## Test of Correlation

Power (also called true positive rate, hit rate, sensitivity, or recall) is defined as $$1 - \beta$$ It is the probability of a statistical test to detect an efect of a given size. Therefore, designing an experiment to have a good chance to find an efect means making sure its power is high enough. High power is a necessary condition for valid inference. A high power value can be considered when the proportion of significant results is about 0.8 or higher.

## 2-sample t-test for independent samples

Two-sample t-test tests the hypothesis $$H_0: \mu_x-\mu_y=\delta=0$$, where $$\mu_x$$ and $$\mu_y$$ are the means of each sample. The present application generates 2000 times a pair of samples based on the parameters that are entered below and at each iteration performs a t-test and calculates the accompanying p-value. Power is the proportion of times where the test actually gave a signicant result (p<0.05).