# 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

$\overline{x}=1.2175$

$\overline{x}=0.965$

$\overline{x}=1.4275$

$\overline{x}=1.6075$

$\overline{x}=1.304375$

**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 $\alpha$=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.