I saw some researchers who used this formula:
(n-1) / n
where n is the maximum number in the used scale. For example in five-point Likert scale, n is equal 5. So, the interval size can be calculated as 0.80. I just need a confirmation or precise evidence.
Dear Tamer,
Although the method you mention is common practice, it has a lot of drawbacks. The distances between response options depend to a large extent to the context of the scale and the language used for the labelling. We recently published a paper on this for response scales for happiness and life satisfaction, which I have attached. In that paper you can find an illustrative example of why the method you mention falls short in Sec. 3 and a number of examples on how the context of the scale affects the interpretation of the response options and thus the distances between them.
What is the reason that you want to perform a numerical transformation to your survey data?
Kind regards,
Tineke de Jonge
Caclulating interval sizes for Likert scales (that are ordinal) is nonsense. Some people argue that treating Likert scales as if they were (quasi-)interval scaled to make it possible to apply some common statistics and tests. There may be cases where this could be appropriate - if interpreted with adequate care. But since this procedure is anyway frankly ignoring pretty much of the principles of data analysis, I would not mind how "precisely" such intervals are defined. The word "precise" has no precise meaning here anyway.
The whole analysis (of Likert data on a quasi-interval scale) is arbitrary anyway and so is the meaning of the sizes of the intervals. Why should they be equal? And if there are good reasons that the intervals are quantitatively equal, that reasonable and measurable differences can be given - then why on earth is the data on a Likert scale at all?
Dear Tamer,
Although the method you mention is common practice, it has a lot of drawbacks. The distances between response options depend to a large extent to the context of the scale and the language used for the labelling. We recently published a paper on this for response scales for happiness and life satisfaction, which I have attached. In that paper you can find an illustrative example of why the method you mention falls short in Sec. 3 and a number of examples on how the context of the scale affects the interpretation of the response options and thus the distances between them.
What is the reason that you want to perform a numerical transformation to your survey data?
Kind regards,
Tineke de Jonge
I would not agree wholeheartedly that calculating means for scales made up of ordinal items is meaningless. Each item divides the underlying construct into five categories, and we assume that if there is a sufficient number of these items the scale will approach the properties of an equal interval scale.
The advantage, for communication purposes, in mapping the scale score onto the original item scoring system is that it gives it an interpretability that, however approximate, is better than leaving the original meaningless number.
Johen's comment is just right. I cannot agree, that usage of ordinal Likert-like scale includes automatic assumption on equality of distances between levels of agreement or disagreement. It only allows the respondent to choose softer type od response, they don't have to pick full agreement or disagreement.
Just had a look a the paper linked by Tineke above. Excellent and very thought-provoking.
It also occurred to me that we don't make sufficient use of Ridit scaling when combining items with ordinal scores. Here's a link to a rather interesting paper
http://onlinelibrary.wiley.com/doi/10.1016/S1090-3801(98)90018-0/abstract;jsessionid=6053C68BA4B647CF1523C60314521A7C.f02t04
Thanks for all. Tineke, the reason that I want to perform a numerical transformation to my survey data is "most of the mean values are lying around 3 so I can not interpret the results".
My study is descriptive and I have used a simple likert-scale from 1 to 5.
Hope I get a simple solution
Regards for all
Tamer, if you want to get a simple solution, than probably the way in which National Statistical Offices use there verbal scale measurements is an option. These offices normally do not calculate means based on verbal response scales, but just present the percentage of people who rated each response option. You can find an example through the following link to a table of perceived health from Statistics Netherlands: http://statline.cbs.nl/Statweb/publication/?DM=SLEN&PA=03799ENG&D1=91-93&D2=3-7&D3=a&D4=l&LA=EN&VW=T
From my point of view the paper about Ridit scaling Ronan Michael Conroy pointed at is very interesting. I had never heard of the method, but the idea of using a reference distribution corresponds to a certain extent to the use of a reference distribution in the Reference Distribution Method that we recently developed to overcome the incomparability of survey results about the same topic due to the use of different (verbal) response scales. In contrast to the Ridit method we however, do not use an empirical distribution itself as a reference distribution, but derive a continuous beta distribution from an empirical distribution to serve as a reference to bring the survey results from other surveys to a mutually comparable level. Below are the links to two papers that we have published about this method.
http://link.springer.com/article/10.1007%2Fs11205-013-0335-6
http://link.springer.com/article/10.1007%2Fs11205-014-0735-2
If you wish to categorize your data for an appropriate interpretation, convert the raw scores to standardized T-score. The score shifts between 20 and 80, then categorize it to 3 parts including 60. For this purpose, first convert raw score to Z-score, then multiply the z-scores by 10 and finally add 50 to the scores or simply do:
raw score to Z-score
(Z-score X 10) + 50= T-score
Dear Yarnold,
Good discussion. Would you please enlighten us what is the best parsing method?
Kind Regards,
Abdollahim
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