Exploratory Data Analysis
1.3. EDA Techniques
1.3.6. Probability Distributions
18.104.22.168. Tables for Probability Distributions
|How to Use This Table
This table contains the critical values of the
chi-square distribution. Because of the
lack of symmetry of the chi-square distribution, separate tables are
provided for the upper and lower tails of the distribution.
A test statistic with ν degrees of freedom is computed from the data. For upper-tail one-sided tests, the test statistic is compared with a value from the table of upper-tail critical values. For two-sided tests, the test statistic is compared with values from both the table for the upper-tail critical values and the table for the lower-tail critical values.
The significance level, α, is demonstrated with the graph below which shows a chi-square distribution with 3 degrees of freedom for a two-sided test at significance level α = 0.05. If the test statistic is greater than the upper-tail critical value or less than the lower-tail critical value, we reject the null hypothesis. Specific instructions are given below.
Given a specified value of α:
Upper-tail critical values of chi-square distribution with ν degrees of freedom
Probability less than the critical value ν 0.90 0.95 0.975 0.99 0.999
Lower-tail critical values of chi-square distribution with ν degrees of freedom
Probability less than the critical value ν 0.10 0.05 0.025 0.01 0.001