Odds Ratio

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Probability and Odds are the two commonly used terms to describe the chances of an event to occur. Both these terms are casually been used interchangeably but these terms and mathematically not equivalent because these terms gives likeliness of an event in different contexts.

Probability: The probability that an event will occur is the fraction of times you expect to see an event in given number of trials. Probabilities always range between 0 and 1.

Odds: The odds are defined as the probability that the event will occur divided by the probability that the event will not occur. More specifically if P(E) the probability of an event to occur then Odds can be calculated from below equation:

 

Let us understand relation between Probability and Odds Ratio with following example while using the above equation:

We can read the above table as:

  1. If the probability of the event occurring = 0.90, then the odds are 0.90 / (1-0.90) = 0.90/0.10 = 9 (i.e., 9 to 1)
  2. If the probability of the event occurring = 0.80, then the odds are 0.80 / (1-0.80) = 0.80/0.20 = 4 (i.e., 4 to 1)
  3. If the probability of the event occurring = 0.50, then the odds are 0.50 / (1-0.50) = 0.50/0.50 = 1 (i.e., 1 to 1)

Important Points to Notice:

  1. If probability of an event is 1 then odds of the event equal to infinity
  2. If Probability of an event is 0 then odds of the event equal to 0
  3. If Probability of an event is equal to .5 then odds of the event equal to .5

Summary:

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