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ANOVA Application

ANOVA Application

Introduction

The analysis of variance (ANOVA) of a factor used to compare several groups in a quantitative variable. It is, therefore, a generalization of the two-sample independent t-test in case when independent variable has more than two categories. Categorical variable (either nominal or ordinal) defines the groups of independent variable that should be compared to the dependent variable. Analysis of Variance effectively defines the homogeneity with respect to dependent variable for particular variable categories.

Importance of ANOVA

ANOVA helps in predicting the relation between variable groups towards the dependent variable based on coherent properties of the independent variable. Thus, ANOVA statistical measurement method can be performed on each group and find out whether there are differences between them (Ott, 2008). The one-way ANOVA provides information on the outcome of that comparison. That is, to conclude whether the test subjects for different categories or variable segment vary the performance measure used to define the relationship with dependent variable selected (Triebold, 2007).

The hypothesis tested in the one-way ANOVA is that the population means are equal. If the population means are equal, this means that the groups do not differ in their properties; consequently, factor is independent of defined variables (Hardle, 2007). The strategy to test the hypothesis of equal means is to obtain a statistic called F, which reflects the degree of similarity between the means to be comparable. The numerator of the F statistic is an estimate of the population variance based on the variability between the means of each group. The denominator of F-statistic is also an estimate of the population variance, but based on the variation that exists within each group (Hardle, 2007). If the sampled populations are normal and their variances are equal, the F-statistic is distributed according to the probability model of Fisher-Snedecor F (degrees of freedom numerator is the number of groups minus 1, the denominator, the total number of observed ...

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