ANOVA Lecture ACTIVITY 8
ANOVA
Oneway Analysis of Variance (ANOVA) is used with one categorical independent variable and one continuous variable. The independent variable can consist of any number of groups (levels).
A statistical technique by which we can test if three or more means are equal. It tests if the value of a single variable differs significantly among three or more levels of a factor.
Example:
Problem: Susan Sound predicts that students will learn most effectively with a constant background sound, as opposed to an unpredictable sound or no sound at all. She randomly divides twentyfour students into three groups of eight. All students study a passage of text for 30 minutes. Those in group 1 study with background sound at a constant volume in the background. Those in group 2 study with noise that changes volume periodically. Those in group 3 study with no sound at all. After studying, all students take a 10 point multiple choice test over the material. Their scores follow:
Group
Test Scores
1) Constant sound
7
4
6
8
6
6
2
9
2) Random sound
5
5
3
4
4
7
2
2
3) No Sound
2
4
7
1
2
1
5
5
Ho: X1 = X2 = X3
Procedure:
Variable view: follow format and labels
Data View:
Oneway ANOVA
Dialog box of OneWay ANOVA

test scores should be placed in the dependent list and sound background in the Factor
Select Post Hoc then after, in the dialog box check Tuckey then click Continue and OK (Oneway ANOVA).
The Output would be:
Interpretation
Susan can conclude that her hypothesis may be supported. The means are as she predicted, in that the constant music group has the highest score. However, the significant F only indicates that at least two means are significantly different from one another, but she can't know which specific mean pairs significantly differ until she conducts a posthoc analysis (e.g., Tukey's HSD)
TwoWay ANOVA
A TwoWay ANOVA is useful when we desire to compare the effect of multiple levels of two factors and we have multiple observations at each level. OneWay ANOVA compares three or more levels of one factor. But some experiments involve two factors each with multiple levels in which case it is appropriate to use TwoWay ANOVA.
Factors and Levels
A TwoWay ANOVA is a design with two factors.
Suppose that the Human Resources Department of a company desires to know if occupational stress varies according to age and gender. The variable of interest is therefore occupational stress as measured by a scale.
There are two factors being studied  age and gender.
Further suppose that the employees have been classified into three groups or levels:
age less than 40,
40 to 55
above 55
In addition employees have been labeled into gender classification (levels):
male
female
In this design, factor age has three levels and gender two. In all, there are 3 x 2 = 6 groups or cells. With this layout, we obtain scores on occupational stress from employee(s) belonging to the six cells.
PROBLEM
A research study was conducted to examine the impact of eating a high protein breakfast on adolescents' performance during a physical education physical fitness test. Half of the subjects received a high protein breakfast and half were given a low protein breakfast. All of the adolescents, both male and female, were given a fitness test with high scores representing better performance. Test scores are recorded below.
Group
Males
Females
High Protein
Low Protein
10
5
7
4
9
7
6
4
8
5
5
3
4
4
6
5
3
1
2
2
PROCEDURE:
(1) Input data with the following format and label;
(2) … Analyze > General Linear Model > Univariate;
(3) …Fitness Test Protein and Gender Post Hoc…
(4) … Protein and Gender check Tukey then click...
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