Tetrachoric correlation is a measure of the correlation between two binary variables – that is, variables that can only take on two values like “yes” and “no” or “good” and “bad.”
This type of correlation is often used in surveys and personality tests in which the questions being asked only have two possible response values.
The value for a tetrachoric correlation can range from -1 to 1 where:
- -1 indicates a strong negative correlation between the two variables.
- 0 indicates no correlation between the two variables.
- 1 indicates a strong positive correlation between the two variables.
For this correlation to be reliable, it’s assumed that both variables come from a normal distribution.
How to Calculate Tetrachoric Correlation
Suppose we have the following 2×2 table with two variables, x and y, that both take on two values:
The formula to calculate the tetrachoric correlation between the two variables in this table is:
Tetrachoric correlation = COS(π/(1+√(ad/b/c)))
where:
- COS represents the cosine function
- π represents the numerical value Pi, equal to 3.141592…
- a, b, c, d represent the numerical values in the cells of the 2×2 table
If you have two ordinal variables (that can take on more than just two values) then you can instead calculate the polychoric correlation.
Here is the youtube video of Tetrachoric correlation ..
Try to attend the questions about basic Skills of Language Learning
Here is the graphical representation of the data
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