Question

I am conducting ANOVA two ways tests. With two independent variables and one independent variable.

the testing is about whether gender and income affect the purchase.

after getting the result, how can I know which independent variables that affect the most? and why?

Answer 1

Answer:

The difference can be seen by either calculating the effect size (eta-square) for each significant independent variable or by comparing the difference in mean among levels for each independent variable.

Explanation:

ANOVA model

The independent and dependent variables for the ANOVA model are defined as,

Dependent variable: Sales

Independent variable 1: Gender (Levels: males and Females)

Independent variable 2: Income (Levels: Group 1, Group 2, Group 3,.....)

Significance of the independent variable

Decision Rule: If the p-value is less than the significance level => significant main effect.

Effect size (eta square)

The effect size (eta-square) is used to calculate the proportion of variance that is explained by the independent variable. The eta square value can be obtained using the following formula,

by comparing the values of eta square we can tell which factor has a larger effect on the sales. larger the value of eta square larger will be the effect.

mean difference

To see the main effect of each independent variable, take the difference of mean among levels as shown below (For example),

The difference in means is larger for Gender which means the effect of gender on sales is larger compared to income.

Reason:

There can be many reasons => Income influences the consumer behavior, for example, income level affects the decision making, whether a person can afford a product or service?. Similarly, gender also affect consumer purchasing behavior