## Lecture 11.2

### ANOVA: AN INTUITIVE APPROACH

I. What is variability?

II. What is between groups variability?

III. What causes between groups variability?

A. Random error

B. Treatment effects?

IV. What is within groups variability?

V. What causes within groups variability?

Random error

VI. If the treatment has an effect, then
between groups variance (treatment effects + random error)
should be bigger than
within groups variance (random error)

VI. Two things you can quickly determine by looking at an ANOVA summary table.

A. How many levels of treatment there were (because treatment levels -1= treatment df)

B. How many participants there were (because total number of participants - 1 = total df)

Start of ANOVA Summary Table:

 Source df Between groups(Treatment) 3 Within groups (Error) 26 Total 29

How many groups were used?

How many participants?

Example 1: Results from a three-group experiment

GROUP 1 GROUP 2 GROUP 3
555
555
555
Mean=Mean=Mean=
ANOVA Summary Table for the above experiment:

SourceSum of Squaresdf Mean Square
Between groups
Treatment
_2 _
Within groups S/A (Error)_ 6 _
Total _ 8 _

Example 2: Results from a three-group experiment

GROUP 1GROUP 2GROUP 3
366
366
366
Mean=3Mean=6Mean=6

Note: In this case, SS Treatment = 18

ANOVA Summary Table
SourceSum of Squaresdf Mean Square
Between groups
Treatment
__ _
Within groups S/A (Error)_ _ _
Total _ _ _

Example 3: The results from a three-group experiment

GROUP 1GROUP 2GROUP 3
255
366
477
Mean=3Mean=6Mean=6

Note: To compute the within groups sum of squares, start with group 1. Find the mean (3). Subtract each of the scores in that group from that mean, square those differences, and then sum them. Do this for each group.

Thus, in this example:

GROUP 1 GROUP 2 GROUP 3
2-3=1 -12=1 5-6=-1 -12=1 5-6=-1 -12=1
3-3=0 02=0 6-6=0 02=0 6-6=0 02=0
4-3=1 12=1 7-6=1 12=1 7-6=1 12=1
Mean=3; SSG1=2 Mean=6; SSG2=2 Mean=6; SSG3=2

SS within = 2 + 2 + 2 = 6

ANOVA Summary Table based on Example 3
SourceSum of Squaresdf Mean Square F
Between groups
Treatment
__ __
Within groups S/A (Error)_ _ _
Total _ _ _

Example 4: The results from a three-group experiment

GROUP 1GROUP 2GROUP 3
253
366
479
Mean=3Mean=6Mean=6

ANOVA Summary Table
SourceSum of Squaresdf Mean Square F
Between groups
Treatment
__ _2.46
Within groups S/A (Error)_ _ _
Total _ _ _

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