A common question when comparing two sets of measurements is whether to use a parametric or non-parametric testing procedure. Most often, several parametric and non-parametric tests are compared using simulation, such as the t-test, normal test (parametric tests), Wilcoxon levels, Van der Walden scores, etc. (non-parametric).
Parametric tests assume underlying statistical distributions in the data. Therefore, several conditions of reality must be satisfied for their result to be reliable. Nonparametric tests do not depend on any distribution. Thus, they can be applied even if the parametric reality conditions are not met. In this article, we will consider the parametric method, namely, the Student's correlation coefficient.
Parametric comparison of samples (t-Student)
Methods are classified based on what we know about the subjects we are analyzing. The basic idea is that there is a set of fixed parameters that define a probabilistic model. All types of Student's coefficient are parametric methods.
These are often those methods, when analyzed, we see that the subject is approximately normal, so before using the criterion, you should check for normality. That is, the placement of features in the Student's distribution table (in both samples) should not differ significantly from the normal one and should correspond or approximately agree with the specified parameter. For a normal distribution, there are two measures: the mean and the standard deviation.
Student's t-test is applied when testing hypotheses. It allows you to test the assumption applicable to the subjects. The most common use of this test is to test whether the means of two samples are equal, but it can also be applied to a single sample.
It should be added that the advantage of using a parametric test instead of a nonparametric one is that the former will have more statistical power than the latter. In other words, a parametric test is more likely to lead to the rejection of the null hypothesis.
Single sample t-Student tests
A single-sample Student's quotient is a statistical procedure used to determine whether a sample of observations can be generated by a process with a special mean. Suppose the average value of the considered feature Mхis different from a certain known value of A. This means that we can hypothesize H0 and H1. With the help of the t-empirical formula for one sample, we can check which of these hypotheses we have assumed is correct.
The formula for the empirical value of Student's t-test:
Student t-tests for independent samples
The independent Student's quotient is the use of it when two separate sets of independent and equally distributed samples are obtained, one from each of the two comparisons being compared. Under the independent assumption, it is assumed that the members of the two samples will not form a pair of correlated feature values. For example, suppose we evaluate the effect of a medical treatment and enroll 100 patients in our study, then randomly assign 50 patients to the treatment group and 50 to the control group. In this case, we have two independent samples, respectively, we can formulate the statistical hypotheses H0 and H1and test them using the formulas given to us.
Formulas for the empirical value of Student's t-test:
Formula 1 can be used for approximate calculations, for samples close in number, and formula 2 for accurate calculations, when samples differ markedly in number.
T-Student test for dependent samples
Paired t-tests usually consist of matching pairs of the same units orone group of units that was double-tested (the "re-measurement" t-test). When we have dependent samples or two data series that are positively correlated with each other, we can, respectively, formulate the statistical hypotheses H0 and H1 and check them using the formula given to us for the empirical value of the Student's t-test.
For example, subjects are tested before treatment for high blood pressure and tested again after treatment with a blood pressure lowering drug. By comparing the same patient scores before and after treatment, we effectively use each one as our own control.
Thus, correctly rejecting the null hypothesis can become much more likely, with statistical power increasing simply because random variation between patients is now eliminated. Note, however, that the increase in statistical power comes by evaluation: more tests are required, each subject must be double-checked.
Conclusion
A form of hypothesis testing, the Student's quotient is just one of many options used for this purpose. Statisticians should additionally use methods other than the t-test to examine more variables with larger sample sizes.
