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I have a data set that was collected in form of a Likert scale through questioners. Now I am trying to eliminate or identify outliers in my data. By far, from all that I have been able to search, outliers do not apply to my type of data since it is a Likert scale: the only possible values are between 1 and 5, and thus no possible value can be an outlier.

What I am looking for is any thesis stating that outliers do not apply since data is on a 5 point scale. So that i can cite that thesis in my thesis ?

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    $\begingroup$ What constitutes an "outlier" is up to you. If I had a dataset of a hundred replies on a five point scale, and one is a 5 but the others are all 1s and 2s, I would likely characterize the 5 as an outlier. More subtly--this happened to me once on a teaching evaluation--what if one respondent systematically misinterpreted the scale, writing "1" instead of "5," "2" instead of "4," and so on. It's possible such responses wouldn't look out of place on any individual question, but collectively would be obviously very different. Thus, I strongly doubt there is any such thesis to cite. $\endgroup$
    – whuber
    Aug 24 '19 at 13:49
  • $\begingroup$ Strictly a Likert scale is the sum of responses on several Likert items. Using a scale from 1 to 5 for individual items is common, but if I understand correctly it is not part of any definition. $\endgroup$
    – Nick Cox
    Jul 2 '21 at 15:17
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I agree with whuber. Instead of looking for outliers on restricted scales such as Likert, it is more convenient to identify suspicious responses. Three of the categories you should check carefully include:

  • Straight lining (respondents mark all answers with the same score).

  • Diagonal lining (scores follow a diagonal pattern, from the smallest score to the largest, or vice versa).

  • Alternating extreme pole responses (scores are assigned following a zig zag pattern like an ECG).

After identifying such cases, it is important to reason whether to include them in the subsequent analysis or to eliminate them. The nature of the measurement itself and the underlying theory help in this decision.

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If you want a specific citation about the impact (or lack of impact) of outliers on Likert scales, could you provide more context regarding what the impact would be on and your sample size? For example, here is a paper on the impact of outliers in Likert scales on alpha. But, the answer will change depending on what kind of analyses you are running. Some analyses are more robust or sensitive to outliers.

As Pavel noted above, it is useful to try and determine the cause of outliers. However, in my experience, you often can have a reasonable guess, but not know the cause. The cause of the outlier and the impact on specific analyses will affect what you do with it. For instance, see here and here.

In my experience, if you don't have strong evidence to support removal (e.g., a lot of deviant responding), I have found it beneficial and reviewer-friendly to run analyses with and without the outlier(s) and report whether the results changed at all. It's more work re-running analyses, but ultimately it is transparent and saves you from trying to argue for either their inclusion or removal (often on grounds that make assumptions).

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