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Description of the Differences Between Techniques

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Description of the Differences Between Techniques

The primary differences between these statistical tests stem from the design it was conceived to investigate; the number of independent variables, whether group comparisons are qualitative or quantitative, and the number of dependent variables. The simplest test is a one-sample t-test. That is, it operates by itself and compares the mean of a single group with some prespecified population value, where there is no manipulation of the independent variable. With one independent variable and only two levels, the corresponding test is a t-test (Yu et al., 2022). If either group consists of different subjects, the test must be an independent samples t-test; if the same subjects are measured twice, then the test is a paired samples t-test.

The ANOVA procedure or analysis must be adopted when more than two groups or variables are compared. A one-way ANOVA is merely the step-up test into an independent samples t-test when one independent variable has three or more levels or groups arrived at through different subjects. Repeated measures ANOVA is the extension of the paired samples t-test when the same subjects undergo measurement on three or more occasions or under three or more levels of a single independent variable. A two-way ANOVA must be used when two independent variables are present in a research design. It can test for the main effect of each independent variable on the dependent variable and for the interaction effect of the independent variables being tested, checking if the effect of one variable depends on the levels of the other variable (Yu et al., 2022). The most complex design involves both within-subject and between-subject factors and is analyzed via a mixed factorial ANOVA. This two-way mixed factor ANOVA can distinguish the main effects of single factors and their interaction while considering the dependency among the repeated measurements.

Reference

Yu, Z., Guindani, M., Grieco, S. F., Chen, L., Holmes, T. C., & Xu, X. (2022). Beyond t-test and ANOVA: applications of mixed-effects models for more rigorous statistical analysis in neuroscience research.  Neuron,  110(1), 21–35.