For some random webpages, we show ads with blue-colored themes, while for the other webpages, yellow-colored theme ads are shown. We want to test if the weight is significantly different for different genders. There are 2 sample sets, one is the weights of 30 men and the other is the weights of 30 women. We compare these 2 sets to see if one color is significantly more attractive than the other. After a day, we have 2 sets of sample data, one contains the average click-through rate (for ads) of each webpage when blue ads are shown, the other contains the same measure for yellow ads. For each of our webpages, blue-colored theme ads are shown for some guests while yellow-colored theme ads are shown to the others. We measure the performance of our company’s employees before and after learning the course to see if this course enhances employee productivity. When the requirement of correspondence for the Paired 2-sample T-test does not hold. When each observation in a sample set is semantically related to one and only one observation in the other set. In contrast to the Unpaired 2-sample T-test, we also have the Paired 2-sample T-test. This is also abbreviated as an Unpaired T-test or Independent T-test.
Thus, in summary, an Unpaired 2-sample T-test takes as input 2 sample sets that are independent of each other, and the test’s outputs follow a T-distribution. Unpaired means these 2 sample sets are independent of each other, each observation in one sample set does NOT correspond to one and only one observation in the other set (it is opposite to the case of Paired Test).
Two-sample means we have 2 sets of samples, and our target is to verify if the means of the 2 distributions that generate these 2 sample sets are equal. A T-test is a statistical test whose outcomes follow a T-distribution. Let’s analyze this definition from scratch.