We have learned the following things about a t-test:
Converting from t-values to p-values is usually done by software but you can do it by hand by looking values up in a table. This page explains how.
- The t-test produces a single value, t, which grows larger as the difference between the means of two samples grows larger;
- t does not cover a fixed range such as 0 to 1 like probabilities do;
- You can convert a t-value into a probability, called a p-value;
- The p-value is always between 0 and 1 and it tells you the probability of the difference in your data being due to sampling error;
- The p-value should be lower than a chosen significance level (0.05 for example) before you can reject your null hypothesis.
T-tables are filled with t-values. Each t-value is in a column that is specific to a given significance level. The t-values shown in the table are known as critical values. If your t-value is greater than or equal to the critical value in the table, then you can conclude that your p-value is less than the significance level you have chosen. The procedure is simple. Once you have chosen your significance level you look to see whether your t-value is larger than the critical t-value shown in the column relating to your chosen significance level. If it is, then you can say that p is less than your chosen significance level.
The t-table has more than one row of t-values. Each row corresponds to a given number of degrees of freedom. Degrees of freedom are explained at level on of this topic. Use the row of the table that corresponds to the degrees of freedom in your data.
The final thing that you need to know about using t-tables is that you must read them differently depending on whether your test is one-tailed or two-tailed. The rule is simple enough:
The p-value for a two tailed test is twice what it would be for a one tailed test.
Some tables (such as the ones on this page) show a p-value heading for both one and two-tailed tests to make it easier. If your test is one tailed, find the p-value you need in the top row. If your test is two tailed, find your p-value in the second row. Notice how the p-values for the two tailed test are simply double those for the one tailed test.
Unfortunately, some tables show only one-tailed values and some show only two-tailed values. If you are using a table from a book or from the internet, make sure you know what it shows. You can easily convert from one to two or two to one by remembering the p for two-tailed tests is twice what it is for one-tailed tests.
Reporting p-Values and t-Values
You report the results of a t-test in the following way:
Where df is the degrees of freedom of your data, t is the t-value you found and p is the p-value you found.