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Tab signify 0 rac signify 0* rbc signif.* 0* rab.c signif.* 0 Tac.b signif.* 0 Tbc.a signif.* 0

Figure 4.11 Predictions of the four possible models of causal relationships involving three variables, in terms of the expected values for the simple and partial linear correlation coefficients. 'rab signify 0' means that, under the model, the correlation must be significantly different from zero. 'rab not signif.' means that the correlation is not necessarily significantly different from zero at the pre-selected significance level. * Model 4 holds even if one, but only one, of these two simple correlation coefficients is not significant. Adapted from Legendre (1993).

• Comparison of partial correlation values. Consider the partial correlation formula for rab.c (eq. 4.36). Is it true that lrab.cl < lraJ ? The relationship rac = rabTbc allows one to replace rac by rabTbc in that equation. After a few lines of algebra, the inequality

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