T-test
The idea behind parametric tests is to provide the researcher with a statistical inference about the population by conducting statistically significant tests (like t-test) on the sample drawn from the population. The parametric test called t-test is based on a student’s t statistic. This statistic assumes that the normal population draws variables. This statistic of the t-test assumes that researchers know the population mean. The distribution, called t-distribution, has a similar shape to that of a normal distribution, i.e. a bell shaped appearance.
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The parametric test called t-test is useful for testing those samples whose size is less than 30. The reason behind this is that if the size of the sample is more than 30, then the distribution of the t-test and the normal distribution will not be distinguishable.
Researchers use the parametric test to conduct statistically significant tests in hypothesis testing. There are basically three types of t-tests: one sample, two independent sample and paired.
In the case of a one sample, if a researcher in the field of psychology is working on a study where he wants to make sure that at least 65% of students will pass the IQ test, he can use the t-test. They will use the one-sample test after formulating the hypothesis in this particular case. The parametric test is then calculated by selecting an appropriate formula of t-test. In this case, the appropriate formula will be a test for a single mean. They select the level of significance to check the t-test of the null hypothesis.
Usually, the researcher takes 0.05 as the appropriate level of significance while conducting it. The level of significance refers to the minimum probability that there will be a false rejection of the null hypothesis. If the calculated value exceeds the tabulated value, researchers reject the null hypothesis. Similarly, if the calculated value is less than the tabulated value, researchers accept the null hypothesis.
In two independent samples, two samples that are not at all related to each other are tested. The two independent samples compare two independent data samples to draw statistical inferences. For example, in psychology, a two independent samples is useful to compare the IQ levels of students in region A and region B. The region A and the region B are not at all related to each other, i.e. they are independent of each other. The procedure for conducting it is the same, except that now the sample number is double instead of single. Also, in the case of t-test for single mean and two independent samples, there are different formulas for the degree of freedom. The degree of freedom is referred to as the restriction that a researcher puts forward while conducting parametric tests, like t-test in this case.
The paired sample refers to that type of sample in which the variables form paired categories. A paired sample compares male and female smokers, such as chain smokers or occasional smokers.
Reference:
Introduction to the theory of statistics: Mood A.M., Graybill F.A., Boes D.C