Factorial Design



Factorial Design

Hypothesis 1

            H0: The population means of the obese and non obese are equal.

            HA: The population means of the obese and non obese are not equal.

Hypothesis 2

            H0: The population means of the coffee drinkers and non coffee drinkers are equal.

            HA: The population means of the coffee drinkers and non coffee drinkers are not equal.

Hypothesis 3

            H0: There is no interaction between obese and non obese against the variation in coffee drinkers and non coffee drinkers.

            HA: There is interaction between obese and non obese against the variation in coffee drinkers and non coffee drinkers.



Descriptive Statistics

 

Coffee Drinkers/ Non-Obese

Coffee Drinkers/ Obese

Non-Coffee Drinkers/ Non-Obese

Non-Coffee Drinkers/ Non-Obese

Mean

6.4

7.6

8.9

12.5

Median

6

8

9

12.5

Mode

10

8

10

14

Standard Deviation

2.5473

2.1186

1.7919

1.7795

Sample Variance

6.4888

4.4888

3.2111

3.1666

Post hoc test cannot be completed for obese and non obese also for coffee and non coffee drinkers because there are fewer than two groups. In order to determine the simple main effects 2 x 2 factorial design we require at least 3 variable categorical groups to distinguish the variation within the groups.

The results of Two way ANOVA shows that obesity in the sample respondents significantly affecting the maze time (minutes) [f = 13.275, p = 0.001] which leads to the rejection null hypothesis 1. This shows that obesity has a significant role in completing the maze time. Further, our results also show that the coffee addiction is also significantly affecting the respondents to complete the maze time [f = 31.552, p = 0.000] which also rejects the null hypothesis 2 and the conclusion is similar to that in obesity. Now, the obesity and coffee addiction did not significantly impacting the maze time completion with a = 0.05 i.e. [f = 3.319, p = 0.077] which statistically enforced us to not reject the null hypothesis and leads to the conclusion that there is no interaction between obese and non obese against the variation in coffee drinkers and non coffee drinkers.

Tests of Between-Subjects Effects

Dependent Variable: Maze Time (Minutes)

Source

Type III Sum of Squares

df

Mean Square

F

Sig.

Obesity

57.6

1

57.6

13.275

0.001

Coffee Addiction

136.9

1

136.9

31.552

0

Obesity * Coffee Addiction

14.4

1

14.4

3.319

0.077

Error

156.2

36

4.339

 

 

PART II

Two-Way ANOVA with Age at First Marriage as the dependent variables with religion and region as independent variables

Table 1: Tests of Between-Subjects Effects

Dependent Variable: Age at first marriage

Source

Type III Sum of Squares

df

Mean Square

F

Sig.

region

17.652

3

5.884

.449

.718

religion

22.455

1

22.455

1.714

.191

region * religion

98.758

3

32.919

2.514

.057

Error

18689.384

1427

13.097

 

 

Total

439378.000

1435

 

Corrected Total

18897.097

1434

a. R Squared = .011 (Adjusted R Squared = .006)

Two-Way ANOVA with Age at First Intercourse as the dependent variables with the same two independent variables

Tests of Between-Subjects Effects

Dependent Variable: Age at first sexual intercourse

Source

Type III ...