A common question when comparing two sets of measurements is whether to use the parametric testing procedure or nonparametric. Most often, using a simulation, several parametric and nonparametric tests are compared, such as a t-test, normal test (parametric criteria), Wilcoxon level, Van der Walden estimates, etc. (nonparametric).
Parametric tests assume basic statistical distributions in the data. Therefore, it is necessary to fulfill several conditions of reality so that their result is reliable. Nonparametric tests are independent of any distribution. Thus, they can be applied even if the parametric conditions of reality are not satisfied. In this article we will consider the parametric method, namely, the student correlation coefficient.
Parametric method for comparing 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 kinds of student coefficient are parametric methods.
They are often those methods in the analysis of which we see that the subject is approximately normal, therefore, before using the criterion, a check for normality should be carried out. That is, the placement of signs in the student distribution table (in both samples) should not differ significantly from the normal one and must correspond or approximately agree with the specified parameter. For a normal distribution, there are two indicators: mean and standard deviation.
The use of the t student test is performed when testing hypotheses. It allows you to check the assumption applicable to the subjects. Most often, this criterion is used to check whether the average values in two samples are equal, but can also be applied to one.
It should be added that the advantage of using a parametric test instead of a nonparametric test is that the former will have greater statistical power than the latter. In other words, a parametric test is more capable of leading to a rejection of the null hypothesis.
T-student criteria for one sample
The application of the Student coefficient for one sample is a statistical procedure used to determine whether an observation sample can be created by a process with a special mean value. Suppose the average value of the trait under consideration M x is different from a certain known value of A. This means that we can put forward hypotheses H 0 and H 1. Using the t-empirical formula for one sample, we can check which of these hypotheses are valid.
The formula for the empirical value of the t-student criterion:
T-student criteria for independent samples
An independent student coefficient is its use when two separate sets of independent and equally distributed samples are obtained, one from each of the two compared comparisons. With an independent assumption, it is assumed that the members of the two samples do not constitute a pair of correlating values of the attribute. For example, suppose we evaluate the effect of 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 draw up the statistical hypotheses H 0 and H 1 and test them using the formulas given to us.
Formulas for the empirical value of the t-student criterion:
Formula 1 can be used for approximate calculations, for those that are close in number of samples, and formula 2 - for clear calculations, when the samples differ markedly in number.
T-student criteria for dependent samples
Paired t-tests usually consist of matching pairs of identical units or one group of units that has been tested twice (“re-measurement” of the t-test). When we have dependent samples or two series of data that are positively correlated with each other, we can accordingly draw up the statistical hypotheses H 0 and H 1 and test them using the empirical formula of the t-student criterion given to us.
For example, subjects are tested before treatment with high blood pressure and are tested again after treatment with the drug to reduce it. Comparing the same indicators of patients before and after treatment, we effectively use each of them as our own control.
Thus, the correct rejection of the null hypothesis can become much more likely, with the statistical power increasing simply because the random variation between patients is now eliminated. Please note, however, that the increase in statistical power is estimated: more tests are required, each subject must be double checked.
Conclusion
A form of testing hypotheses, Student's coefficient is just one of many options used for this purpose. Statisticians should additionally use methods other than the t-test to study more variables with large sample sizes.