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Odds and likelihood ratios
Likelihood ratios can help in diagnostic testing and decisions.
During the pandemic, people get different tests. Someone may do a rapid lateral flow device test. If that is positive, they could then get a polymerase chain reaction (PCR) swab test. What if the PCR test returns negative, thus giving conflicting results?
Odds and probabilities
In classical statistics, probabilities are relative frequencies of an event over many trials. If you roll a fair six-sided die lots of times, it will come up ‘5’ one-sixth of the time.
Odds are a ratio. It is the probability an event will occur divided by the probability that event will not occur. For our fair die, the odds of the die coming up ‘5’ are one to five (or 0.2). This is because there is one side that our chosen event, versus five other sides. If there was an event with 80% probability, then the odds would be four to one (or 4).
We can also convert those odds to the probabilities. The probability is the odds number, divided by the odds number plus 1. For instance, suppose the odds were 0.2 (or one to five). The probability is then 0.2 divided 1.2, or 1/6. That recovers the probability of a ‘5’ on a fair six-sided die.
