Variance Explained in 2 x 2 Contingency Tables (2 of 3)
The data could therefore be coded as follows:
Condition Outcome
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 0
1 0
0 1
0 0
0 0
0 0
0 0
0 0
0 0
0 0
0 0
0 0
Of the 10 subjects in Condition 1 (Experimental Condition), 8 have scores
of 1 (success) and 2 have scores of 0 (failure). Of the 10 subjects in Condition
2 (Control Condition) 1 has a score of 1 (success) and 9 have scores of
0 (failure). Pearson's correlation between these two variables is 0.7035.
Therefore, φ
= 0.7035. Since the proportion of variance explained in correlation is
the correlation
coefficient squared, the
proportion of variance explained is: φ² =
0.7035² = 0.495. Therefore, about 50% of the variance in outcome
is explained by the treatment effect.