T-test Calculation

Calculating the T-test for Comparing Two Means

Calculating the G-statistic | Critical values for G- and t-tests, and Chi-square

The t-test is often used to calculate the significance of observed differences between the means of two samples. The t-test is generally used with scalar variables, such as length and width, and so on. The null hypothesis is that there are no significant difference between the means.

As in the G-test, we first calculate a test statistic, t, and then compare that value to the critical t-value in a table for a given degrees of freedom. To calculate your t-value, you need to first calculate the mean (x bar) and the sample variance (s2) of EACH of your samples. Most hand-held calculators will perform these calculations for you. However, if you do not know how to use your calculator, you can do it by hand with the following method:

1) First, calculate the variance in each of your samples:

2) Second, calculate the t-value

3) Third, calculate the degrees of freedom

Calculate the degrees of freedom by adding the samples of both means (n) which leads to the overall sample size (N).
N = n1 +n2 and df = N –1

4) Compare your t-value with the critical t-value

For a given df, if your t-value is larger than than the value in the table, the null hypothesis of no difference between the means should be rejected. Again, biologists use a p-value of 0.05 or less as an indicator of significance.

5) Report the results of your t-test

"We found no significant difference between the weights of the dominant and subordinate males (t = 0.73, p > 0.05, d.f. = 15)."

OR if you did find an effect:

"Dominant males weighed significantly more than subordinates (t = 6.73, p < 0.05, d.f. = 15)."