An independent-measures t-test uses two independent samples in research to compare a dependent variable’s mean difference in two conditions. For example, a t test of independent-measures design can be implemented in order to determine whether or not the difference in self-esteem level between men and women was statistically significant; in the experiment, two independent samples, for instance, 50 men and 50 women, could be selected from two completely separate populations. According to Gravetter and Wallnau (2013), an independent-measures design is ideal for a research in comparison of men and women in terms of their differences.
In a t test for two independent samples, the null hypothesis (H0) states that there is no difference in the measured level between the two populations (represented by the two independent samples); the alternative hypothesis (H1) states that there is a significant difference in the measured level between the two populations. the investigation of the hypothesis uses the t Distribution Table (Gravetter & Wallnau, 2013, p. 703). For example, a critical value at the degree of freedom (df) 39 is found to be 2.021 at an alpha level of 0.05 for a two-tail test. If a t value is calculated to be t = 2.01, then it is determined that the t is not in the critical region, the null hypothesis is accepted, thus it is said that the difference in the measured level between the two samples is not statistically significant for alpha = .05. On the other hand, if the alpha level is increased to 0.10, then the critical value is determined to be 1.684 and the t value falls in the critical region, thus the alternative hypothesis is accepted which concludes that the measured level is significantly different for alpha = 0.10.
Gravetter, F. J. & Wallnau, L. B. (2013). Statistics for the behavioral sciences (9th ed.). Belmont, CA: Wadsworth.