Likert scales are a way for participants to respond to a question with a level of agreement, disagreement, satisfaction, and so on. The major defining factor among Likert scale data is that, on its own, it appears ordinal, and has a tendency to rise when opinions sway toward the higher anchor, and fall when opinions sway toward the lower anchor. Although these scales are technically ordinal in that they consist of a series of ordered categories, there are several authors who have researched this trait of Likert type data, and have found consistent support for the use of these variables as approximately continuous. There are two major ways to go about this:
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The first method is not the most common, but is helpful for understanding the second. This rationale centers on the fact that Likert, or ordinal variables with five or more categories can often be used as continuous without any harm to the analysis you plan to use them in (Johnson & Creech, 1983; Norman, 2010; Sullivan & Artino, 2013; Zumbo & Zimmerman, 1993). In cases like this, researchers usually refer to the variable as an “ordinal approximation of a continuous variable,” and cite the five or more categories rule above.
The second method is more common; take the sum or mean of two or more ordinal variables to create an approximately continuous variable. This is something many researchers encounter when using surveys; participants respond to Likert scale type (i.e., ordinal) questions and the administrator must either sum all responses or calculate a mean response across a set of questions. These both result in a number of categories much higher than the ordinal Likert scales they’re calculated from, which results in an approximately continuous variable.
For example, adding together two Likert scales with 3 categories each results in 5 possible categories: a minimum score of 2 for those who answered with “1” on both questions, and a maximum of 6 for those who answered “3” on both. It’s common to refer to this logic and support it with the first method’s reference material, if necessary, but most readers already make the assumption that most common Likert-type surveys result in scales with continuous data.
Norman, G. (2010). Likert scales, levels of measurement and the “laws” of statistics. Advances in Health Sciences Education, 15(5), pp. 625-632. Retrieved from: https://link.springer.com/article/10.1007%2Fs10459-010-9222-y#citeas.
Zumbo, B. D., & Zimmerman, D. W. (1993). Is the selection of statistical methods governed by level of measurement? Canadian Psychology, 34, 390-400.