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Generally, t-test include five assumptions that have to be taken into consideration at all times when the analysis is executed. As discussed by Kim and Park (2019), first, the scale of measurement applied to the collected information follows an ordinal or continuous scale. Second, the data is derived from a simple random sample of the total population. Third, when plotted, the data results in a bell-shaped distribution curve, representing a normal distribution with a specified level of probability as a criterion for acceptance. Forth, t-tests usually use a relatively large sample size which allows for the results to approach a bell-shaped curve. Fifth, the method is associated with the homogeneity of variance which exists when the standard deviations of samples are more or less equal (Kim & Park, 2019). In case one and more of these assumptions are missing, one should not run an independent t-test.
According to Gerald (2018), a researcher needs to satisfy two conditions to run a t-test: one continuous dependent variable and one independent categorical variable with two levels. The collected output data should be organized into groups with the variable selected based on the occurred reaction. With the usage of descriptive statistics, the group sizes need to be compared and held to the scrutiny of the five aforementioned assumptions. If the p-value turns out to be > 0.05, one can run an independent samples t-test. In case of the p-value <0.05, the Mann-Whitney U test should be used instead (Gerald, 2018).
A p-value of <0.05 is statistically significant, thus highly preferable for the researcher. As explained by Kim (2015), such result demonstrates strong evidence that the null hypothesis is invalid, giving only a 5% probability that the null is correct while the obtained results are random. Getting a p-value of <0.05 usually indicates that the null hypothesis can be rejected, and the alternative hypothesis can be accepted. Despite the high probability of the null hypothesis to be faulty, it is strongly advisable to consider that the research hypothesis does not have a 95% probability to be true (Kim, 2015). Before jumping to the foregone conclusions, it is necessary to consider that the p-value is conditional if the null hypothesis is unrelated to the research hypothesis.
References
Gerald, B. (2018). A brief review of independent, dependent and one sample t-test. International Journal of Applied Mathematics and Theoretical Physics, 4(2), 50-54. Web.
Kim T. K. (2015). T test as a parametric statistic. Korean Journal of Anesthesiology, 68(6), 540546. Web.
Kim, T. K., & Park, J. H. (2019). More about the basic assumptions of t-test: Normality and sample size. Korean Journal of Anesthesiology, 72(4), 331335. Web.
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