Two Way Manova Example

Statistical Test

Two way MANOVA

Research question and hypothesis.

Dependent variables: WWW hours per week and Email hours per week

Independent variables: Generation by age range and Sex

Research question.

Q1. (a)Are there significant mean differences in the combined DV of WWW hours per week and Email hours per week for individuals of different generation?

(b) Are there significant mean differences in the combined DV of WWW hours per week and Email hours per week for individuals of different sex?

(c ) Is there a significant interaction between generation and sex on the combined DV of WWW hours per week and Email hours per week?

Q2. (a) Are there significant mean differences in the WWW hours per week for individuals of different generation?

(b) Are there significant mean differences in the WWW hours per week for individuals of different sex?

(c ) Is there a significant interaction between sex and generation on WWW hours per week?

Q3. (a) Are there significant mean differences in the Email hours per week for individuals of different generation?

(b) Are there significant mean differences in the Email hours per week for individuals of different sex?

(c ) Is there a significant interaction between sex and generation on Email hours per week?

Hypotheses.

Question 1.

H10: There are no significant mean differences in the combined DV of WWW hours per week and Email hours per week for individuals of different generation.

H1a: There are significant mean differences in the combined DV of WWW hours per week and Email hours per week for individuals of different generation.

H20: There are no significant mean differences in the combined DV of WWW hours per week and Email hours per week for individuals of different sex.

H2a: There are significant mean differences in the combined DV of WWW hours per week and Email hours per week for individuals of different sex.

H30: There are no significant interaction between generation and sex on the combined DV of WWW hours per week and Email hours per week.

H3a: There are significant interaction between generation and sex on the combined DV of WWW hours per week and Email hours per week.

Question 2.

H40: There are no significant mean differences in the Email hours per week for individuals of different generation.

H4a: There are significant mean in the Email hours per week for individuals of different generation.

H50: There are no significant mean differences in the WWW hours per week for individuals of different sex.

H5a: There are significant mean differences in the WWW hours per week for individuals of different sex.

H60: There are no significant interaction between sex and generation on WWW hours per week.

H6a: There are significant interaction between sex and generation on WWW hours per week.

Question 3.

H70: There are no significant mean differences in the WWW hours per week for individuals of different generation.

H7a: There are significant mean differences in the WWW hours per week for individuals of different generation.

H80: There are no significant mean differences in the Email hours per week for individuals of different sex.

H8a: There are significant mean differences in the Email hours per week for individuals of different sex.

H90: There are no significant interaction between sex and generation on Email hours per week.

H9a: There are significant interaction between sex and generation on Email hours per week.

Research design

In this study the effect of generation by age range and sex on WWW hours per week and Email hours per week. The generation by age range was divided into 6 categories, 1= Gen Y (Millennials) Born 1977-1990 Ages 18-33, 2=Gen X Born 1965-1976 Ages 34-45, 3= Younger Boomers Born 1955-1964 Ages 46-55, 4= Older Boomers Born 1946-1954 Ages 56-64, 5= Silent Generation Born 1937-1945 Ages 65-73, 6= G.I. Generation Born -1936 Age 74+ and sex of each participant (with two groups: "males" and "females") and how much WWW hours per week (n, -1 = IAP, 998 = DK, 999 = NA) and Email hours per week (n, -1 = IAP, 998 = DK, 999 = NA) .

In order to understand whether there was an effect of generation and sex on WWW hours per week and Email hours per week, a two-way MANOVA was run with generation and sex as the two independent variables and the WWW hours per week and Email hours per week as the two dependent variables.

Screening the data

1. Missing data

No missing data.

2. Outliers

There were no univariate outliers in the data, as assessed by inspection of a boxplot for values greater than 1.5 box-lengths from the edge of the box.

The Mahalanobis distance found were in the range of 6.63088 - .82023 and well below the critical value for two dependent variables of 13.82.

There were no multivariate outliers in the data, as assessed by Mahalanobis distance (p > .001).

3. Normality

WWW hours per week and Email hours per week were normally distributed, as assessed by Shapiro-Wilk's test (p > .05).

4. Linearity of Dependent Variables

There was a linear relationship between the dependent variables, as assessed