Notes on Likert Scales
Stanley L. Sclove, Ph.D.
Copyright © 2001 Stanley Louis Sclove
Likert scales are the four, five, six, seven, eight or nine point scales
much used in various fields of research.
Often the scale is used as a semantic differential.
A statement
is given, and the endpoints correspond to agree strongly and disagree strongly.
Use of the scales is practical and interesting.
Scales with an even number
of points do not have a midpoint and in that sense force a choice.
disagree disagree agree agree
strongly somewhat somewhat strongly
----|------------|------------|--------------|----
Figure. A four-point semantic differential, Likert scale
Five-point Likert scales are perhaps most commonly used. With a five-point
scale the points can be labelled, agree strongly, agree somewhat, neutral,
disagree somewhat, disagree strongly. It is interesting to consider different
patterns of probabilities across a population of potential respondents.
There could be consistency, inconsistency (without polarization)
or polarization of response.
1 2 3 4 5
disagree disagree neutral agree agree
strongly somewhat somewhat strongly
----|------------|------------|----------|--------------|----
probability distribution showing consistency of response:
.1 .1 .1 .6 .1
probability distribution showing
inconsistency of response (without polarization):
.2 .2 .2 .2 .2
probability distribution showinginconsistency of response (with polarization):
.35 .1 .1 .1 .35
probability distribution showing complete polarization:
.5 0 0 0 .5
The standard deviation can be used as a measure of consistency.
A pattern like the completely polarized one has the highest standard
deviation. The highest possible standard deviation achievable for a 5-point
scale on 1,2,3,4,5 is given by the distribution {.5,0,0,0,.5}; the value
of sigma for this distribution is 2. As a rough guide, 5-point Likert scale
response distributions with sigma less than 1 could be called consistent;
with sigma more than 1, inconsistent.
Exercise.
Compute sigma for each of the distributions above.
See Distributions on Likert scales for solutions and for a tabulation of the standard deviation of distributions on three-point Likert scales.
APPENDIX (Optional)
Variance as a Function of the Mean
There are some technical difficulties with Likert scales. (These
are usually ignored.) Suppose comparisons across groups,
e.g., age/gender
combinations, are to be made. It is to be hoped that the mean response
will vary across the groups, so that the data reveal something interesting.
The problem is that then the variances will also differ, making the analysis
difficult. The variance has to be less at the ends of the scale, as there
is no alternative response to one side of the endpoint.
For example, with
a five-point scale, the variance would be expected to be largest at 3 and
smallest at 1 and 5. In other words, the variance is parabolic, as with
the binomial. A possibility is to use the arc sine square root transformation.
The responses are divided by 5, to yield a number between zero and one.
The square root is taken (still between 0 and 1).
The angle whose trigonometric
sine is that number is the transformed response.
lastest revision 6-Oct-2001