How does this calculator help me?
This calculator is helpful if you would rather not look at a table of values to locate the p-value, which is often difficult to do for new statistics students. There is not much need to learn how to learn these tables now that technology is so prevalent.
This calculator helps to convert a given t-value and the associated degrees of freedom to a probability. The three probabilities given are the left, right, and two-tailed regions of the t-distribution. You most likely only want one of these three numbers depending on your test.
The degrees of freedom, "df", is usually just the sample size subtracted by one. If you have 20 numbers in your data set, then your degrees of freedom is 19.
If you are testing whether a sample mean is smaller than another hypothesized mean, you will most likely want the left-tailed probability, as this corresponds to a left-tailed hypothesis test.
If you are testing whether a sample mean is larger than another hypothesized mean, you will most likely want the right-tailed probability, as this corresponds to a right-tailed hypothesis test.
If you are testing to see whether a sample mean is different than a hypothesized value (your hypothesis statement does not say "less than" or "greater than"), then you will most likely want the two-tailed probability, as this corresponds to a two-tailed hypothesis test.
In these scenarios, the probability is the p-value for your hypothesis test. If the p-value is smaller than a given alpha, α, then your conclusion should be to reject the null hypothesis. Your test is statistically significant. It means that the sample mean was different enough from the hypothesized value so that we are relatively sure that this result didn't happen by chance.
This video demonstrates the steps of a hypothesis test that uses t-values: