I think that my memory must be really rusty regarding the order and correspondence between standardized coefficients (betas or beta weights) and their respective p values.
I am looking at an empirical journal article that lists results for a multiple linear regression as follows:
Predictor 1 (interval level): beta = -.09 p = .036
Predictor 2 (categorical/dichotomous): beta = .68 p = .011
Predictor 3 (interval level) x: beta = .09 p = .031
Predictor 4 (categorical/dichotomous): beta = -.05 p = .168
Predictor 5 (categorical/dichotomous): beta = .09 p = .019
Predictor 6 (interaction term – cross of P 1 * P 2): beta = -.74 p = .006
I thought that as the absolute value of beta increases, the corresponding p values decreases. Is my memory incorrect?
Yes. A standardized beta coefficient compares the strength of the effect of each individual independent variable to the dependent variable. The higher the absolute value of the beta coefficient, the stronger the effect and therefore the lower the p value.
1) If the value of P is small, the evidence is high, which means that the incidence is significant but does not necessarily mean that the incidence is high.
Best!
The results that you listed seem to agree with your assertion: smaller betas have larger p-values. If you sort these six predictors by their betas, you find that the p-values will also be sorted: p4 -> p1, p3, p5 -> p2 -> p6. (The p-values for predictors 1, 3, and 5, are all smaller than predictor 4 but larger than predictor 2.)
However, I don't think this rule is true in general; in particular, if some predictors are correlated with one another, then this multicollinearity will inflate their standard errors and hence their p-values, regardless of their estimated betas.
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