Your English writing platform
Discover LudwigExact(8)
Consider h and k loci in unlinked genes, G1 = { M1,…, M h } and G2 = { M h +1,…, M h + k }.
Figure 2 M(H) curves.
But, applying the inequality between the arithmetic mean and the geometric mean and Lemma 9, we deduce the relation M h [ f 2 ] M h 2 [ g ] + M h [ g 2 ] M h 2 [ f ] ≥ 2 M h [ f 2 ] M h [ g 2 ] M h [ f ] M h [ g ] ≥ 2 M h [ f g ] M h [ f ] M h [ g ].
From this, we obtain the inequality M h [ f 2 ] M h 2 [ g ] − 2 M h [ f g ] M h [ f ] M h [ g ] + M h [ g 2 ] M h 2 [ f ] ≥ 0. Consequently the statement is true.
Proof We calculate the difference of the terms which appear in inequality (12) and (21), thus: M h [ f 2 ] M h [ g 2 ] − M h 2 [ f g ] − [ var h ( f ) var h ( g ) − cov h 2 ( f, g ) ] = M h [ f 2 ] M h 2 [ g ] − 2 M h [ f g ] M h [ f ] M h [ g ] + M h [ g 2 ] M h 2 [ f ].
In addition to "O," the Ganz auction featured versions "M," "H," and "K".
Similar(51)
Hsu A-L, Tang P-F, Jan M-H.
M-H: Mantel-Haenzel, CI: confidence interval.
The inset shows their M-H curves.
SMDs and Mantel-Haenszel (M-H) odds ratios were determined.
Let N n = Diff ( M ) - H n ¯.
Write better and faster with AI suggestions while staying true to your unique style.
Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com