1.3.6.7.4. Critical Values of the Chi | Chi-square critical value
HowtoUseThisTableThistablecontainsthecriticalvaluesofthechi-squaredistribution.Becauseofthelackofsymmetryofthechi-squaredistribution,separatetablesareprovidedfortheupperandlowertailsofthedistribution.Ateststatisticwithνdegreesoffreedomiscomputedfromthedata.Forupper-tailone-sidedtests,theteststatisticiscomparedwithavaluefromthetableofupper-tailcriticalvalues.Fortwo-sidedtests,theteststatisticiscomparedwithvaluesfromboththetablefortheupper-tailcriticalvaluesandthetableforthelower-tailcriticalv...
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.