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Statistics LibreTexts

22.5: Odds Ratios

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  • We can also represent the relative likelihood of different outcomes in the contingency table using the odds ratio that we introduced earlier, in order to better understand the size of the effect. First, we represent the odds of being stopped for each race:

    oddssearched|black=NsearchedblackNnotsearchedblack=121936244=0.034 odds_{searched|black} = \frac{N_{searched\cap black}}{N_{not\ searched\cap black}} = \frac{1219}{36244} = 0.034

    oddssearched|white=NsearchedwhiteNnotsearchedwhite=3108239241=0.013 odds_{searched|white} = \frac{N_{searched\cap white}}{N_{not\ searched\cap white}} = \frac{3108}{239241} = 0.013 oddsratio=oddssearched|blackoddssearched|white=2.59 odds\ ratio = \frac{odds_{searched|black}}{odds_{searched|white}} = 2.59

    The odds ratio shows that the odds of being searched are 2.59 times higher for black versus white drivers, based on this dataset.

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