Calculate Critical t-Value in R (3 Examples)

 

In this article, I’ll illustrate how to calculate critical t-values in R.

Table of contents:

So without further additions, let’s dive right into the examples.

 

Example 1: Calculate Critical t-Value of One-Tailed t-Test

The following R programming code illustrates how to compute the critical t-values for a one-sided t-test.

In this example, we are using a confidence level of 0.05 with five degrees of freedom.

For this, we can apply the abs and qt functions as shown below:

abs(qt(p = 0.05, df = 5))                                  # 95% confidence, 5 DF, one-sided
# [1] 2.015048

The RStudio console returns the result: Student’s t critical value for a one-sided confidence interval with p = 0.05 and df = 5 is 2.015048.

 

Example 2: Calculate Critical t-Value of Two-Tailed t-Test

This example illustrates how to compute critical values for a two-sided t-test.

For this, we simply have to divide our confidence level by 2 within the qt function (i.e. p = 0.05 / 2):

abs(qt(p = 0.05 / 2, df = 5))                              # 95% confidence, 5 DF, two-sided
# [1] 2.570582

In this case, the critical value is 2.570582.

 

Example 3: Create Matrix of Critical t-Values

In case you want to look up a larger amount of t-statistic values for different confidence levels and degrees of freedom, you may create your own table of critical t-values.

First, we have to specify the confidence levels that we want to calculate:

conf_levels <- c(0.0001, 0.001, 0.01, 0.05, 0.1)           # Vector of confidence levels

Next, we can create a table where each column corresponds to different degrees of freedom:

data_t <- round(data.frame(DF1 = abs(qt(p = conf_levels, df = 1)),  # Create data.frame
                           DF2 = abs(qt(p = conf_levels, df = 2)),
                           DF3 = abs(qt(p = conf_levels, df = 3)),
                           DF4 = abs(qt(p = conf_levels, df = 4)),
                           DF5 = abs(qt(p = conf_levels, df = 5)),
                           DF10 = abs(qt(p = conf_levels, df = 10)),
                           DF25 = abs(qt(p = conf_levels, df = 25)),
                           DF50 = abs(qt(p = conf_levels, df = 50))), 2)
rownames(data_t) <- conf_levels

Finally, we can print our matrix of critical Student’s t values:

data_t                                                     # Print data frame

 

table 1 data frame critical t value

 

Video, Further Resources & Summary

I have recently published a video on my YouTube channel, which explains the contents of this tutorial. You can find the video below.

 

The YouTube video will be added soon.

 

In addition, you might have a look at the other tutorials which I have published on my website. A selection of interesting articles about statistics in R can be found below:

 

Summary: In this article, I have illustrated how to find critical t-statistic values in the R programming language. In case you have additional questions, tell me about it in the comments section below.

 

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