After reading a lot through research papers and available literature, I am confused about whether we can perform arithmetic mean on a 5-point Likert type scale which is ordinal in nature. There exist research papers that have calculated the mean of the responses collected through the Likert scale. On the other hand, many statements are made that it is inappropriate to measure arithmetic mean for ordinal data.
Can someone please give a solution to this question?
I would suggest after scale development try ordinal logistic regression. See the attached notes for some ideas. Best wishes David Booth
Hello Aditya,
Let me summarize the argument for doing so (summing or averaging responses):
Rensis Likert (see link below) proposed that summated scores (arithmetic sums of responses over a set of related items, each with a "Likert-type" response scale) be used as (pseudo) continuous scores to identify levels of belief / perception / opinion / or sentiment.
His argument for this was that the ordinal (1,2,3...) scaling of response options yielded values that correlated in the .90s with what (at that moment in time) represented more rigorously scaled values.
Since that time, many researchers have been content to consider summated (or the linear transformation thereof to an average) scores as sufficiently close to interval, continuous values to treat as such.
Let me summarize the argument against doing so:
Ordinal variables do not have equal intervals, and therefore arithmetic operations such as summation or averaging do not yield meaningful values.
As well, as Professor Booth correctly notes, there are available methods that are more than capable of handling ordinal scores appropriately.
Finally, IRT models, such as the graded response model, offer a way to calibrate interval-level values onto a scale comprised by ordinal-level responses.
Good luck with your work.
Reference:
https://legacy.voteview.com/pdf/Likert_1932.pdf
From a statistical point of view, this is absolutely irrelevant. It is beyond statistics to define how an observable is operationalized. The operationalization defines the practical value of the variable, but this is out of the scope of statistics. The categories "sick", "healthy" and "dead" may be coded by numeric values and you might calculate logarithms, squares or averages. The problem may be that the average of "dead" and "healthy" may get a similar numeric value as the average of two "sick" - but is has an entirely different meaning. But this is a matter of the construction of the scale, the operationaliztion, and its internal and external validity.
Once you have some numerical scale (no matter how you got there), you can ask yourself with what kind of statistical model one can encode what we know about such a variable, and what observations will be able to tell us.
The finer the granularity of the possible values, the more sense it makes to use some kind of continuous approximation. And given a continuous approximation is justifiable, it is very likely that a sensible model will not based on the normal distribution. Often, a normalized score can be modelled well by a beta distribution, at least when the distribution is expected to be unimodal.
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