Statistical Research Methods and Selection of Statistical Tests
This article discuss the factors to be considered in selecting the appropriate statistical dessign of research method and the statistical test to be applied to test the significance at a given level of significance level appropriately choosen by the researcher.
Statistics – Research Methods relating to non metric independent variables with metric dependent variables
Introduction
In this statistical article I will discuss the situation of the suitability of a t- test and research problems related to it when non-metric independent variable and a metric variable is involved. As well I will discuss different variance analysis such as one-way ANOVA, Factorial ANOVA, extraneous variables and ANCOVA, one-way ANCOVA, factorial ANCOVA, discriminant analysis and MANOVA, one-way MANOVA, factorial MONOVA, one-way MANCOVA and factorial MANCOVA relating to non-metric independent variables and dependent variables.
Research methods, number of independent non-metric variables, number of metric variables, co-variates and the simultaneous impact of non-metric independent variables on dependent variables
If one binary non-metric independent variable and one independent variable then one must use a t-test design. For example, if one wants to study the impact of black students and white students on the duration of secondary school students then the researcher must use a t-test design selecting a fairly small sample of equal size or non equal size and use a t-test assuming the variances are equal and normally distributed to calculate the t-test at appropriate significance level to accept or reject the null-hypothesis that they are same.
If the non-metric independent variable is not binary and it has more than 2 levels then if it has one metric dependent variable then one must use a one way ANOVA design. For example if a researcher wants to study the effect of school duration of white, black and ethnic students then the researcher must use a one way ANOVA design to study the differences in variation within and between groups.
If the research question is related to more than one non-metric independent variable then one must use a factorial ANOVA. For example if a researcher wants to study the effect of different races of students and gender differences on secondary school duration then the researcher must use 3*2 two-way factorial ANOVA. If there is a co-variate then the researcher must use a factorial ANCOVA instead of factorial ANOVA. For example if the researcher in addition to the race and gender wants to study for adjusting for prior marks the students get in previous exams then ANOVA is inappropriate and they must use ANCOVA design and analysis of variance.
In one-way MANOVA the non-metric independent variable is one and the number of dependent variables is more than one. In this situation they can use one-way MANOVA design and analysis of variance. For example if a researcher wants to study the impact of different race of students on school study duration and average prior marks in the subjects studied then they must use one-way MANOVA design and analysis of variance. If the number of non-metric variables and metric variables increases one must use more complex version of MANOVA depending on the number of independent and dependent variables. If there is co-variates use MANCOVA design.
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