Week_10_ANOVA

Question 1

What is ANOVA used for?

Answer 1

used as a test of means for two or more populations. The null hypothesis, typically, is that all means are equal.

Question 2

Categorical independent variables are also called factors.

Answer 2

True.

Question 3

One-way analysis of variance definition

Answer 3

Only one categorical variables or single factor that affect dependent variable. Treatment is the same as factor level.

Question 4

What is treatment in variance analysis?

Answer 4

A particular combination of factor levels, or categories

Question 5

two or more factors are involved, the analysis is termed n-way analysis of variance.

Answer 5

True

Question 6

Analysis of covariance.

Answer 6

If the set of independent variables consists of both categorical and metric variables, the technique is called analysis of covariance (ANCOVA). In this case, the categorical independent variables are still referred to as factors, whereas the metric-independent variables are referred to as covariates.

Question 7

What is the formula of one-way ANOVA?

Answer 7

SSy = SSx + SSerror

Question 8

The value of gita2 varies between 0 and 1. It assumes a value of 0 when all the category means are equal indicating that X has no effect on Y.

Answer 8

True

Question 9

Assumptions in ANOVA

Answer 9

1. Ordinarily, the categories of the independent variable are assumed to be fixed. Inferences are made only to the specific categories considered. This is referred to as the fixed-effects model.
2. The error term is normally distributed, with a zero mean and a constant variance. The error is not related to any of the categories of X.
3. The error terms are uncorrelated. If the error terms are correlated (i.e., the observations are not independent), the F ratio can be seriously distorted.

Question 10

N-way ANOVA examples

Answer 10

• How do advertising levels (high, medium, and low) interact with price levels (high, medium, and low) to influence a brand’s sale?
• Do educational levels (less than high school, high school graduate, some college, and college graduate) and age (less than 35, 35-55, more than 55) affect consumption of a brand?
• What is the effect of consumers’ familiarity with a department store (high, medium, and low) and store image (positive, neutral, and negative) on preference for the store?