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Many studies in the social sciences use Likert scales. When is it appropriate to use Likert data as ordinal and when is it appropriate to use it as interval data?

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Technically Likert scales are the sum of Likert-type items and as such end up being a reasonable approximation (at least according to many psychometricians in Psychology) of an interval data point. –  rpierce Jul 20 '10 at 8:03
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@drknexus - So, multiple items serve as a measurement triangulation for construct scales? If yes, what are the criteria for determining that a researcher has enough relevant data points (i.e., items) to use the scale as an interval measurement? –  A Lion Jul 20 '10 at 15:06
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I'm not sure; that might be a worthy question for the community in general. I'd guess that it is probably in part a value judgement on the part of the researcher & area. Some areas are completely willing to treat a single Likert item as interval even though it clearly is ordinal. A reasonable answer might be to use a different analysis method, e.g. a permutation or bootstrapped test. Another answer might be to conduct a simple test of normality, so long as the aggregate doesn't significantly depart from normality you are probably okay. –  rpierce Jul 21 '10 at 0:07
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... but in general it seems like one could evoke the central limit theorem and suggest that 20 to 30 items should be sufficient to use the scale as an interval measurement. –  rpierce Jul 21 '10 at 0:26

4 Answers 4

up vote 19 down vote accepted

Maybe too late but I add my answer anyway...

It depends on what you intend to do with your data: If you are interested in showing that scores differ when considering different group of participants (gender, country, etc.), you may treat your scores as numeric values, provided they fulfill usual assumptions about variance (or shape) and sample size. If you are rather interested in highlighting how response patterns vary across subgroups, then you should consider item scores as discrete choice among a set of answer options and look for log-linear modeling, ordinal logistic regression, item-response models or any other statistical model that allows to cope with polytomous items.

As a rule of thumb, one generally considers that having 11 distinct points on a scale is sufficient to approximate an interval scale (for interpretation purpose, see @xmjx's comment)). Likert items may be regarded as true ordinal scale, but they are often used as numeric and we can compute their mean or SD. This is often done in attitude surveys, although it is wise to report both mean/SD and % of response in, e.g. the two highest categories.

When using summated scale scores (i.e., we add up score on each item to compute a "total score"), usual statistics may be applied, but you have to keep in mind that you are now working with a latent variable so the underlying construct should make sense! In psychometrics, we generally check that (1) unidimensionnality of the scale holds, (2) scale reliability is sufficient. When comparing two such scale scores (for two different instruments), we might even consider using attenuated correlation measures instead of classical Pearson correlation coefficient.

Classical textbooks include:
1. Nunnally, J.C. and Bernstein, I.H. (1994). Psychometric Theory (3rd ed.). McGraw-Hill Series in Psychology.
2. Streiner, D.L. and Norman, G.R. (2008). Health Measurement Scales. A practical guide to their development and use (4th ed.). Oxford.
3. Rao, C.R. and Sinharay, S., Eds. (2007). Handbook of Statistics, Vol. 26: Psychometrics. Elsevier Science B.V.
4. Dunn, G. (2000). Statistics in Psychiatry. Hodder Arnold.

You may also have a look at Applications of latent trait and latent class models in the social sciences, from Rost & Langeheine, and W. Revelle's website on personality research.

When validating a psychometric scale, it is important to look at so-called ceiling/floor effects (large asymmetry resulting from participants scoring at the lowest/highest response category), which may seriously impact on any statistics computed when treating them as numeric variable (e.g., country aggregation, t-test). This raises specific issues in cross-cultural studies since it is known that overall response distribution in attitude or health surveys differ from one country to the other (e.g. chinese people vs. those coming from western countries tend to highlight specific response pattern, the former having generally more extreme scores at the item level, see e.g. Song, X.-Y. (2007) Analysis of multisample structural equation models with applications to Quality of Life data, in Handbook of Latent Variable and Related Models, Lee, S.-Y. (Ed.), pp 279-302, North-Holland).

More generally, you should look at the psychometric-related literature which makes extensive use of Likert items if you are interested with measurement issue. Various statistical models have been developed and are currently headed under the Item Response Theory framework.

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Just for clarification: Nunnally/Bernstein suggest to treat a variable as continuous if it has at least 11 distinct values (p. 115). Where is that "12 points imply interval scale" rule of thumb from? –  xmjx Dec 31 '11 at 15:09

The simple answer is that Likert scales are always ordinal. The intervals between positions on the scale are monotonic but never so well-defined as to be numerically uniform increments.

That said, the distinction between ordinal and interval is based on the specific demands of the analysis being performed. Under special circumstances, you may be able to treat the responses as if they fell on an interval scale. To do this, typically the respondents need to be in close agreement regarding the meaning of the scale responses and the analysis (or the decisions made based on the analysis) should be relatively insensitive to problems that may arise.

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John Tukey wrote otherwise (back in 1960) in a monograph "Data Analysis and Behavioral Science" (published in Collected Works v. III). One result he obtained is that if you're getting better than about 10% test-retest agreement, your scale isn't narrow enough! –  whuber Oct 8 '10 at 20:17

In addition to what has already been said above about summated scales, I'd also mention that the issue can change when analysing data at the group-level. For example, if you were examining

  • life satisfaction of states or countries,
  • job satisfaction of organisations or departments,
  • student satisfaction in subjects.

In all these cases each aggregate measure (perhaps the mean) is based on many individual responses (e.g., n=50, 100, 1000, etc.). In these cases the original Likert item begins to take on properties that resemble an interval scale at the aggregate level.

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likert scale always in ordinal form : A method of ascribing quantitativevalue to qualitative data, to make it amenable to statistical analysis. A numerical value is assigned to each potential choice and a mean figure for all the responses is computed at the end of the evaluation or survey.

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Welcome to our site! Please attribute your quotation or, in general, any words that you are borrowing from someone else. –  whuber Oct 23 '12 at 17:37

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