ChiSquare (Χ²) Table  Examples & Downloadable Table
The chisquare (Χ^{2}) distribution table is a reference table that lists chisquare critical values. A chisquare critical value is a threshold for statistical significance for certain hypothesis tests and defines confidence intervals for certain parameters.
Chisquare critical values are calculated from chisquare distributions. They’re difficult to calculate by hand, which is why most people use a reference table or statistical software instead.
Download chisquare table (PDF)
When to use a chisquare distribution table
You will need a chisquare critical value if you want to:
 Calculate a confidence interval for a population variance or standard deviation
 Test whether the variance or standard deviation of a population is equal to a certain value (test of a single variance)
 Test whether the frequency distribution of a categorical variable is different from your expectations (chisquare goodness of fit test)
 Test whether two categorical variables are related to each other (chisquare test of independence)
 Test whether the proportions of two closely related variables are equal (McNemar’s test)
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Chisquare distribution table (righttail probabilities)
Use the table below to find the chisquare critical value for your chisquare test or confidence interval or download the chisquare distribution table (PDF).
The table provides the righttail probabilities. If you need the lefttail probabilities, you’ll need to make a small additional calculation.
How to use the table
To find the chisquare critical value for your hypothesis test or confidence interval, follow the three steps below.
Step 1: Calculate the degrees of freedom
There isn’t just one chisquare distribution—there are many, and their shapes differ depending on a parameter called “degrees of freedom” (also referred to as df or k). Each row of the chisquare distribution table represents a chisquare distribution with a different df.
You need to use the distribution with the correct df for your test or confidence interval. The table below gives equations to calculate df for several common procedures:
Test or procedure  Degrees of freedom (df) equation 

Test of a single variance
Confidence interval for variance or standard deviation 
df = sample size − 1 
Chisquare goodness of fit test  df = number of groups − 1 
Chisquare test of independence  df = (number of variable 1 groups − 1) * (number of variable 2 groups − 1) 
McNemar’s test  df = 1 
Step 2: Choose a significance level
The columns of the chisquare distribution table indicate the significance level of the critical value. By convention, the significance level (α) is almost always .05, so the column for .05 is highlighted in the table.
In rare situations, you may want to increase α to decrease your Type II error rate or decrease α to decrease your Type I error rate.
To calculate a confidence interval, choose the significance level based on your desired confidence level:
α = 1 − confidence level
The most common confidence level is 95% (.95), which corresponds to α = .05.
Step 3: Find the critical value in the table
You now have the two numbers you need to find your critical value in the chisquare distribution table:
 The degrees of freedom (df) are listed along the lefthand side of the table. Find the table row corresponding to the degrees of freedom you calculated.
 The significance levels (α) are listed along the top of the table. Find the column corresponding to your chosen significance level.
 The table cell where the row and column meet is your critical value.
Lefttailed and twotailed probabilities
The table provided here gives the righttail probabilities. You should use this table for most chisquare tests, including the chisquare goodness of fit test and the chisquare test of independence, and McNemar’s test.
If you want to perform a twotailed or lefttailed test, you’ll need to make a small additional calculation.
Lefttailed tests
The most common lefttailed test is the test of a single variance when determining whether a population’s variance or standard deviation is less than a certain value.
To find the critical value for a lefttailed probability in the table above, simply use the table column for 1 − α.
Twotailed tests
The most common lefttailed test is the test of a single variance when determining whether a population’s variance or standard deviation is equal to a certain value.
A twotailed test has two critical values. To find the critical values, use the table columns for and .
Practice questions
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Frequently asked questions about chisquare tables
 How do I find a chisquare critical value in R?

You can use the qchisq() function to find a chisquare critical value in R.
For example, to calculate the chisquare critical value for a test with df = 22 and α = .05:
qchisq(p = .05, df = 22, lower.tail = FALSE)
 How do I find a chisquare critical value in Excel?

You can use the CHISQ.INV.RT() function to find a chisquare critical value in Excel.
For example, to calculate the chisquare critical value for a test with df = 22 and α = .05, click any blank cell and type:
=CHISQ.INV.RT(0.05,22)
 What properties does the chisquare distribution have?

A chisquare distribution is a continuous probability distribution. The shape of a chisquare distribution depends on its degrees of freedom, k. The mean of a chisquare distribution is equal to its degrees of freedom (k) and the variance is 2k. The range is 0 to ∞.
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