Can odds be greater than 100%?

Odds represent the probability of an event occurring divided by the probability of an event not occurring. Although related, probability and odds are not the same. Probability values can only range from 0 to 1 (0% to 100%), whereas odds can take on any value.

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Odds Ratio

Quantitative Results

Odds Ratio (OR) measures the association between an outcome and a treatment/exposure. Or in other words, a comparison of an outcome given two different groups (exposure vs. absence of exposure). OR is a comparison of two odds: the odds of an outcome occurring given a treatment compared to the odds of the outcome occurring without the treatment. Odds represent the probability of an event occurring divided by the probability of an event not occurring. Although related, probability and odds are not the same. Probability values can only range from 0 to 1 (0% to 100%), whereas odds can take on any value. An OR value of 1 indicates no effect on the odds from the exposure to the outcome; of OR values less than 1 indicate that lower odds of the outcome are attributed by the exposure; and of OR values greater than 1 indicated that higher odds of the outcome are attributed by the exposure. OR can be used to assess if a particular treatment is considered a ‘risk factor’ for a particular outcome.

To calculate OR, the frequencies of two dichotomous variables are required.

For example: a study consist 263 participants, where the aim of the study is to assess the OR of having the flu virus given the presence of a diet pill. The two dichotomous variables to be examined are flu virus (yes vs. no) and diet pill consumption (takes regularly vs. does not take regularly). Of the 100 participants: 45 participants have the flu virus and regularly consume diet pills, 86 participants have the flu virus and do not take diet pills regularly, 32 participants do not have the flu virus and take diet pills regularly, and 100 participants do not have the flu virus and do not take diet pills regularly. To calculate the OR, we make sure the numerator and denominator are in the correct location: the numerator of the ratio is the number of participants who have the flu and take diet pills regularly (45) divided by the number of participants who do not have the flu virus and take diet pills regularly (32); and the denominator of the ratio is the number of participants who have the flu and do not take diet pills regularly (86) divided by the number of participants who do not have the flu and do not take diet pills regularly (100). OR = (45/32) / (86/100) = 1.63 Thus, the odds of having the flu are 1.63 higher given the regular consumption of diet pills compared to not taking diet pills regularly.

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