Many different statistical tests of significance can be applied in research studies. Factors such as the scale of measurement represented by the data, method of participant selection, number of groups being compared and number of independent variables determine which test of significance should be used in a given study. It is important that the researcher select the appropriate test because an incorrect test can lead to an incorrect decision of Type I or Type II error (Gay, Mills & Airasian, 2011).
The t test is used to determine whether two groups of scores are significantly different at a selected probability level. Simple ANOVA is a test of significance used to determine whether scores from two or more groups are significantly different at a selected probability level. Whereas, the t test is appropriate test of difference between the means of two groups at a time (e.g., boys and girls). It is also possible to compute a series of t tests, one for each pair of means. ANOVA is the test for multiple group comparison (Gay, Mills & Airasian, 2011).
MANOVA is the extended form of ANOVA. If a research study uses a factorial design to investigate two or more independent variables and the interactions between them, the appropriate statistical analysis is factorial, or multifactor analysis of variance. This analysis yields a separate F ratio for each independent variable and one for each interaction. When two or more independent variables are analyzed, multivariate analysis of variance MANOVA is used. For example, suppose that we want to consider whether gender and economic status both affect students’ college achievement. MANOVA will allow us to consider both independent variables (gender and economic status) and multiple dependent variables (e.g., college GPA as well as other test scores we may have from maths or language classes). As you can imagine, however, we need a large data set to run increasingly complex analysis with multiple independent and independent variables (Gay, Mills & Airasian, 2011).