Better CIs (and p-values?) for std-coefs

[mattansb]

Originally posted on https://github.com/easystats/parameters/issues/655

@bwiernik:

Strictly speaking, both the p values and CIs we currently report for standardized effects aren't strictly accurate because they don't include uncertainty in the means or SDs used to standardize. This is usually ignored by most folks. But, ideally we would include options to compute CIs accounting for those (cf. here and here).

@strengejacke

The supplemental (https://static-content.springer.com/esm/art%3A10.1007%2Fs11336-013-9380-y/MediaObjects/11336_2013_9380_MOESM2_ESM.pdf) has code how to do this, if I understand right. Must take a closer look at it.

[bwiernik]

From the fungible package which implements those methods

https://github.com/cran/fungible/blob/master/R/seBeta.R

https://github.com/cran/fungible/blob/master/R/seBetaCor.R

https://github.com/cran/fungible/blob/master/R/seBetaFixed.R

And somewhat cleaner implementation of the normal-theory methods

https://github.com/psychmeta/psychmeta/blob/b9e27791563f4b98b5e1aaeb5bc97d97bb28d055/R/lm_mat.R#L483