The process of carrying out the t-test involves the single interval dependent variable and a dichotomous independent variable when the researcher wishes to conduct the t-test for the difference of means. The process of the t-test is also used for making a comparison in the means for two dependent samples and two independent samples. The process of the t-test is also used to carry out a test between a sample mean and a known mean, which is also called the t-test for one sample.
The t-test is basically parametric test that makes a very popular assumption, which is that of normal distribution. It should be further noted by the researcher that if all the assumptions of the t-test are met, then the t-test becomes one of the most powerful tests.
The t-test is basically used in those situations in which the size of the sample is generally less than 30. If the sample size is larger than 30, then the t-test cannot be used, and instead the researcher opts for the z test.
The process of the t-test is basically based upon the student’s t distribution. The calculation of the t-test is different for comparison between the independent and the dependent samples, but the inference drawn from the t-test is the same.
The critical value in the t-test is basically the value that is found in the table of values of the t distribution for a given level of significance. If the value, which has been calculated by using the t-test, is more than the critical t value, then the null hypothesis that has been assumed in the t-test is rejected. But if the value that has been calculated by using the t-test is less than the critical t value, then the null hypothesis that is assumed in the t-test is accepted.
The confidence limits in the t-test basically construct the upper bound and the lower bound on an estimate for a given level of significance. The confidence interval in the t-test basically provides the range within these bounds. Such limits are employed in the t-test as such limits provide additional information on the relative meaningfulness of the estimates.
The following are some assumptions that have been assumed in the t-test:
The first assumption in the t-test is that the distribution or the population under consideration is that of a normal distribution or a normal population. In order to satisfy this assumption, there are certain tests for normality. The researchers should note that the t-test can draw invalid conclusions when two samples come from widely different shaped distributions. It is suggested by some statisticians that the t-test should be normally distributed for the sample size, which is mainly less than 15.
The second assumption made in the t-test is that of homogeneity of variances in the sample. SPSS employs a test for testing the homoscedastic nature of the sample in the t-test. This test is called “Levene’s Test for Equality of Variances,” with the F value and corresponding significance. The researcher should note that the t-test would result in invalid inferences if the two samples are unequal in size and also have unequal variances.
The third assumption is that in the t-test, it does not matter whether the sample is dependent or independent. This is because the inference drawn from the t-test would remain the same whether the sample is independent or dependent; only the calculation of the t-test would differ.
