*48*

A hypothesis test is a formal statistical test we use to reject or fail to reject a statistical hypothesis.

Whether we conduct a hypothesis test for a mean, a proportion, a difference in means, or a difference in proportions, we often end up with a t statistic for our test.

Once we have a t statistic, we can then find a corresponding p-value that we can use to reject or fail to reject the null hypothesis of our test.

This tutorial explains three different ways to find a p-value from a t statistic.

**Three Ways to Find a P-Value from a t Statistic**

In each of the following examples, we’ll find the p-value for a right-tailed test with a t statistic of **1.441 **and **13 **degrees of freedom.

**Technique 1: t Score to P Value Calculator**

The first way to find a p-value from a t statistic is to use an online calculator like the T Score to P Value Calculator. We can simply enter the value for t and the degrees of freedom, then select “one-tailed”, then click the “Calculate” button:

The corresponding p-value is **0.08662**.

**Technique 2: t Distribution Table**

Another way to find the p-value for a given t statistic is to use the t distribution table.

Using the table, look up the row that has degrees of freedom (DF) = 13, then find the values that 1.441 lies between. It turns out to be 1.35 and 1.771. Next, look up at the top of the table for “one-tail” and you’ll notice that these values correspond with 0.1 and 0.05. This tells us that the corresponding p-value is somewhere between 0.05 and 0.1.

Notice the drawback of using the t distribution table: it does not tell us the exact p-value; it only gives us a range of values.

**Technique 3: TI-83 or TI-84 Calculator**

Another way to find the p-value for a given t statistic is to use a graphing calculator like a TI-83 or TI-84.

On your calculator, click **2ND VARS** (to get to **DISTR**), scroll down, and click the **tcdf** function. The syntax to use this function to find the p-value for a right-tailed test is as follows:

tcdf(smaller value, larger value, degrees of freedom)

Since we are conducting a right-tailed test, we can use 1.441 as the smaller value, 9999 as the larger value, and 13 as the degrees of freedom:

tcdf(1.441, 9999, 13)

This returns a value of **0.08662**, which matches the p-value that we got from the online calculator.