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Table 4 Table of example for the transformation of Beta-Values to M-values and the differences, respectively. The Beta-value difference between the Placebo group and the Treatments group is constant at 10%. Due to the transformation, the M-values differ and the differences in M-values can not be mapped to the differences in Beta-values

From: Estimands in epigenome-wide association studies

Grp\(_{Placebo}\) Grp\(_{Treatment}\) \(\Delta _{Beta}\) \(\Delta _{M}\) Regression formula
Beta-value M-value Beta-value M-value    on M-values
0.001 \(-\)9.96 0.101 \(-\)3.15 0.10 6.81 \(-\)9.96 + 6.81 \(\cdot\) Grp\(_{Treatment}\)
0.101 \(-\)3.15 0.201 \(-\)1.99 0.10 1.16 \(-\)3.15 + 1.16 \(\cdot\) Grp\(_{Treatment}\)
0.201 \(-\)1.99 0.301 \(-\)1.22 0.10 0.77 \(-\)1.99 + 0.77 \(\cdot\) Grp\(_{Treatment}\)
0.301 \(-\)1.22 0.401 \(-\)0.58 0.10 0.64 \(-\)1.22 + 0.64 \(\cdot\) Grp\(_{Treatment}\)
0.401 \(-\)0.58 0.501 0.01 0.10 0.59 \(-\)0.58 + 0.59 \(\cdot\) Grp\(_{Treatment}\)
0.501 0.01 0.601 0.59 0.10 0.58 0.01 + 0.58 \(\cdot\) Grp\(_{Treatment}\)
0.601 0.59 0.701 1.23 0.10 0.64 0.59 + 0.64 \(\cdot\) Grp\(_{Treatment}\)
0.701 1.23 0.801 2.01 0.10 0.78 1.23 + 0.78 \(\cdot\) Grp\(_{Treatment}\)
0.801 2.01 0.901 3.19 0.10 1.18 2.01 + 1.18 \(\cdot\) Grp\(_{Treatment}\)
0.901 3.19 0.999 9.96 0.10 6.77 3.19 + 6.77 \(\cdot\) Grp\(_{Treatment}\)