In this tutorial, we are going to use data visualization to guide our interpretation of the paired sample t-test. In this post, we will use Pandas import data into a dataframe and to calculate summary statistics.
Pandas is also a very great Python package for someone carrying out data analysis with Python, whether a data scientist or a psychologist. This means, of course, that if you are going to carry out the data analysis using Pingouin you will get SciPy installed anyway. In this tutorial, we are going to use it to test the assumption of normality as well as carry out the paired sample t-test. This package is, furthermore, a dependency of all the other packages that we are going to use in this tutorial. SciPy is one of the essential data science packages. In the next three subsections, you will find a brief description of each of these packages. Finally, we are also going to use Seaborn to visualize the data. Furthermore, to read the dataset we are going to use Pandas. In this tutorial, we are going to use both SciPy and Pingouin, two great Python packages, to carry out the dependent sample t-test.
Python Paired Sample T-test using SciPy.That's true of many of the commonly used hypothesis tests - that the null (when combined with the assumptions) amounts to assuming equal distributions. The assumption of equal variances is the default for the scipy implementation of this test, but set otherwise it doesn't assume equal variances and then the null doesn't imply that distributions are the same. Usually the hypothesis that people wish to test with this hypothesis test is $H_0: \mu_X=\mu_Y$, but when accompanied by the assumptions of the usual equal variance two sample t-test, that's the same as saying they come from the same distribution. Therefore I'm thinking what they really mean is that the Null Hypothesis is that both samples come from the same distribution. However, you were understandably misled by it and if a student wrote that I would certainly mark it wrong (since it does seem to suggest that it is the sample means being tested for equality, just as it did to you). Is a reference to the population means not the sample means it is otherwise misleading and should certainly be clearer but they do t least say "(expected) values", which can only be a reference to population means from which the samples were drawn. This is a two-sided test for the null hypothesis that 2 independent samples have identical average (expected) values.
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