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| 1 | +--- |
| 2 | +layout: post |
| 3 | +title: Odds and Odds Ratio |
| 4 | +subtitle: Explaining Odds and Odds Ratio with the help of example |
| 5 | +cover-img: /assets/img/path.jpg |
| 6 | +thumbnail-img: /assets/img/thumb.png |
| 7 | +share-img: /assets/img/path.jpg |
| 8 | +gh-repo: arpithub/arpithub.github.io |
| 9 | +gh-badge: [star, fork, follow] |
| 10 | +tags: [statistics,book] |
| 11 | +comments: true |
| 12 | +--- |
| 13 | + |
| 14 | +Currently, I am reading the book **The Art of Statistics** by Sir David John Spiegelhalter and wanted to touch on the Odds and Odds ratio. |
| 15 | +We see these concepts everywhere, odds of an event, odds of winning something. |
| 16 | +The definition of Odds is: |
| 17 | + __Chance of an event happening / Chance of an event not happening__ |
| 18 | + |
| 19 | +Odds Ratio: It's the ratio of odds. |
| 20 | +__Odds of an event happening / Odds of an event not happening__ |
| 21 | + |
| 22 | +In the medical domain, the Odds ratio helps to understand if an intervention works or not and to what degree. |
| 23 | + |
| 24 | +For example, we want to test the effectiveness of a vaccine campaign. We will first calculate the odds of the Intervention group and the odds of the Control group. |
| 25 | +Let's say there are 500 people in the **Intervention group** which consists of people seen the vaccine campaign and the **Control group** which consists of 500 people who haven't seen the campaign. |
| 26 | +Among the Intervention group, 400 people have taken the vaccine, and the remaining 100 people haven't taken the vaccine. |
| 27 | +In the Control group, 275 people have taken the vaccine and the remaining 225 people haven't taken the vaccine. |
| 28 | + |
| 29 | +Odds of getting the vaccine in the Intervention group = No. of people who took the vaccine / No. of people who haven't taken the vaccine |
| 30 | + |
| 31 | +Plugging in the numbers from the above example, |
| 32 | +Odds of getting vaccine in Intervention group = 400/100 = 4 |
| 33 | + |
| 34 | +Odds of getting the vaccine in the Control group = No. of people who took the vaccine / No. of people who haven't taken the vaccine |
| 35 | + |
| 36 | +Plugging in the numbers from the above example, |
| 37 | +Odds of getting vaccine in Intervention group = 275/200 ~ 1.23 |
| 38 | + |
| 39 | +To find the effectiveness of the vaccine campaign we will calculate the Odds Ratio. |
| 40 | +ie. Ratio of Odds of Intervention group (saw campaign) to Odds of Control group (didn't see campaign). |
| 41 | + |
| 42 | +Plugging in the numbers: |
| 43 | +Odds Ratio = 4/1.23 = 3.25 |
| 44 | + |
| 45 | +How to interpret Odds Ratio: |
| 46 | +If, |
| 47 | +Odd Ratio = 1 then it means there wasn't any effect of an action on a task, here campaign (Action) has no effect on taking the vaccine (task). |
| 48 | + |
| 49 | +Odd Ratio > 1 means people who were exposed to action were more likely to perform a task, here people who saw the campaign were more likely to take the vaccine as compared to people who haven't seen the campaign. |
| 50 | + |
| 51 | +Odd Ratio < 1 means people who were exposed to action were less likely to perform a task, here people who saw the campaign were less likely to take the vaccine as compared to people who haven't seen the campaign. |
| 52 | + |
| 53 | +In our example since the Odds Ratio is greater than 1 that means the vaccine campaign was effective as people who saw the campaign (Intervention group) are more likely to take the vaccine. |
| 54 | +The Odds ratio value of 3.25 tells us that people in the Intervention group have 3 times more odds of taking the vaccine as compared to the Control group. |
| 55 | + |
| 56 | +Note - Odds Ratio greater or less than 1 can be a positive or negative finding depending on the outcome. |
| 57 | +The Odds Ratio is like R-squared which shows the relationship between two things. In the above example, a relationship between Exposing to Vaccine Campaign and Getting the vaccine. |
| 58 | + |
| 59 | +To further validate the relationship between the vaccine campaign and getting the vaccine, we can perform some Significant tests. We can check if the Odds Ratio is statistically significant or not. |
| 60 | +Here are the 3 Signifincant Tests we can perform: |
| 61 | +1. Fisher's Exact Test |
| 62 | +2. Chi-Square Test |
| 63 | +3. Wald Test |
| 64 | + |
| 65 | +Although the Odds Ratio is a powerful tool but it should be used very carefully. |
| 66 | + |
| 67 | +References: |
| 68 | +1. [https://www.youtube.com/watch?v=5zPSD_e_N04] |
| 69 | +2. [https://www.youtube.com/watch?v=8nm0G-1uJzA] |
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