STRAIGHT STATISTICS

Critical Values of the Chi-Square Distribution

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: For a two-sided test, find the column corresponding to 1-α/2 in the table for upper-tail critical values and reject the null hypothesis if the test statistic is greater than the tabled value. Similarly, find the column corresponding to α/2 in the table for lower-tail critical values and reject the null hypothesis if the test statistic is less than the tabled value. For an upper-tail one-sided test, find the column corresponding to 1-α in the table containing upper-tail critical and reject the null hypothesis if the test statistic is greater than the tabled value. For a lower-tail one-sided test, find the column corresponding to α in the lower-tail critical values table and reject the null hypothesis if the computed test statistic is less than the tabled value.  By; J-Lynn B. Ramos