Analysis of variance (ANOVA)
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Intros
Examples
Lessons
- Determining Degrees of Freedom
A test was done to study the reaction time of car drivers at different periods of the day
Reaction Time of Drivers (seconds)
Morning:
Afternoon:
Evening:
Night:
1.32
0.25
2.34
1.54
0.71
1.48
1.75
1.98
2.27
1.24
0.64
1.76
0.57
0.89
0.98
1.15
- Determining the Sum of Squares
The following case study was done on what type of beverages office workers drink in the morning and their productivity.
Juice/Milk Drinkers:
Tea Drinkers:
Coffee Drinkers:
3
5
8
5
5
6
3
6
7
1
4
7
- What is the Total Sum of Squares (TSS or SST) for this case study? Also what are the degrees of freedom for this group?
- What is the Sum of Squares Within Groups (SSW)? Also what is the number of degrees of freedom for all these groups?
- What is the Sum of Squares Between Groups (SSB)? Also what is the number of degrees of freedom for this calculation?
- Verify that: TSS=SSW+SSB for both the variation and the degrees of freedom.
- Hypothesis Testing with F-Distribution
The following case study was done on what type of beverages office workers drink in the morning and their productivity.
Juice/Milk Drinkers:
Tea Drinkers:
Coffee Drinkers:
3
5
8
5
5
6
3
6
7
1
4
7
With a significance level of =0.05 test the claim that "what you drink in the morning does not affect how productive you are at work."
Use the fact that in the previous example we found that SSW=12 with 9 degrees of freedom. And we also had that SSB=32 with 2 degrees of freedom.