Table 1

Possible conversions of some effect sizes to equivalent ORs

ConversionJustification
IRR to
RR
The following formula, straightforwardly derived from the definitions of incidence rate ratio (IRR) and risk ratio (RR), converts the former into the latter:
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Fortunately, if the incidences are small enough, the average follow-up times are similar in exposed and non-exposed, the fraction in the left is approximately 1 and thus:
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RD to
RR
The following formula, straightforwardly derived from the definitions of risk difference (RD) and RR, converts the former into the latter:
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Thus, analysts might need an estimation of the probability of developing the disease (p) in the non-exposed.
RR to
OR
The following formula, straightforwardly derived from the definitions of RR and OR, converts the former into the latter:
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Fortunately, if the probabilities of developing the disease (p) are small enough, the fraction in the left is approximately 1, and thus:
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RoM to
MD
The following formula, straightforwardly derived from the definitions of ratio of means (RoM) and mean difference (MD), converts the former into the latter:
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Thus, analysts might need an estimation of the mean (m) in controls.
MD to
Glass'Δ
The following formula, straightforwardly derived from the definitions of mean difference (MD) and Glass' Δ, converts the former into the latter:
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Thus, analysts might need an estimation of the SD (s) in controls.
Glass'Δ to
Cohen’s d
The following formula, straightforwardly derived from the definitions of Glass'Δ and Cohen’s d, converts the former into the latter:
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Fortunately, if the variances (s 2) in cases and controls are similar enough, the square root in the left is approximately 1, and thus:
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Hedge’s g to Cohen’s d The following formula, straightforwardly derived from the definitions of Hedge’s g and Cohen’s d, converts the former into the latter:
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Fortunately, if the sample sizes are large enough, the small-sample correction factor (J) is approximately 1, the fraction in the left is approximately 1 and thus:
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Pearson’s r to Cohen’s d The following standard formula23 converts a Pearson’s r into an approximate Cohen’s d:
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