StATS: Transformation of a Likert scale (January 4, 2006)

Someone asked me about a survey where they asked questions along the line of How much company turnover have you experienced in the past six months? with a response of

Much lower                   Much Higher
-5 -4 -3 -2 -1 0 1 2 3 4 5

In order to code this properly, this person converted all the numbers to the left of 0 to negative values, leading to a variable which ranged from -5 to +5. Then he worried that the negative numbers might confuse SPSS, so he came up with a different coding where the lowest  value received a 1 and the highest value received an 11. He wanted to know which approach made the most sense.

It turns out that the two scales differ only in that you add the constant 6 to the first scale to get the second scale. So any statistic that is invariant with respect to linear transformations will work just fine on either scale. This includes things like a t-test or a correlation coefficient.

There is a controversy over whether you can average values on a scale like this. See my weblog entry Summing ordinal data (April 5, 2005) for details.

Additional reading

Likert Scaling. Trochim WMK. Accessed on 2006-01-04.

[Excerpt] Like Thurstone or Guttman Scaling, Likert Scaling is a unidimensional scaling method. Here, I'll explain the basic steps in developing a Likert or "Summative" scale.

My comments: This is a useful guide for survey preparation.

Likert scale. Wikipedia. Accessed on 2006-01-04.

[Excerpt] A Likert scale (pronounced 'lick-ert') is a type of psychometric scale often used in questionnaires. It asks respondents to specify their level of agreement to each of a list of statements. It was named after Rensis Likert, who invented the scale in 1932.

So You Want to Use a Likert Scale?. Mogey N, Learning Technology Dissemination Initiative. Accessed on 2006-01-04.

[Excerpt] A typical question using a Likert Scale might pose a statement and ask the respondent whether they Strongly Agree - Agree - Undecided - Disagree or Strongly Disagree. The responses elicited may be coded e.g. 1-2-3-4-5, but this remains just a coding. It makes no sense to add a response of agree (coded as 2) to a response of undecided (coded as 3) to get a ‘mean’ response of 2.5 (what would it mean?).

This page was written by Steve Simon while working at Children's Mercy Hospital. Although I do not hold the copyright for this material, I am reproducing it here as a service, as it is no longer available on the Children's Mercy Hospital website. Need more information? I have a page with general help resources. You can also browse for pages similar to this one at Category: Descriptive statistics.