobody challenges your choice.

4. Use an exact test, such as the CLES or Cliff's dominance statistic. Both are non-parametric, but have pretty straightforward interpretations. CLES: The proportion of times a randomly selected case from batch A has a score that exceeds that of a randomly selected case from batch B. This is found by enumerating the results of all n1 x n2 pairwise comparisons. Dominance statistic: The CLES after subtracting the proportion of times that B cases exceed A cases in value.

Good luck with your work.

David Morse is correct. There is a long thread of these questions on here. You could directly use ordinal logistic regression by choosing you IVs appropriately. David tends to say choice 3 but that is of course a very poor alternative that does exist because David knows that many people use OLS methods incorrectly. IMO this just encourages that. In any Case, if U choose one of David's other choices you will be on firm ground. Best, D. Booth

David Morse and David Eugene Booth Thank you!

As stated by David, unequal sample size is not an issue.

Likert scale data are ordinal on an average strength; means that the response choices have a meaningful order(usually 1-5 or 1-7 levels of ordinal choices, with discrete response(counts)). Hence, tests such as the Mann-Whitney U test or the Wicoxon signed ranks test can always be used (as with all ordinal data.) However, it is common to see ordinal data analyzed using parametric tests, such as the t-test [N30 up to 500] if the variance of the two population can be assumed to be equal or are approximately equal but the sampling distribution (not data) must follow the Normal Distribution. Sometimes it is not, but both non Parametric and Parametric can be done.

According to de Winter, J.C.F. and D. Dodou (2010),

"it doesn’t matter which of the two statistical analyses you use to analyze your Likert data. If you have two groups and you’re analyzing five-point Likert data, both the 2-sample t-test and Mann-Whitney test have nearly equivalent type I error rates and power." Try the two test, and if not the same, then it's difference in power!

#Reference: de Winter, J.C.F. and D. Dodou (2010), Five-Point Likert Items: t test versus Mann-Whitney-Wilcoxon, Practical Assessment, Research and Evaluation, 15(11).

*I think [am not too convinced about it having enough power and validity for inference] but you can avoid using non-parametric tests and create scales by combining the items in each set, which will allow you to treat the data as interval. Set of resources to address it:

https://www.researchgate.net/post/How_can_one_help_people_create_simple_scales_from_Likert-scored_items

Abiodun Christian Ibiloye Thanks. Noted.

Agreed with @ David Eugene Booth