I used t test for my data in likert scale with 115 observations, based on an answer to a similar question (see gung, 12 June 2016). Can somebody help to find a credible source to justify my decision? I spent many hours on this with no result.
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1$\begingroup$ Likert scale data are discrete and ordinal but the t-test assumes data are continuous and ratio. You should not be looking for a credible source for the wrong choice! Please ask a different question or, preferably search the existing questions for help in analysing Likert data. $\endgroup$– Michael LewCommented Jan 19, 2018 at 3:22
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$\begingroup$ @Michael The t test does not make any such assumption: certainly not that measurements are of ratio type and in practice not even interval type is needed. It only assumes that the sampling distribution of the test statistic $t$ is close enough to a Student $t$ distribution that you can use it as a reference distribution for hypothesis testing. Indeed, t tests have frequently been used, to great effect, for binary data. For an intriguing example (although technically a t test was not applied, it just as well could have been) see is.muni.cz/el/1421/podzim2009/PSA_004/um/t01/lord.pdf. $\endgroup$– whuber ♦Commented Jan 19, 2018 at 16:20
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$\begingroup$ @Whuber Sounds like you have supplied the requested credible source! $\endgroup$– Michael LewCommented Jan 19, 2018 at 20:25
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I'll add some comments from a non-statistician perspective.
First idea: Can you re-do your analysis with something more appropriate for your data? That is, more satisfying for the reviewer. Would that be easier than mounting a defense of the t-test?
Second: It is usually important to be clear if you are talking about a Likert item (e.g. a single question on, say, a 1 to 5 scale) or a Likert scale (e.g. the sum of a whole bunch of Likert items, that has a wide range of values). The former is less likely to approximate the t-test's assumptions about the distribution of the data, and you are usually better off treating it like ordinal data.
Perhaps the best defense is to explain that your data met the assumptions of the test you used (to a reasonable degree). That you looked at the distribution of each group and that is was reasonably normal or t-like. And that the groups showed homogeneity (if that's an assumption of t-test you used). And any other assumptions that should be made explicit.
Another piece of defense would be to find good published literature in your field as examples. That doesn't necessarily mean it is correct, but might hold some weight with the reviewer in your field.
Finally, it might help to be explicit about assumptions that make your data interval and continuous in nature. Specifically, that you are assuming that the numbers in the Likert items are evenly spaced, and that they represent an underlying continuous distribution.
answered Jan 19, 2018 at 17:27