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Textbook: Writing for Statistics and Data Science

If you are looking for my textbook Writing for Statistics and Data Science here it is for free in the Open Educational Resource Commons. Wri...

Sunday 14 February 2021

How does Polychoric Correlation Work? (aka Ordinal-to-Ordinal correlation)

Let's say you've got data of many paired cases of two ordinal variables, like you might when you ask a large number of people the same two Likert scale questions (e.g. "poor", "fair", "good", "very good", "excellent").

 

What could you learn from the data from those two questions?

Here's a few common approaches:

 

1) Compare the means of each variable by abusing a t-test.

2) Compare the distribution of each variable with a chi-squared goodness-of-fit test.

3) Check for a relationship between responses of each variable with a chi-squared independence test.

4) Estimate the strength of such a relationship with a Spearman correlation.