Editing Likert scale (section)

== Level of measurement ==

The five response categories are often believed to represent an interval [[level of measurement]]. However, this can only be the case if the intervals between the scale points correspond to empirical observations in a metric sense. Reips and Funke (2008)<ref>{{cite journal |last1=Reips |first1=Ulf-Dietrich |last2=Funke |first2=Frederik |year=2008 |title=Interval level measurement with visual analogue scales in Internet-based research: VAS Generator |journal=Behavior Research Methods |volume=40 |issue=3 |pages=699–704 |doi=10.3758/BRM.40.3.699 |pmid=18697664|doi-access=free}}</ref> show that this criterion is much better met by a [[visual analogue scale]]. In fact, there may also appear phenomena which even question the ordinal scale level in Likert scales.<ref>{{cite conference |last1=Johanson |first1=George A. |last2=Gips |first2=Crystal J. |title=Paired Comparison Intransitivity: Useful Information or Nuisance? |conference=The Annual Meeting of the American Educational Research Association |location=Atlanta, GA |date=April 12–16, 1993 |url=http://files.eric.ed.gov/fulltext/ED399296.pdf}}</ref> For example, in a set of items {{var|A}},&thinsp;{{var|B}},&thinsp;{{var|C}} rated with a Likert scale circular relations like {{var|A}}&nbsp;>&nbsp;{{var|B}}, {{var|B}}&nbsp;>&nbsp;{{var|C}} and {{var|C}}&nbsp;>&nbsp;{{var|A}} can appear. This violates the [[Armstrong's axioms#Axioms (primary rules)|axiom of transitivity]] for the ordinal scale.

Research by Labovitz<ref>{{cite journal |last=Labovitz |first=S. |title=Some observations on measurement and statistics|journal=Social Forces|year=1967|volume=46|issue=2|pages=151–160|doi=10.2307/2574595|jstor=2574595}}</ref> and Traylor<ref>{{cite journal|last=Traylor|first=Mark|title=Ordinal and interval scaling|journal=Journal of the Market Research Society|date=October 1983|volume=25|issue=4|pages=297–303}}</ref> provide evidence that, even with rather large distortions of perceived distances between scale points, Likert-type items perform closely to scales that are perceived as equal intervals.  So these items and other equal-appearing scales in questionnaires are robust to violations of the equal distance assumption many researchers believe are required for parametric statistical procedures and tests.