How To Convert A Percent To An Odds Ratio

A percentage can be used to measure successful attempts per 100 tries. For example, a 20 percent chance of success means you will succeed 20 times out of 100. Odds ratios are reported as the number of failures per success. For example, an odds ratio of 4-to-1 means that four failures occur for each success, or one success per five attempts. If you have two probabilities, one measured as a percentage and the other as an odds ratio, you may have to convert to compare the relative probabilities.

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TL;DR (Too Long; Didn't Read)

To write a percentage as an odds ratio, convert the percentage to a decimal ​_x_​, then calculate as follows:

(1/​_x_​) – 1 = first number in the odds ratio, while the second number in the odds ratio is 1.

1. Convert From Percentage to Decimal

Divide the percentage by 100 to convert from a percentage to a decimal. For example, consider that you're asked to convert a 40 percent chance of success into an odds ratio:

\(\frac{40}{100} = 0.4\)

2. Divide by the Decimal

Divide 1 by the percentage expressed as a decimal. In this example, this gives you:

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\(\frac{1}{0.4} = 2.5\)

3. Find the First Number of the Odds Ratio

Subtract 1 from your result in Step 2 to find the first number of the odds ratio. In this example, you have:

\(2.5 – 1 = 1.5\)

4. Substitute Into the Odds Ratio

Substitute your result from Step 3 for ​X​ in the odds ratio ​X​-to-1. In this example, the result from Step 3 is 1.5. So your original 40 percent success ratio, written as an odds ratio, is 1.5-to-1.

Cite This Article

MLA

Kennan, Mark. "How To Convert A Percent To An Odds Ratio" sciencing.com, https://www.sciencing.com/convert-percent-odds-ratio-8685477/. 8 December 2020.

APA

Kennan, Mark. (2020, December 8). How To Convert A Percent To An Odds Ratio. sciencing.com. Retrieved from https://www.sciencing.com/convert-percent-odds-ratio-8685477/

Chicago

Kennan, Mark. How To Convert A Percent To An Odds Ratio last modified March 24, 2022. https://www.sciencing.com/convert-percent-odds-ratio-8685477/

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