Analysis of Variance (ANOVA)

Posted: August 26th, 2021

Parametric Test

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Institutional Affiliation

PARAMETRIC TEST

Analysis of Variance (ANOVA)

            I have always found the ANOVA test challenging in testing, analyzing, and interpreting statistics, which is made harder due to the various ANOVA tests.  This includes One-way, Two-way, and Multi-variate ANOVA (MANOVA) that compares the means of more than two groups in parametric tests statistics. Furthermore, the ANOVA test employs the use of variance of more than two groups, indicating a statistically significant difference in the groups compared in the null and alternative hypotheses. More so, the null hypothesis is rejected if the group variance exceeds the expected variance terms indicating that there is a positive and significant relationship between the independent variable. However, through research and training, I have realized the three types of ANOVA are employed in determining significant variation in the means of two groups or more. Still, they have few differences when performing statistical experiments, as discussed below.

           One-way ANOVA, also referred to as a unidirectional test, involves comparing the mean squares of two groups, one independent variable affecting one dependent variable. The test uses the F-statistic that is determined by F-test. The F-test is given by the division of variance between groups and variance within groups. Furthermore, the sum of squares in the test is expressed as, for error and the total sum of squares. Besides, the mean squares are given by the division of the sum of squares and degrees of freedom. When  is taken to represent freedom treatment degree and  residual freedom degrees, the mean squares and degrees of freedom  as expressed as follows;

Therefore, the F-statistic is calculated as;

            On the other hand, a two-way ANOVA or bidirectional test is an extension of one-way ANOVA. It analyzes the impact of independent variables against the expected outcome and provides the relationship to the outcome. Additionally, the calculations are the same as the one-way test, but in this case, there are two independent variables. Multivariate ANOVA (MANOVA) involves comparing the statistical means where there are multiple independent variables against dependent variables on an outcome. Therefore, the ANOVA test’s calculations are the same in the three types, but the only difference is the number of independent and dependent variables in a hypothesis.