**Hypothesis Testing**

When hypothesis testing, when might you use one-independent sample t-test versus a two-independent samples t-test? Provide an example of each for a proposed research study.

In statistical analysis, independent sample t-tests are used when the statistician wants to compare the means of two groups. In independent sample t-tests, taking two samples from a similar population means that the mean for the two samples may become the same (Mishra et al., 2019). But, if the two samples are taken from different populations, the sample mean may differ. This explains the difference between a one-independent sample t-test and a two-independent samples t-test. In hypothesis testing, statisticians either use one independent sample t-test or a two-independent samples t-test. A one independent sample t-test is used to compare a sample mean to a hypothesized value for the population mean to determine if the two sample means have a significant difference (Mishra et al., 2019). On the other hand, a two independent sample t-test is used to determine whether a statistically significant difference exists between the sample means in two unrelated groups. A good example of a one-independent sample t-test is when comparing the results of an expected value. For example, do male students score higher marks than the average mark of 70% on a math test if the exam time changes to 8 a.m.? In this t-test, the test variable’s mean is compared against a “test value,” which is a hypothesized or known value of the population’s mean. In a two-independent sample t-test, the means of two different data sets are compared. For example, if group one’s mean is 10%, and the mean of group two is 6%, the difference is 4%. The default null hypothesis for a 2-sample t-test is that the two groups are equal. Also, a two independent sample t-test is used to compare unrelated observations. For example, do test scores significantly differ if students take a maths test at 8 a.m. or 1 p.m.?

**References**

- Mishra, P., Singh, U., Pandey, C. M., Mishra, P., & Pandey, G. (2019). Application of student’s t-test, analysis of variance, and covariance.
*Annals of Cardiac Anaesthesia, 22*(4), 407.