Quick overview of effect size for t-test, ANOVA and correlation

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