Shared VarianceImproved Prediction

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.

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.

Effect size could be measured with Cohen’s d as follows:

d = .2 or less is a small effect sized between .2 and .8 is a medium effect sized greater than .8 is a large effect size

deviation standard

difference meand

r2 can also be computed after a t-test using the equation:

Interpretation: The percent of variability in the variable that is due to treatment group.

dfr

2

22

t

t

Same idea of shared variance as we saw in r2

Interpretation: The percent of variability in the variable that is due to treatment group.

totalSS

between2 SS

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