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The t-test is a statistical test that is used to determine if there is a significant difference between the mean or average scores of two groups. The t-test essentially does two things:
First, it determines if the means are sufficiently different from each other to say that they belong to two distinct groups. This is done by getting the average score of each group, and then getting the difference of the two means.
Let's say you want to compare two different methods in teaching vocabulary to see which one is more effective. You will get two groups of students and then use one method (Method 1) to teach Group A, and then another method (Method 2) to teach Group B the same set of words. Afterwards, you give both groups a 100-item vocabulary test, and then get the average of each group. If Group A scored an average of 90 points and Group B got an average score of 80 points, the difference between the two scores would be 10 points.
Second, the T-Test also takes into account the variability in scores of the two groups. This is called the standard error, which simply answers the question: "how far is each score from the group mean?" If scores do not deviate far from the mean, the standard error will be low, which is what you want. But if there is a lot of fluctuation in the scores, you will get a high standard error.
The difference between means, with the standard error taken into account, will give a T-Value. The T-Value is the basis for determining if the 10-point difference is enough for you to conclude that Method 1 is more effective in teaching vocabulary than Method 2, or if that result is something that could have happened by chance.