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Log Odds Ratio

The log odds ratio is a way to quantify how strongly the presence or absence of property A is associated with the presence or absence of property B in a given population.

The log odds ratio equals the logarithm of the ratio of the product of the first sample proportion and 1 minus the second sample proportion and the product of the second sample proportion and 1 minus the first sample proportion.

Formula

QuantityVariable["r", "Unitless"] == Log[(QuantityVariable[Subscript[OverHat["p"], "1"], "Unitless"]*(1 - QuantityVariable[Subscript[OverHat["p"], "2"], "Unitless"]))/((1 - QuantityVariable[Subscript[OverHat["p"], "1"], "Unitless"])*QuantityVariable[Subscript[OverHat["p"], "2"], "Unitless"])]

symbol description physical quantity
r log odds ratio "Unitless"
pHat1 first sample proportion "Unitless"
pHat2 second sample proportion "Unitless"

Forms

Examples

Get the resource:

In[1]:=
ResourceObject["Log Odds Ratio"]
Out[1]=

Get the formula:

In[2]:=
FormulaData[ResourceObject["Log Odds Ratio"]]
Out[2]=

Use some values:

In[3]:=
FormulaData[ResourceObject["Log Odds Ratio"], {QuantityVariable[ \!\(\*SubscriptBox[ OverscriptBox[\("p"\), \(^\)], \("1"\)]\),"Unitless"] -> 0.5`, QuantityVariable[ \!\(\*SubscriptBox[ OverscriptBox[\("p"\), \(^\)], \("2"\)]\),"Unitless"] -> 0.2`}]
Out[3]=

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