How to Read a t-Distribution Table (Step by Step)

A t-distribution table gives you critical values of Student’s t-distribution — the cut-off points you compare a test statistic against, or use to build a confidence interval, when you are working with a small sample and do not know the population standard deviation.

Each critical value depends on two things: the degrees of freedom (which depend on your sample size) and the significance level (how strict you want to be). Reading the table is just a matter of finding the row and column where those two meet.

The rows of a t-table are labelled by degrees of freedom (df). For a one-sample t-test or a confidence interval for a single mean, the degrees of freedom are the sample size minus one:

So a sample of 15 observations has 14 degrees of freedom — you would use row 14. As the degrees of freedom grow, the t-distribution gets closer and closer to the standard normal (z) distribution.

The columns are labelled by significance level (alpha), and it matters whether your test is one-tailed or two-tailed:

• One-tailed — you are testing for a difference in a single direction (greater than, or less than). Use the column for your alpha, e.g. 0.05.
• Two-tailed — you are testing for any difference (not equal). Split alpha between the two tails, so a 0.05 two-tailed test uses the 0.025 column.

Find the row for your degrees of freedom and the column for your (adjusted) alpha. The number where they meet is your critical t-value. For example, with df = 14 and a two-tailed test at α = 0.05 (the 0.025 column), the critical value is about 2.145.

That means: for a confidence interval, you multiply the standard error by 2.145; for a hypothesis test, you reject the null hypothesis if your calculated t-statistic is more extreme than ±2.145.

You measure 10 samples and want a 95% confidence interval for the mean:

1. Degrees of freedom: n − 1 = 10 − 1 = 9.
2. Confidence interval → two-tailed → use the 0.025 column.
3. Row 9, column 0.025 gives a critical value of about 2.262.
4. The interval is the sample mean ± 2.262 × the standard error.

Use the t-table when the sample is small and the population standard deviation is unknown (the usual real-world case). Use the z-table when the population standard deviation is known or the sample is large — beyond about 30 degrees of freedom, the two are almost identical, which is why many t-tables stop there and hand off to z.