ANALYSIS OF VARIANCE

Analysis Of Variance

Analysis Of Variance

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.

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 (Bernard, 2006). 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 (Creswell, 2009).

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 (Creswell, 2009). 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 (Jackson, 2008). 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 observations minus the number of groups) (Hardle, 2007).

In order to conduct the Analysis of Variance (One-way ANOVA) for this research paper, data has been taken from the General Social Survey (GSS) Data Disk file of Year 2008 labeled as 2008 Cross Panel Data. These include “Race of the Household” as Independent Variable and the “Respondent Income in Dollars” as the Dependent Variable. Race of the Household is a nominal variable and the “Respondent Income in Dollars” is continuous variable measuring the income level of every respondent on Likert scale. Race of the household is categorized in five segments that are included in the analysis. Segments were categorized on the basis of origin. These include White Americans, Black Americans, Amer Indian, Asiatic Oriental, and Other Mixed race groups.

Null and Alternate Hypothesis

Null hypothesis:

Ho = µ1 = µ2 = µ3 = µ4 = µ5

There is no statistically significant difference between average income level of respondents belonging to White American, Black American, Amer Indian, Asiatic Oriental, and Other race groups

Numeric form: µ (Respondent Income of White American) = µ (Respondent Income of Black American) = µ (Respondent Income of Amer Indian) = µ (Respondent Income of Asiatic Oriental) = µ (Respondent ...