This tutorial explains how to read and interpret the t-Distribution table. Show
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:
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 TableThe following examples explain how to use the t-Distribution table in several different scenarios. Example #1: One-tailed t-test for a meanA 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 meanA 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? Answer: For a t-test with one sample, the degrees of freedom is equal to n-1, which is 18-1 = 17 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 0.10, so the corresponding critical value in the t-distribution table is 1.74. Example #3: Determining the critical valueA 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 statisticA 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 ResourcesFor a complete list of critical value tables, including a binomial distribution table, a chi-square distribution table, a z-table, and more, check out this page. How do you use tThe t-value measures the size of the difference relative to the variation in your sample data. Put another way, T is simply the calculated difference represented in units of standard error. The greater the magnitude of T, the greater the evidence against the null hypothesis.
What is the T table for?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)
How do you find tTo find the t value: Subtract the null hypothesis mean from the sample mean value. Divide the difference by the standard deviation of the sample. Multiply the resultant with the square root of the sample size.
How do you find the tFind the critical value of t in the two-tailed t table. Multiply the critical value of t by s/√n. 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.
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