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Odds ratio

As explained in Grokking Statistics

An odds ratio is the quotient of two odds, measuring how the relative likelihood of an event changes between conditions.

An odds ratio is the quotient of two odds. It measures how the relative likelihood of an event changes between conditions, such as different values of x. section 8.4

Read an odds ratio by connecting probability, odds, and change:

  • Convert probability to odds with O(X) = P(X) / (1 - P(X)). section 8.4
  • Compare odds at two conditions by dividing one by the other; the result shows the relative change in odds. section 8.4
  • In logistic regression, the odds increase or decrease per unit of x, while the linear expression represents log-odds. section 8.4

A toddler-meltdown comparison

A logistic model gives a meltdown probability of about 0.8532 at four hours, corresponding to odds of 5.813. Python can calculate the odds at four and six hours, then divide O(6) by O(4) to measure the change. section 8.4

How Grokking Statistics covers it

How deep it goes
Explains probability-to-odds conversion, log-odds, and Python comparison, stopping short of a formal derivation.
Examples
Uses toddler-meltdown risk at four versus six hours, with logistic probabilities, odds, and Python calculations.
What it assumes
Assumes probability and odds, while connecting their conversion to logistic regression and log-odds.
What you can do after
Apply it via Python to convert predicted probabilities into odds and compare odds between two conditions.
How it connects
Connects odds ratio with probability, odds, log-odds, logistic regression, and the logistic function.
Cover of Grokking Statistics
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