Many Faces of the Correlation Coefficient

Figures & data

Table 1. Joint Probability Distribution with Two Dichotomous Variables

	X
Y	0	1	Total
1	p01	p11	p. 1
0	p00	p10	p. 0
Total	p0.	p1.	1

Table 2. Binomial Effect Size Display: A 2 × 2 Frequency Distribution with r_xy = .32 (Based on Rosenthal and Rubin 1982, Table 1)

Y (treatment outcome)	X (condition)
	0 (control)	1 (treatment)	Total
1 (alive)	34	66	100
0 (dead)	66	34	100
Total	100	100	200

Table 3. Bivariate Probability Distributions with Correlation Coefficient .034 (Based on the Data in Table 2 of Rosnow and Rosenthal 1989)

Y (treatment outcome)	X (condition)
	0 (control)	1 (treatment)	Total
(a) Original data
1 (alive)	.4913	.4954	.9867
0 (dead)	.0086	.0047	.0133
Total	.4999	.5001	1.0000
(b) BESD
1 (alive)	.2415	.2585	.5000
0 (dead)	.2585	.2415	.5000
Total	.5000	.5000	1.0000

Table 4. Probabilities of All Possible Genotypes, with Two Alleles and Inbreeding Coefficient I

Value of sperm: Y	Value of egg: X
	0	1	Total
1	(1 – I)pq	Ip + (1 – I)p^2	p
0	Iq + (1 – I)q^2	(1 – I)pq	q
Total	q	p	1

Rosenthal, R., and Rubin, D. B. (1982), “A Simple, General Purpose Display of Magnitude of Experimental Effect,” Journal of Educational Psychology, 74, 166–169.

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Rosnow, R. L., and Rosenthal, R. (1989), “Statistical Procedures and the Justification of Knowledge in Psychological Science,” American Psychologist, 44, 1276–1284.

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