Following articles reach quite different conclusion and I start to believe that there is no clear answer to this problem. The conclusions are below and the first author reacts on second author. My question here is, what approach is appropriate (given following situation) when we want to analyse Likert Scales in Social research, MANOVA fits our research design (two or more DV based on Likert Scale), we have N = 180 but these two contradictory opinions?
Parametric statistics can be used with Likert data, with small sample sizes, with unequal variances, and with non-normal distributions, with no fear of ‘‘coming to the wrong conclusion’’. These findings are consistent with empirical literature dating back nearly 80 years. The controversy can cease (but likely won’t).
- Norman, Geoff. "Likert scales, levels of measurement and the “laws” of statistics." Advances in health sciences education 15.5 (2010): 625-632. 10.1007/s10459-010-9222-y
(...)the researcher should decide what level of measurement is in use (to paraphrase, if it is an interval level, for a score of 3, one should be able to answer the question "3 what?"); non-parametric tests should be employed if the data is clearly ordinal, and if the researcher is confident that the data can justifiably be classed as interval, attention should nevertheless be paid to the sample size and to whether the distribution is normal.
- Jamieson, S. (2004). Likert scales: how to (ab)use them. Medical education, 38(12), 1217-1218. DOI: 10.1111/j.1365-2929.2004.02012.x