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This is a question I have when I am doing a research project in social science.

I have a control group A and experiment group B. At point 0, A and B received a test. After some time, at point 1, A and B received the test again. During that time, only B was treated with treatment T.

I want to test if treatment T improved the performance in test.

I don't know what test to use in this case. Thanks!

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    Probably better to ask this at Cross-Validated. – 2017-01-17
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    How you measuring successes/performance? – 2017-01-17
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    @spiceisdarkgreen. Very basic statistics questions such as this one often get good answers on this site. I would routinely recommend Cross-Validated for questions with that have a largely multivariate, 'big-data', or data mining flavor. – 2017-01-17

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I assume you have test scores at both time points. Call the original scores $X_i$ and the scores after treatment $Y_i.$ Assuming scores are nearly normally distributed, you should do a paired t test to compare performance before and after. Let $D_i = Y_i - X_i.$ Then the t statistic is

$$T = \frac{\bar D}{S_D/\sqrt{n}},$$

where $\bar D$ and $S_D$ are the sample mean and SD, respectively, of the differences, and $n$ is the number of subjects.

Reject for large values of $T$ if you are testing the one-sided research hypothesis that the treatment improves scores, and for large values of $|T|$ if you are testing the two-sided research hypothesis that the treatment changes the scores. You can find critical values in a printed table of Student's t distribution. Or you can use a statistical software package to do the computations and give you a P-value.

If test scores are not nearly normally distributed, you should do a Wilcoxon signed-rank test (not to be confused with a Wilcoxon rank sum test). This test is explained in most elementary statistics books, and computations can be done with most statistical software.