The document discusses shared variance and effect size. It explains that shared variance, as measured by r-squared, indicates the percentage of variability between two variables that is explained by their relationship. Effect size can be measured by Cohen's d or eta-squared and indicates the size of the difference or amount of variability explained by a treatment group. Calculating measures of shared variance and effect size provides information about the strength and importance of relationships in statistical analyses beyond just significance.

1. Shared Variance
Improved Prediction

2.  Significance:
Is there evidence that this event would be
unlikely, if the null hypothesis were true?
 An result can be significant but the size of the
difference might be very small
 If sample size is very large
 If variability is quite small
 Effect size can also be measured and
compared.

3.  In Correlation, we computed r2 to see the
amount of shared variability between two
variables.
 A correlation of r = .7 meant that 49% of the
variability was “shared” or “explained” by the
relationship of the two variables.
 This gave us a measure that increased in a
linear way (unlike r) to talk about the size of
the correlation.

4. Effect size could be measured with Cohen’s d
as follows:
mean difference
standard deviation
d 
d = .2 or less is a small effect size
d between .2 and .8 is a medium effect size
d greater than .8 is a large effect size

5. r2 can also be computed after a t-test using the
equation:
df
r
2
t

 2
2
t
Interpretation: The percent of variability in
the variable that is due to treatment group.

6. Same idea of shared variance as we saw in r2
2 between SS
 
total SS
Interpretation: The percent of variability in
the variable that is due to treatment group.

7.  Enter data for our sample problem
 Instead of Group ABC, use codes
1, 2 and 3.
 Add value labels for praise levels
 Add variable names
 Consult Cronk book
 Do your own write-up of the
results, including a measure of
Effect Size.
Group X
A 7
A 6
A 5
A 8
A 3
A 7
B 4
B 6
B 4
B 7
B 5
B 7
C 3
C 2
C 1
C 3
C 4
C 1
ΣX 83
Mean 4.6111