Table 1.

Recoding a phased genotype using three orthogonal terms

Phased genotype	Freq	Add Code	Std add	Dom code	Std dom	POE code	Std POE
$a_{mo}{a}_{fa}$	$q^2$	0	$-\sqrt{2p/q}$	0	$-p/q$	0	0
$a_{mo}{A}_{fa}$	$pq$	1	$\left(q-p\right)/\sqrt{2pq}$	$2p$	1	− 1	$-1/\sqrt{2pq}$
$A_{mo}{a}_{fa}$	$pq$	1	$\left(q-p\right)/\sqrt{2pq}$	$2p$	1	1	$1/\sqrt{2pq}$
$A_{mo}{A}_{fa}$	$p^2$	2	$\sqrt{2q/p}$	$4p-2$	$-q/p$	0	0

The minor allele is $A$, with frequency $p$, major allele $a$ with frequency $q=1-p$. $A_{mo}$: maternally inherited $A$ allele; $A_{fa}$: paternally inherited $A$ allele. “Freq” expected frequency of the genotype under Hardy–Weinberg equilibrium. “Add Code” additive coding of the phased genotype. “Std Add” standardized additive coding based on mean $2p$ and variance $2pq$. “Dom Code” dominance coding of the phased genotype. “Std Dom” standardized dominance coding based on mean $2p^2$ and variance $4p^2{q}^2$. “POE Code” parent-of-origin effect coding of the phased genotype. “Std POE” standardized parent-of-origin effect coding based on mean $0$ and variance $2pq$