Variance Explained in 2 x 2 Contingency Tables (2 of 3)

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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.
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