1. Introduction to Analysis of Variance: The LOGIC of ANOVA
Suppose an employer wants to evaluate how long it takes his employees to perform a typing task. He knows that his company has three levels of training: Beginner, Intermediate, and Advanced Typing. He would like to know if these groups differ in the amount of time it takes them to type a paragraph of text. Below are the results.
BEGINNER INTERMEDIATE ADVANCED
16 sec sec sec

2. Introduction to Analysis of Variance: The LOGIC of ANOVA
Suppose an employer wants to evaluate how long it takes his employees to perform a typing task. He knows that his company has three levels of training: Beginner, Intermediate, and Advanced Typing. He would like to know if these groups differ in the amount of time it takes them to type a paragraph of text. Below are the results.
BEGINNER INTERMEDIATE ADVANCED
16 sec sec sec

3. Calculation of ANOVA (The F statistic):

4. Experimental example Student Mean performance Effect of stress on
measured intelligence.
Or performance on an
intelligence test.
(a=.05)
The Data
With Alone 2 3
Help tasks tasks
IQ scores

5. H1: There is an effect of stress on measured intelligence.
H0: There is no effect of stress on measured intelligence.
Critical Value: ANOVA has TWO degrees of freedom terms.
dfnumerator = k-1
dfdenominator= N-k
Where k = the number of groups and N = total number of people in whole experiment
Critical Value:
From F-table: Fcrit(3,8) = 4.07 (alpha=.05)
Obtained Statistic:

6. Calculation example X =115.33 SS1 114.00 108.67 60.67 SS2 50.00 116.00
With Alone 2 3
Help tasks tasks
With Alone 2 3
Help tasks tasks
108.67
116.00
SS2
50.00
SS3
88.67
SS4
50.00
X =115.33
114.00
SS1
60.67

7. Calculation example X =115.33 SS1 114.00 108.67 60.67 SS2 50.00 116.00
With Alone 2 3
Help tasks tasks
With Alone 2 3
Help tasks tasks
108.67
116.00
SS2
50.00
SS3
88.67
SS4
50.00
X =115.33
114.00
SS1
60.67

8. Calculation example Fcrit(3,8) = 4.07
With Alone 2 3
Help tasks tasks
With Alone 2 3
Help tasks tasks
Fcrit(3,8) = 4.07
Decision: Retain the null hypothesis.

10. “Unplanned comparisons”
One-Way ANOVA: POST-HOC tests
“Unplanned comparisons”
If and only if our ANOVA is significant, we conduct a post-hoc test. In this class, we will use Tukey’s post-hoc test.
Example Data:
Splenda
Equal
Sweet & Low 3 6 4 1 2 5 7