Let’s suppose our significance level ( ) is 0.05. The weights are shown in the table below, where each row represents 1 person. We gauss the weights of 10 people before and after practicing the diet to verify if there is any statistical difference. Suppose we want to measure the effectiveness of a diet. divide by n-1 instead of n).Īfter getting the T-statistics and the degree of freedom, we can verify our hypothesis using the T-table (or with the help of Python, or other means) as previously described here. Note that this is the sample std, so we compute the unbiased std (i.e. as the set of differences between each observation in with the correspondence in.and as the 2 sets, where the i-th observation of ( ) is related to the i-th observation of ( ).This transformation can be elaborated by restating the problem: we want to test if the 2 sample sets are generated by the same distribution, which is identical to test if the differences between them are generated by a distribution with mean 0. Put it another way, we can transform the Paired T-test into a One-sample T-test. The Paired 2-sample T-test is just a One-sample T-test in disguise. That is, we usually assume the variances of the 2 distribution are equal, then we test if the means are also equal (both the means and variances are equal indicates that the 2 distributions are also the same) or not (implies that 2 distributions are not the same). Note that even though the tests’ general goal is to check if the means of the 2 distributions are equal or not, it is usually the case that it checks whether the 2 distributions are the same or not. In cases there are big-influencers in our data, we may choose to remove it (with care) or switch to a robust test like the Wilcoxon Signed Rank Test, which calculates the ranking thus is not impacted so much by extreme values. Outliers may bias the test, especially when the sample size is small (, which case is often for medical tests). There must not be any big-influencers (outliers). The Paired 2-sample T-test is a parametric test, thus it requires some assumptions to be true (or at least approximately true): if the conditions for a Paired Test hold). Notice that the result taken from the Paired Test is more significant than from the Unpaired Test given the same samples (because the 1-to-1 relationship gives additional information), it is recommended to take the Paired Test if possible (i.e. The sizes of the 2 sample sets must be the same. 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 that is attached with blue ads, the other contains the same measure for webpages with yellow ads. 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. 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 Paired 2-sample T-test, we also have the Unpaired 2-sample T-test. This is also abbreviated as the Paired T-test or Dependent T-test. Thus, in summary, a Paired 2-sample T-test takes as input 2 sample sets that have their observations linked to the other on a 1-to-1 basis, and the test’s outputs follow a T-distribution.

Paired means these 2 sample sets are not independent of each other, each observation in one sample set must correspond to one and only one observation in the other set.

Paired t test jmp