Quantitative Results

Statistical Analysis

Analysis of Variance, i.e. ANOVA in SPSS, is used for examining the differences in the mean values of the dependent variable associated with the effect of the controlled independent variables, after taking into account the influence of the uncontrolled independent variables. Essentially, ANOVA in SPSS is used as the test of means for two or more populations.

ANOVA in SPSS must have a dependent variable which should be metric (measured using an interval or ratio scale). ANOVA in SPSS must also have one or more independent variables, which should be categorical in nature. In ANOVA in SPSS, categorical independent variables are called factors. A particular combination of factor levels, or categories, is called a treatment.

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In ANOVA in SPSS, there is one way ANOVA which involves only one categorical variable, or a single factor. For example, if a researcher wants to examine whether heavy, medium, light and nonusers of cereals differed in their preference for Total cereal, then the differences can be examined by the one way ANOVA in SPSS. In one way ANOVA in SPSS, a treatment is the same as the factor level.

If two or more factors are involved in ANOVA in SPSS, then it is termed as n way ANOVA. For example, if the researcher also wants to examine the preference for Total cereal by the customers who are loyal to it and those who are not, then we can use n way ANOVA in SPSS.

In ANOVA in SPSS, from the menu we choose:

“Analyze” then go to “Compare Means” and click on the “One-Way ANOVA.”

Now, let us discuss in detail how the software operates ANOVA:

The first step is to identify the dependent and independent variables. The dependent variable is generally denoted by Y and the independent variable is denoted by X. X is a categorical variable having c categories. The sample size in each category of X is generally denoted as n, and the total sample size N=nXc.

The next step in ANOVA in SPSS is to examine the differences among means. This involves decomposition of the total variation observed in the dependent variable. This variation in ANOVA in SPSS is measured by the sums of the squares of the mean.

The total variation in Y in ANOVA in SPSS is denoted by SSy, which can be decomposed into two components:

SSy=SSbetween+SSwithin

where the subscripts between and within refers to the categories of X in ANOVA in SPSS. SSbetween is the portion of the sum of squares in Y related to the independent variable or factor X. Thus it is generally referred to as the sum of squares of X. SSwithin is the variation in Y related to the variation within each category of X. It is generally referred to as the sum of squares for errors in ANOVA in SPSS.

The logic behind decomposing SSy is to examine the differences in group means.

The next task in ANOVA in SPSS is to measure the effects of X on Y, which is generally done by the sum of squares of X, because it is related to the variation in the means of the categories of X. The relative magnitude of the sum of squares of X in ANOVA in SPSS increases as the differences among the means of Y in categories of X increases. The relative magnitude of the sum of squares of X in ANOVA in SPSS increases as the variation in Y within the categories of X decreases.

The strength of the effects of X on Y is measured with the help of η2 in ANOVA in SPSS .The value of η2 varies between 0 and 1. It assumes a value 0 in ANOVA in SPSS when all the category means are equal, indicating that X has no effect on Y. The value of η2 becomes 1, when there is no variability within each category of X but there is still some variability between the categories.

The final step in ANOVA in SPSS is to calculate the mean square which is obtained by dividing the sum of squares by the corresponding degrees of freedom. The null hypothesis of equal means, which is done by an F statistic, is the ratio between the mean square related to the independent variable and the mean square related to the error.

N way ANOVA in ANOVA in SPSS involves simultaneous examination of two or more categorical independent variables, which is also computed in a similar manner.

A major advantage of ANOVA in SPSS is that the interactions between the independent variables can be examined.