Risks and Odds (2)
1 Risk
Let’s think about risk:
\[\text{risk} = P(\text{event happened}) = \frac{\text{number of events}}{\text{number of events} + \text{number of non-events}}\]
2 Odds
The odds are the probability that an event happened divided by the probability that it did not happen
\[\text{odds} = \frac{P(\text{event happened})}{P(\text{event didn't happen})}\]
\[= \frac{\frac{\text{number of events}}{\text{number of events} + \text{number of non-events}}}{\frac{\text{number of non-events}}{\text{number of events} + \text{number of non-events}}}\]
which incidentally reduces to
\[= \frac{\text{number of events}}{\text{number of non-events}}\]
3 Visualize The Risk And Odds
Imagine an Event X. This event could be entering a program, exiting a program, or getting a diagnosis of a mental health or physical health condition.
Click on the table below and/or hover over the graph below to explore various scenarios.