Student's t Table (Free Download) | Guide & Examples

Student’s t table is a reference table that lists critical values of t. Student’s t table is also known as the t table, t-distribution table, t-score table, t-value table, or t-test table.

A critical value of t defines the threshold for significance for certain statistical tests and the upper and lower bounds of confidence intervals for certain estimates. It is most commonly used when:

  • Testing whether two means are significantly different (two-sample t tests)
  • Testing whether two variables are significantly related (linear regression or correlation)
  • Calculating confidence intervals (of means or regression coefficients)

Download the table

The critical values of t are calculated from Student’s t distribution. Student’s t distribution is the distribution of the test statistic t. The critical values of t are difficult to calculate by hand, which is why most people use a t table or computer software instead.

Student’s t table for one- and two-tailed tests

Use the tables below to find the critical values of t or learn how to use the t table

Critical values of t for two-tailed testsCritical values of t for one-tailed tests

Download the table

How to use the t table

If you need to find a critical value of t to perform a statistical test or calculate a confidence interval, follow this step-by-step guide.

Example: A t test case study
Imagine you’re conducting a small trial for a new medicated acne cream. You randomize the participants into a treatment group that receives the acne cream and a control group that receives an unmedicated placebo cream.

To discover whether the acne cream is effective, you decide to compare the mean number of pimples on participants in the treatment and control groups using an independent samples t test.

  • Null hypothesis: The treatment group and control group participants have the same mean number of pimples.
  • Alternative hypothesis: The treatment group and control group participants differ in their mean numbers of pimples.

You calculate the t value for the sample. To know whether to reject the null hypothesis, you need to compare this t value to the critical value of t.

Step 1: Choose two-tailed or one-tailed

Two-tailed tests are used when the alternative hypothesis is non-directional.

  • A non-directional hypothesis states that a population parameter (such as a mean or regression coefficient) is not equal to a certain value (such as 0). Two-tailed tests are appropriate for most studies.
  • If you’re calculating a confidence interval, choose two-tailed.

One-tailed tests are used when the alternative hypothesis is directional.

  • A directional hypothesis states that a population parameter is greater than or less than a certain value.
  • Your alternative hypothesis is directional if it includes words such as “greater than,” “less than,” “increases,” “decreases,” or the “<” or “>” sign. If it doesn’t include these (or similar), it is probably non-directional.
Example: Choosing two-tailed or one-tailed tests
  • Alternative hypothesis: The treatment group and control group participants differ in their mean numbers of pimples.

This alternative hypothesis is non-directional. It doesn’t state whether the mean of the treatment group is greater or less than the mean of the control group, just that the means differ.

Since the alternative hypothesis is non-directional, it should be tested with a two-tailed test.

Step 2: Calculate the degrees of freedom

The degrees of freedom (df) of a statistic are calculated from the sample size (n). The equation you need to use depends on what type of test or procedure you’re performing.

Calcuting degrees of freedom (df)
Test or procedure Degrees of freedom (df) equation
  • One-sample t test
  • Confidence interval of a mean
df = n – 1
  • Independent samples t test
df = n1 + n2 – 2

Where n1 is the sample size of group 1 and n2 is the sample size of group 2

  • Dependent samples t test
df = n – 1

Where n is the number of pairs

  • Linear regression
  • Pearson correlation
  • Spearman rank correlation
  • Confidence interval of a regression coefficient
df = n – 2
Example: Calculating the degrees of freedom
The degrees of freedom (df) equation for independent t tests is

df = n1 + n2 – 2

If you conducted an experimental trial with 14 participants in the placebo group and 17 participants in the treatment group, then

df = 14 + 17 – 2

df = 29

Step 3: Choose a significance level

By convention, the significance level (α) is almost always .05. The α = .05 column is highlighted in the table since it is the most commonly used significance level.

In certain situations, you may want to decrease your risk of Type I error by decreasing α, or decrease your risk of Type II error by increasing α.

If you’re calculating a confidence interval, choose the significance level based on your desired confidence level:

α = 1 – confidence level

The most common confidence level is 95% (or .95, when expressed as a proportion), corresponding to α = .05.

Example: Choosing a significance level
You choose α = .05 to test your hypothesis, since this is the significance level used by most researchers.

Step 4: Find the critical value of t in the t table

Now that you know whether your test is two-tailed or one-tailed, the degrees of freedom (df), and the significance level, you have all the information you need to use the t table.

  • If the test is two-tailed or if you’re calculating a confidence interval, use the first table. If the test is one-tailed, use the second table.
  • The degrees of freedom (df) are listed along the left side of the table. Find the table row for the df you calculated in Step 2. If you need a df that isn’t listed, then round down to the next smallest number (e.g., use df = 40 instead of df = 46).
  • The significance levels are listed along the top of the table. Find the column for the significance level that you chose in Step 3. In most cases, you will use the highlighted column (α = .05).
  • The critical value of t for your test is found where the row and column meet.
Example: Finding the critical value of t in the t table
Using the t table, you find that for a two-tailed test with df = 29 and α = .05 the critical value of t is 2.045.

You can now compare this critical value of t to the t that you calculated for your sample. This comparison will allow you to decide whether to reject the null hypothesis.

t table interpretation

What can proofreading do for your paper?

Scribbr editors not only correct grammar and spelling mistakes, but also strengthen your writing by making sure your paper is free of vague language, redundant words and awkward phrasing.

See editing example

Practice questions

powered by Typeform

Frequently asked questions about Student's t table

How do I find the critical value of t in R?

You can use the qt() function to find the critical value of t in R. The function gives the critical value of t for the one-tailed test. If you want the critical value of t for a two-tailed test, divide the significance level by two.

Example: Calculating the critical value of t in R
To calculate the critical value of t for a two-tailed test with df = 29 and α = .05:

qt(p = .025, df = 29)

How do I find the critical value of t in Excel?

You can use the T.INV() function to find the critical value of t for one-tailed tests in Excel, and you can use the T.INV.2T() function for two-tailed tests.

Example: Calculating the critical value of t in Excel
To calculate the critical value of t for a two-tailed test with df = 29 and α = .05, click any blank cell and type:

=T.INV.2T(0.05,29)

How do I test a hypothesis using the critical value of t?

To test a hypothesis using the critical value of t, follow these four steps:

  1. Calculate the t value for your sample.
  2. Find the critical value of t in the t table.
  3. Determine if the (absolute) t value is greater than the critical value of t.
  4. Reject the null hypothesis if the sample’s t value is greater than the critical value of t. Otherwise, don’t reject the null hypothesis.
How do I calculate a confidence interval of a mean using the critical value of t?

To calculate a confidence interval of a mean using the critical value of t, follow these four steps:

  1. Choose the significance level based on your desired confidence level. The most common confidence level is 95%, which corresponds to α = .05 in the two-tailed t table.
  2. Find the critical value of t in the two-tailed t table.
  3. Multiply the critical value of t by s/n.
  4. Add this value to the mean to calculate the upper limit of the confidence interval, and subtract this value from the mean to calculate the lower limit.
Why is the t distribution also called Student’s t distribution?

The t distribution was first described by statistician William Sealy Gosset under the pseudonym “Student.”

Is this article helpful?
Shaun Turney

During his MSc and PhD, Shaun learned how to apply scientific and statistical methods to his research in ecology. Now he loves to teach students how to collect and analyze data for their own theses and research projects.