How Do I Calculate Odds From a Bivariate Table?

The phrase "the odds of something happening" refers to how likely it is to happen. In statistical terms, it is defined as the probability of an event happening divided by the probability that it won't happen. Sometimes people refer to the odds as a ratio, for example 2:1 odds of winning a race. This is just a different way of displaying the same concept.

Instructions

Calculating Odds

• 1

  Start with setting up a bivariate (two-by-two) table. Say we are evaluating how good a medical test is at detecting disease, and we have tested 100 people. We would have four numbers in our table corresponding to four groups, and might see numbers like this:

  Positive test/Have the disease (70)

  Positive test/Don't have the disease (10)

  Negative test/Have the disease (5)

  Negative test/Don't have the disease (15)

• 2

  Calculate how many ways your event can happen. In our example, if we want to know the odds of our test being accurate, we would add up the numbers in two cells of our table:

  Positive test/Have the disease (70)

  Negative test/Don't have the disease (15)

  Total ways event can happen: (85)

  These would be considered a "success" for the event of interest and will be the numerator in our final calculation.

• 3

  Calculate how many ways your event can NOT happen. In our example, we would look at the numbers for:

  Positive test/Don't have the disease (10)

  Negative test/Have the disease (5)

  Total ways event can not happen: (15)

  This will be the denominator in your calculation.

• 4

  Calculate the odds by dividing the number of ways your event can happen by the number of ways it can not happen. In our example, this would be (85)/(15)=5.67. This shows the test is almost six times more likely to give the right answer than it is to give the wrong answer.

• 5

  Display the odds in a ratio format by taking displaying the probability of non-success relative to the probability of success. In our example, this would be 15:85. To make it more user-friendly, reduce the fraction by dividing by five and display the result as 3:17. So the odds of the test giving the right answer are pretty good.