How to Find the Chi-Square Critical Value in R


When you conduct a Chi-Square test, you will get a test statistic as a result. To determine if the results of the Chi-Square test are statistically significant, you can compare the test statistic to a Chi-Square critical value. If the test statistic is greater than the Chi-Square critical value, then the results of the test are statistically significant.

The Chi-Square critical value can be found by using a Chi-Square distribution table or by using statistical software.

To find the Chi-Square critical value, you need:

  • A significance level (common choices are 0.01, 0.05, and 0.10)
  • Degrees of freedom

Using these two values, you can determine the Chi-Square value to be compared with the test statistic.

How to Find the Chi-Square Critical Value in R

To find the Chi-Square critical value in R, you can use the qchisq() function, which uses the following syntax:

qchisq(p, df, lower.tail=TRUE)

where:

  • p: The significance level to use
  • df: The degrees of freedom
  • lower.tail: If TRUE, the probability to the left of in the F distribution is returned. If FALSE, the probability to the right is returned. Default is TRUE.

This function returns the critical value from the Chi-Square distribution based on the significance level and degrees of freedom provided.

For example, suppose we would like to find the Chi-Square critical value for a significance level of 0.05 and degrees of freedom = 11.

#find Chi-Square critical value
qchisq(p=.05, df=11, lower.tail=FALSE)

[1] 19.67514

The Chi-Square critical value for a significance level of 0.05 and degrees of freedom = 11 is 19.67514.

Thus, if we’re conducting some type of Chi-Square test then we can compare the Chi-Square test statistic to 19.67514. If the test statistic is greater than 19.67514, then the results of the test are statistically significant.

Note that smaller values of alpha will lead to larger Chi-Square critical values. For example, consider the Chi-Square critical value for a significance level of 0.01, and degrees of freedom = 11. 

#find Chi-Square critical value
qchisq(p=.01, df=11, lower.tail=FALSE)

[1] 24.72497

And consider the Chi-Square critical value with the exact same degrees of freedom, but with a significance level of 0.005:

#find Chi-Square critical value
qchisq(p=.005, df=11, lower.tail=FALSE)

[1] 26.75685

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