Dear list,I have a question regarding the link between p-values and standard errors : two of the studies I want to use for a meta analysis using slopes as the effect size report an estimate of the slope but do not report either the variance or the standard error associated with it.The studies give the degrees of freedom, correlation, and p-value.I think I should be able to retrieve the number of observations from the degrees of freedom,but I don't know if I can retrieve a standard error from simply the p-value and df, and I have not been taught a way to do so.Is there a way for me to get a standard error for the slope from thesemetrics ?Thank you,Norman
[R-meta] getting standard errors from p-values
2 messages · Norman DAURELLE, Wolfgang Viechtbauer
Hi Norman, I am assuming we are talking about regular regression here. The sample size is equal to the df plus the number of coefficients in the model (also counting the intercept). You can then recover the SE of the slope (regression coefficient) from the p-value and the slope. Here is an illustration: set.seed(1234) n <- 100 x1 <- runif(n) x2 <- runif(n) y <- 0.1 * x1 + 0.2 * x2 + rnorm(n) res <- coef(summary(lm(y ~ x1 + x2))) res b <- res[2,1] b p <- res[2,4] p # all you know is b, p, and the df (= n-3 in this example) # this gives the SE of the slope for x1 abs(b) / qt(p/2, df=n-3, lower.tail=FALSE) If b and/or p are rounded, then this will introduce some error into the back-calculation. I wouldn't worry about this unless p is given not as an 'exact' value, but for example as 'p < .05' or something like that. Best, Wolfgang
-----Original Message----- From: R-sig-meta-analysis [mailto:r-sig-meta-analysis-bounces at r-project.org] On Behalf Of Norman DAURELLE Sent: Tuesday, 26 May, 2020 1:28 To: r-sig-meta-analysis at r-project.org Subject: [R-meta] getting standard errors from p-values Dear list,I have a question regarding the link between p-values and standard errors : two of the studies I want to use for a meta analysis using slopes as the effect size report an estimate of the slope but do not report either the variance or the standard error associated with it.The studies give the degrees of freedom, correlation, and p-value.I think I should be able to retrieve the number of observations from the degrees of freedom,but I don't know if I can retrieve a standard error from simply the p-value and df, and I have not been taught a way to do so.Is there a way for me to get a standard error for the slope from thesemetrics ?Thank you,Norman