Hello Badeel,

I'm assuming that you're describing summated scores, not individual responses given using a Likert-type response scale. If you have the slightest concern that the resultant scores are not interval strength, then use descriptive statistics that work for ordinal (or higher) data:

1. Tukey's five-number summary (minimum, lower hinge, median, upper hinge, maximum)

2. Interquartile range (or Tukey's mid-band spread)

3. Percentile/quantile points

4. Cumulative frequency distributions

In his 1932 monograph (https://legacy.voteview.com/pdf/Likert_1932.pdf) Rensis Likert pointed out that the ordinal values given to the response scale (1, 2, 3,...) correlated so well with what was (for the era) a more rigorous scaling from which interval scores could be derived, that there was little to be gained by the additional work involved with the scaling. So, there are many folks who do treat the summated/averaged scores (over several items relating to the same target) as if they were interval strength. Technically, they're not. Functionally, it may be hard to tell the difference in many cases.

Good luck with your work.

Hi Badeel,

I think the study of Kuzon (1996) may help you with your question. The author suggests that Likert scales might not be analysed by parametric statistics (sin #1).

Kuzon Jr, W.M., Urbanchek, M.G., and McCabe, S., 1996. The seven deadly sins of statistical analysis. Annals of plastic surgery, 37 (3), 265–272.

I suggest you look at the answers in this post:

My tome on Likert DV’s and ordinal logistic regression can be found here:

https://www.researchgate.net/post/Can_you_help_with_statistical_analysis_advice

More on that topic :

https://www.researchgate.net/post/Pearsons_correlation_coefficient_or_Standardized_beta_coefficient_in_multiple_regression_analysis

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

https://www.google.com/search?q=Montgomery+Design+and+analysis+of+experiments&rlz=1C1CHBF_enUS874US874&oq=Montgomery+Design+and+analysis+of+experiments&aqs=chrome..69i57.30438j0j1&sourceid=chrome&ie=UTF-8

I would recommend (after you look at the link) ordinal logistic regression. I have attached some notes to help you. Best, David Booth PS Be sure to look at attached KJones1 for ideas on what not to do to your Likert data That author can be found on RG and I recommend him highly. @David Morse gives good advice

HTH, David Booth