If I collected data three times by a 4-point Likert scale (1, 2, 3, 4) and aggregated the three responses of an individual, will it be interval now? For example, first measure 2 + second measure 3 + third measure 2 =7. Is this 7 now interval or ratio scale or still it is ordinal?
No it is not possible but definitely other way i.e. interval data can be converted to ordinal data.
Aggregating (multiple) ordinally scaled variables is not that trivial and this is one of the reasons why many researchers prefer to treat Likert-scale items just like they are recorded using an interval scale. The question is if you have a reason to assume that it is truly not an interval scale (e.g., the frequency coding is 1 = never and 2 = rarely 3 = often 4 = all the time). In this case, you see why you cannot simply aggregate over ranks because equidistance ensures a fair weighting of the different response categories. If you want to aggregate over this kind of data, a cluster analysis might help you derive a less biased representation.
Hello Dr / Mr Kadir, I don't know that you can add these together to create a final numerical value as if you did take three likert type scale measures/ ordered categories at three different time points there must be a factor that you are observing ie why did the measurements vary over time - temperature, time of day, outside light, tiredness of the person, I don't know why you have three measures, but if you read this below is this of relevance. http://www.statsoft.com/textbook/nonparametric-statistics/
Descriptive statistics. When one's data are not normally distributed, and the measurements at best contain rank order information, then computing the standard descriptive statistics (e.g., mean, standard deviation) is sometimes not the most informative way to summarize the data. For example, in the area of psychometrics it is well known that the rated intensity of a stimulus (e.g., perceived brightness of a light) is often a logarithmic function of the actual intensity of the stimulus (brightness as measured in objective units of Lux). In this example, the simple mean rating (sum of ratings divided by the number of stimuli) is not an adequate summary of the average actual intensity of the stimuli. I think this above maybe of relevance, but if not just delete and good luck with your work/ project. Kind Regards, Deborah http://sites.google.com/site/deborahhilton/
I think this should help:
http://www.mtabsurveyanalysis.com/dangers-of-converting-an-ordinal-scale-to-its-numerical-equivalent/
https://www.researchgate.net/post/Does_anyone_know_how_to_convert_raw_FIM_scores_from_a_sample_of_patients_from_their_ordinal_scale_to_an_interval_scale
Dear Mohammad
I recomend you to read this article: Nominal, Ordinal, Interval, and Ratio Typologies are Misleading by Paul Velleman and Leland Wilkinson. It is available in internet at: https://www.cs.uic.edu/~wilkinson/Publications/stevens.pdf
Dear Mohammad
If you want to contact professor Paul Villleman this is personal webpage in the Cornell University website: http://stat.cornell.edu/people/faculty/paul-velleman
In some cases it is useful to transform the variable to ridit scores - proportional ranks within the sample (range 0 to 1, mean= 0.5). Disadvantages: there are many... most notably, the variable is 'unitless' and can be difficult to interpret, plus information about frequency in the original response options is lost. Advantages: Ridits are normally distributed, continuous variables so you can use safely use correlations, linear regressions, etc, and get on with your day.
It must be possible and needed, just like converting linguistic information into certain values.
Hello,
Two conditions you need to take heed of using ordinal measures for the parametric test, particularly for behavioral science studies measuring attitudes and judgments of respondents about an item of interest.
1. The scales need to be >/= 5, usually between 5-7.
2. create approximate continuous variables by transforming ordinal scale data to mean scores. Let me know how it goes for you
Best of lucks!
References:
1. Johnson, D. R., & Creech, J. C. (1983). Ordinal measures in multiple indicator models: A simulation study of categorization error Sage Publications Inc. DOI:10.2307/2095231.
2. Norman, G. (2010). Likert scales, levels of measurement and the "laws" of statistics. Netherlands: Springer Netherlands. DOI:10.1007/s10459-010-9222-y.
Hello, you can read this:
https://journals.sagepub.com/doi/abs/10.1177/0013164409344532?journalCode=epma&fbclid=IwAR1AamMqhxqXPpfl6XYeAu46CaG0eVZ0XozQfKL_KhSz3KDgLPYbSkRDdCk
and this:
https://www.jstor.org/stable/3516068
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