Hello,
I've understood that ordinal data such as Likert scales cannot be used in parametric tests such as ANOVAs due to violation of the normality assumption. However, I have come across a study similar to my research question which does exactly this.
After some researching, I've also learned that in some cases, such data can be used in parametric testing if:
* It is 7-point scale as opposed to a 5-point scale
* The scale is ambiguous - that is, only the 0 and 7 points are labelled (e.g. 0 = Not X, 7 = Very X)
I would like to know whether this is widely accepted or not, and if it can be used in parametric testing. The dependent variable in my study is a rating scale responses between two groups that contain two within-factors both with two levels (2 x 2 x 2 ANOVA). I wish to investigate the interactions between the IVs which are categorical. If all else fails, my second guess is that an ordinal regression model is more suitable for this type of question, however I would like to know whether an ANOVA is also possible.
Thanks in advance. Please let me know if anything requires clarification or more information (and apologies if this does not belong here: first question here, sorry!)
Hello Nicholas,
In general, individual Likert-type response items do not conform to the presumption of interval-strength data (though, Likert showed that they correlate quite well with the interval scaled versions). Thus, summary statistics like a mean or SD aren't meaningful values with ordinal data. Rensis Likert's exposition on his approach to measuring sentiment was that one used a summated score over a set of items as a variable--these often behave quite well as a pseudo-continuous score. That said, people use them (individual responses as DVs) quite often in parametric tests, as you have observed.
If there was any doubt in your mind, I'd try a rank-based anova instead of the parametric version. This allows you to ignore: (a) the interval strength scale requirement; and (b) the normality requirement (for model residuals). Note that comparability of variation across groups is still a condition. Exact or resampling/bootstrap tests can allow you to avoid this requirement.
Good luck with your work.
David Morse is correct when he said " That said, people use them (individual responses as DVs) quite often in parametric tests, as you have observed. ", but I'm sure he meant to add but it is still incorrect if you are thinking of ols based models.
Please see my earlier response to such a question here:
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
I also suggest:
https://statisticalanalysisconsulting.com/how-to-analyze-likert-type-dependent-variables/
I have attached an excellent set of notes on ordinal logistic regression. Further ANOVA models can written in regression form:see https://www.google.com/search?q=Writing+ANOVA+Models+in+regression+form&oq=Writing+ANOVA+Models+in+regression+form&aqs=chrome..69i57.22447j0j1&sourceid=chrome&ie=UTF-8
and thus there is no problem in doing your analysis by ordinal logistic regression.
Best wishes, David Booth
- Badges
- Science method
- Similar topics
- Mathematics
- Statistics
- Statistical Modeling
- Analyses of Variance
- ANOVA