Table of Contents
The t-distribution table is a statistical tool used to calculate critical values for the t-distribution, which is commonly used in hypothesis testing. It contains a list of t-values for different degrees of freedom and levels of significance, which can be used to determine the probability of obtaining a certain t-statistic in a sample.
To interpret the t-distribution table, one must first understand that the t-distribution is a probability distribution that is similar to the normal distribution but accounts for smaller sample sizes. The table displays the probability of obtaining a t-value equal to or greater than the value listed in the table. This can be used to determine the critical t-value for a given level of significance and degrees of freedom.
The t-distribution table is commonly used in hypothesis testing, where it is used to determine whether the results of a study are statistically significant. By comparing the calculated t-value from the sample data to the critical t-value from the table, one can determine if the results are significant or if they are likely due to chance.
In addition to hypothesis testing, the t-distribution table can also be used to calculate confidence intervals for a population mean. By using the appropriate t-value from the table, along with the sample mean and standard deviation, one can calculate the range of values within which the true population mean is likely to fall.
In summary, the t-distribution table is a valuable tool for interpreting and analyzing data in statistics. It allows for the determination of critical values, significance levels, and confidence intervals, making it an essential resource for statistical analysis.
Read the t-Distribution Table
This tutorial explains how to read and interpret .
What is the t-Distribution Table?
The t-distribution table is a table that shows the critical values of the t distribution. To use the t-distribution table, you only need to know three values:
- The degrees of freedom of the t-test
- The number of tails of the t-test (one-tailed or two-tailed)
- The alpha level of the t-test (common choices are 0.01, 0.05, and 0.10)
Here is an example of the t-Distribution table, with the degrees of freedom listed along the left side of the table and the alpha levels listed along the top of the table:
When you conduct a t-test, you can compare the test statistic from the t-test to the critical value from the t-Distribution table. If the test statistic is greater than the critical value found in the table, then you can reject the null hypothesis of the t-test and conclude that the results of the test are statistically significant.
Let’s walk through some examples of how to use the t-Distribution table.
Examples of How to Use the t-Distribution Table
The following examples explain how to use the t-Distribution table in several different scenarios.
Example #1: One-tailed t-test for a mean
A researcher recruits 20 subjects for a study and conducts a one-tailed t-test for a mean using an alpha level of 0.05.
Question: Once she conducts her one-tailed t-test and obtains a test statistic t, what critical value should she compare t to?
Answer: For a t-test with one sample, the degrees of freedom is equal to n-1, which is 20-1 = 19 in this case. The problem also tells us that she is conducting a one-tailed test and that she is using an alpha level of 0.05, so the corresponding critical value in the t-distribution table is 1.729.
Example #2: Two-tailed t-test for a mean
A researcher recruits 18 subjects for a study and conducts a two-tailed t-test for a mean using an alpha level of 0.10.
Question: Once she conducts her two-tailed t-test and obtains a test statistic t, what critical value should she compare t to?
Example #3: Determining the critical value
A researcher conducts a two-tailed t-test for a mean using a sample size of 14 and an alpha level of 0.05.
Question: What would the absolute value of her test statistic t need to be in order for her to reject the null hypothesis?
Answer: For a t-test with one sample, the degrees of freedom is equal to n-1, which is 14-1 = 13 in this case. The problem also tells us that she is conducting a two-tailed test and that she is using an alpha level of 0.05, so the corresponding critical value in the t-distribution table is 2.16. This means that she can reject the null hypothesis if the test statistic t is less than -2.16 or greater than 2.16.
Example #4: Comparing a critical value to a test statistic
A researcher conducts a right-tailed t-test for a mean using a sample size of 19 and an alpha level of 0.10.
Question: The test statistic t turns out to be 1.48. Can she reject the null hypothesis?
Answer: For a t-test with one sample, the degrees of freedom is equal to n-1, which is 19-1 = 18 in this case. The problem also tells us that she is conducting a right-tailed test (which is a one-tailed test) and that she is using an alpha level of 0.10, so the corresponding critical value in the t-distribution table is 1.33. Since her test statistic t is greater than 1.33, she can reject the null hypothesis.
Should You Use the t Table or the z Table?
One problem that students frequently encounter is determining if they should use the t-distribution table or the z table to find the critical values for a particular problem. If you’re stuck on this decision, you can use the following flow chart to determine which table you should use:
Additional Resources
For a complete list of critical value tables, including a binomial distribution table, a chi-square distribution table, a z-table, and more, check out .