Here is my problem statement:

I have 5 products namely Product A, Product B, Product C , Product D, Product E.

A survey was conducted on these products. The sample size of the responses is 150. The data is of ordinal- likert scale ranging from 1-7 and also paired since the responses for all 5 products were from the same respondents.

My objective was to determine whether the mean of each product is statistically higher than a hypothesised value , i.e. a one sample t test.

But since the data I have is ordinal, according to me, a one sample t test wouldn’t be suitable as it’s mainly used for the data that is continuous and is not suitable for data which is likert scale.

I found out that an alternative approach of one sample t test is one sample wilcoxon signed rank test. Before using this test, one of the assumptions of wilcoxon signed rank is that the data should be symmetrical in nature, I found out that my data is not at all symmetrical. I really don’t know whether I am going in a right direction to solve this problem statement.

My question is :

1) Is Wilcoxon signed rank test a better option to use rather than one sample t test according to my problem statement mentioned above??

2) If yes, since my data is not symmetrical and is violating the assumption of wilcoxon signed rank test, how should I solve this? Should I use log transformation on ordinal data?? Please suggest.

Thank you!