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The Chi-Square Distribution: Notation

Module by: Susan Dean, Barbara Illowsky, Ph.D.. E-mail the authors

Summary: This module provides an overview of Chi-Square Distribution Notation as a part of Collaborative Statistics collection (col10522) by Barbara Illowsky and Susan Dean.

The notation for the chi-square distribution is:

χ 2 χ 2 ~ χ df 2 χ df 2

where df = df= degrees of freedom depend on how chi-square is being used. (If you want to practice calculating chi-square probabilities then use df = n - 1 df=n-1. The degrees of freedom for the three major uses are each calculated differently.)

For the χ 2 χ 2 distribution, the population mean is μ = df μ=df and the population standard deviation is σ = 2 ⋅ df σ= 2 ⋅ df .

The random variable is shown as χ 2 χ 2 but may be any upper case letter.

The random variable for a chi-square distribution with k k degrees of freedom is the sum of k k independent, squared standard normal variables.

χ 2 = ( Z 1 ) 2 + ( Z 2 ) 2 + ... + ( Z k ) 2 χ 2 =( Z 1 ) 2 +( Z 2 ) 2 +...+( Z k ) 2

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