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.

• Upper Critical: 27.49
  
• df = 15
• 𝛼 = 0.05
• Lower Critical: 6.26
  

If you’re looking these up in a 2-sided table, you may need to look up the Critical Values for 𝛼/2 and for 1 − 𝛼/2. Sometimes two different tables are provided for Upper and Lower Critical Values. Or spreadsheets or software will do this for you.