In most cases, researchers want to describe and compare two groups of data. The means of two distinct data sets are mostly compared using t-tests, to find the differences or the similarities between them. The independent variable t-test poses to be an inferential statistical test used in determining any statistically significant difference that exists between the means of data obtained from two unrelated groups (Derrick et al., 2017). To run an independent t-test, there should be a continuous dependent variable and a categorical and independent variable comprising of two groups. The unpaired groups are the groups of participants who are different, and participants in one group cannot fit in the other group. For instance, when it comes to gender, the individual can be described as either male or female. Assumption of dependent variable normality and homogeneity of variance are adopted in the independent t-test.
The paired samples t-test are used in comparing data groups that are related in some way. The statistical procedure determines if the mean difference between two observable sets is zero. The paired sample tests are mostly applied in repeated-measures design or case-control studies (Zheng et al., 2017). For instance, the impact of a certain program on employees’ performance can be measured by analyzing the difference before and after the program using paired sample t-test. Some of the assumptions in a paired sample t-test are that the dependent variable should be normally distributed, continuous, contain outliers, and observations do not depend on each other. Among the major problems of using repeated measures design include the loss in the degree of freedom.
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References
Derrick, B., Toher, D., & White, P. (2017). How to compare the means of two samples that include paired observations and independent observations: A companion to Derrick, Russ, Toher and White (2017). The Quantitative Methods in Psychology , 13 (2), 120-126.
Zheng, J. Z., Yangyi, L. I., Tuo, L. I. N., Estrada, A., Xiang, L. U., & Changyong, F. E. N. G. (2017). Sample size calculations for comparing groups with continuous outcomes. Shanghai archives of psychiatry , 29 (4), 250.
Equal Variance Assumed and Equal Variance Not Assumed
In the table above, the Levene’s Test for Variance equality column provides a t-test assumption of homogeneous. There should be a statistical adjustment in case the assumption is violated. Violations of assumptions in these tests lead to Type I and Type II errors. There are high probabilities of underestimation or overestimation of inferential tests (Miyoshi & Lau, 2019). The first column provides F statistics and the F probability in the second column, which provides the test. The F test results decide whether to use Equal Variance Assumed or Equal Variance Not Assumed rows in analyzing the t statistics.
What are the decision rules applied in deciding what to use? If the two groups have equal variances, which is Sig. > .05 in the above example, then the equal variance assumed rows should be used. Secondly, the equal variance is not assumed rows should be used when there is a significant difference between the two groups; in this case, Sig. < .05 (Kim, 2015). In the table above, the F value profitability (Sig. = .000) is less than 0.05, which means that the equal variance is not assumed rows should be used because the group variances are not the same. The output provided by Levene’s test helps in making the decision on which row to use. Both the top and bottom rows give the same information, but the test statistics are calculated using different tests. This is the reason why there is a slight difference in the calculations. The table provides values used in determining the confidence interval.
References
Kim, T. K. (2015). T-test as a parametric statistic. Korean Journal of anesthesiology , 68 (6), 540.
Miyoshi, K., & Lau, H. (2019). Realistic Variance Assumptions Favor Metacognitive Heuristics.
