# Thread: Is it correct to use Pearson correlation for variables measured on a "Likert scale"?

1. ## Is it correct to use Pearson correlation for variables measured on a "Likert scale"?

Hi All,

I'm conducting a research testing the relationship of 2 variables which are measured on agreement scales. Is it correct to use Pearson correlation for variables measured on a "Likert scale"?

As i have read in several places, some argue that Likert scale (e.g. agreement scale) data are "ordinal" and some say it can even be considered as an Interval scale.
In which case, i'm a little confused if Pearson Correlation can be used for such variables measured on a likert scale, because Pearson correlation appears to suit mostly Interval scale data.

Cheers,
Sach.

2. ## Re: Is it correct to use Pearson correlation for variables measured on a "Likert scal

Technically, no. The distribution of Pearson's r under the null hypothesis is calculated assuming that the variables are normally distributed. That won't be a good approximation to a stardard 5-value Likert scale.

Unfortunately, I don't really have a clearly correct alternative to offer. Statistics on ordinal sets is a bit outside the mainstream, and as a physical scientist, I deal mostly in continuous quantities, so I have had little reason to delve into it. But I can say two things...

First, of the trio Pearson, Spearman, and Kendall tests of association, Kendall would be closest to being right. Spearman is non-parametric, but since it depends on ranks and since you have only a few possible values, there will be many ties, and the way different Spearman implementations deal with ties is rather arbitrary. (Ties are infinitely unlikely for a continuous variable, so the traditional derivation ignores them.) Kendall is also non-parametric, and has a better-developed theory of ties.

Second, if your N is large and your P very strong, from a practical perspective these quibbles don't matter. The association is real. Only when N is small or P is on the edge of significance are they going to move you across the significance threshold.

3. ## Re: Is it correct to use Pearson correlation for variables measured on a "Likert scal

This is an issue of a lot of debate in the social sciences. Technically the assumptions of parametric tests such as Pearsons r are not met for Likert data, but the extent of the impact of these breaches are not necessarily large.

See:
http://onlinelibrary.wiley.com/doi/1...8.03172.x/full

and for another perspective:
http://www.mededuc.com/articles/topt...kertScales.pdf

Use of Pearsons r will be much more justifiable here if you analysing summated scales of Likert items than individual items themselves.

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