Statistics Tip of the Week: There are 2 different Critical Values for a 2-sided Chi-Square test.
For 2-sided tests using the Test Statistics z and t, which have symmetrical Distributions, there is only one Critical Value. That Critical Value is added or subtracted from the Mean.
Since Chi-Square’s Distributions are not symmetric, the areas under the curve at the left tail and the right tail side have different shapes,for a given value of that area. So, there are two different Critical Values -– an Upper and a Lower –- for a 2-sided Chi-Square test.
Unlike z and t, we do not add or subtract these Critical Values from the Mean. The two Critical Values of Chi-Square produced by tables, spreadsheets, or software are the final values to be used.
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Andrew A. (Andy) Jawlik is the author of the book, Statistics from A to Z -- Confusing Concepts Clarified, published by Wiley.