How to Find t Critical Values in R


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

The t critical value can be found by using a t distribution table or by using statistical software.

To find the t critical value, you need to specify:

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

Using these two values, you can determine the t critical value to be compared with the test statistic.

How to Find the T Critical Value in R

To find the T critical value in R, you can use the qt() function, which uses the following syntax:

qt(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 t distribution is returned. If FALSE, the probability to the right is returned. Default is TRUE.

The following examples illustrate how to find the t critical value for a left-tailed test, right-tailed test, and a two-tailed test.

Left-tailed test 

Suppose we want to find the t critical value for a left-tailed test with a significance level of .05 and degrees of freedom = 22:

#find t critical value
qt(p=.05, df=22, lower.tail=TRUE)

[1] -1.717144

The t critical value is -1.7171. Thus, if the test statistic is less than this value, the results of the test are statistically significant.

Right-tailed test 

Suppose we want to find the t critical value for a right-tailed test with a significance level of .05 and degrees of freedom = 22:

#find t critical value
qt(p=.05, df=22, lower.tail=FALSE)

[1] 1.717144 

The t critical value is 1.7171. Thus, if the test statistic is greater than this value, the results of the test are statistically significant.

Two-tailed test 

Suppose we want to find the t critical values for a two-tailed test with a significance level of .05 and degrees of freedom = 22:

#find two-tailed t critical values
qt(p=.05/2, df=22, lower.tail=FALSE)

[1] 2.073873

Whenever you perform a two-tailed test, there will be two critical values. In this case, the T critical values are 2.0739 and -2.0739. Thus, if the test statistic is less than -2.0739 or greater than 2.0739, the results of the test are statistically significant.

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