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Let's assume I have three constructs measured with different Likert scales

  • Construct 1 - Measured with a 7-point Likert scale
  • Construct 2 - Measured with a 9-point Likert scale
  • Construct 3 - Measured with a 5-point Likert scale

Is it possible to conduct a Pearson correlation with these constructs? Or will the results of such a correlation be wrong, due to the different scales (7-point, 9-point, and 5-point)?

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  • $\begingroup$ A Pearson correlation is even defined for binary variables (say with values 0 and 1 but any two distinct values will do). It is just crucial that neither variable is constant. stats.stackexchange.com/questions/103801/… $\endgroup$ – Nick Cox May 22 '17 at 17:36
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Yes, it is perfectly valid to conduct a Pearson's correlation between variables with different scales. The correlation coefficient is a standardized measure, so it is not influenced by scale.

Here is a small simulation I did. First, I generate data on 7, 9, and 5 point scales. Then, I calculate correlation coefficients between each pair of variables. Then I standardize the variables (so they are all on the same scale), and do the same correlation matrix. As you can see, the correlation matrices are the same.

> set.seed(1839) # set seed for replicability
> c1 <- sample(1:7, 100, TRUE) # generating 7 point scale
> c2 <- sample(1:9, 100, TRUE) # generating 9 point scale
> c3 <- sample(1:5, 100, TRUE) # generating 5 point scale
> data <- data.frame(c1, c2, c3) # making data frame with original scales
> cor(data) # correlation matrix with original scales
           c1         c2         c3
c1 1.00000000 0.06659190 0.08941637
c2 0.06659190 1.00000000 0.02127672
c3 0.08941637 0.02127672 1.00000000
> 
> Zdata <- data.frame(scale(c1), scale(c2), scale(c3)) # making data frame with z-scored variables
> # thus, this makes them all on the same scale
> cor(Zdata) # correlation matrix with z-scored variables
           scale.c1.  scale.c2.  scale.c3.
scale.c1. 1.00000000 0.06659190 0.08941637
scale.c2. 0.06659190 1.00000000 0.02127672
scale.c3. 0.08941637 0.02127672 1.00000000
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