# ODDS Ratio Interpretation Quick Guide

odds ratio interpretation, the probability is a statistical term that relates to the likelihood of an event occurring. It’s calculated as follows:

## Probability:

`P(event) = (Desirable Outcomes) / (Possible Outcomes)`

Let’s say we have a bag with four red cards and one green card in it. If you close your eyes and pick a card at random, the probability of picking a green card is computed as follows.

`p(green) = 1 / 5 = 0.2`

The odds of an event occurring can be calculated as follows.

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## Odds:

`Odds(event) = P(event happens) / 1-P(event happens)`

For example, the odds of picking a green card are (0.2) / 1-(0.2) = 0.2 / 0.8 = 0.25.

The odds ratio is the ratio of two odds.

## Odds Ratio:

`Odds Ratio = Odds of Event A / Odds of Event B`

We could, for example, compute the probability of getting a red or green card.

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The probability of picking a red card is 4/5 = 0.8.

The odds of picking a red card are (0.8) / 1-(0.8) = 0.8 / 0.2 = 4.

The odds ratio for picking a red card compared to a green card is calculated as:

Odds(red) / Odds(green) = 4 / 0.25 = 16.

Thus, the odds of picking a red card are 16 times larger than the odds of picking a green card.

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### When Do You Use Odds Ratios in Real Life?

In the real world, researchers employ odds ratios in a variety of situations when they want to analyze the chances of two occurrences happening.

#### Case 1: Interpreting Odds Ratios

We can consider one common example here, researchers seek to determine if a novel treatment enhances a patient’s chances of having a good health result when compared to an existing treatment.

The table below displays the number of patients who had a favorable or bad health outcome as a result of their medicine.

Calculating the odds ratio with a contingency table

The odds of a favorable outcome for a patient under the new treatment or medicine can be computed as follows,

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```Odds = P(positive) / 1 – P(positive)
= (60/100) / 1-(60/100)
= (60/100) / (40/100)
= 1.5```

The odds of a patient having a favorable outcome under current treatment can be calculated as follows:

```Odds = P(positive) / 1 – P(positive)
= (42/100) / 1-(42/100)
= (42/100) / (58/100)
= 0.7241379```

The following formula can be used to calculate the likelihood of a patient having a favorable result under existing treatment

```Odds Ratio  = 1.5 / 0.7241379
= 2.071429```

This means that the odds of a patient having a favorable outcome with the new treatment are 2.071429 times higher than the chances of a patient having a positive outcome with the present treatment. 