Statistics – Absolute Risk, Relative Risk, Expected Frequencies and Odds Ratios
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Identification
How we communicate risk or reward can be manipulated in different ways. Consider the following:
The absolute risk deals with the change in proportion in each group that would be expected to suffer an adverse effect. Absolute risk is always written as a percentage. It is the ratio of people who experience an event compared to all of the people who could have an event.
The relative risk deals with a comparison of the odds for two groups against each other. Usually written as a percentage but certain groups like the media often say n times more likely or some such multiplier.
The expected frequency is a way to communicate risk in terms of out of a number. It gives perspective and removes some cognitive distress when looking at relative risk.
The odds ratio is the ratio of the chance something will happen against the chance of it not happening.
Example
Absolute Risk: For example, if 6 out of 100 people contract a disease X in their lifetime, the absolute risk is 6/100 or 6%.
Relative Risk: For example, of those who contract the disease X who have a parent with the disease are 18% more likely to contract that disease or 3 times greater; where those who have the disease and have a parent who suffered the disease have a 7% chance, but the difference between 6% and 7% is 18% - the relative risk.
Even though the absolute risk moves from just 6% to 7%, the relative risk reported this way is scarifying and somewhat manipulative.
Expected frequencies is a good way to communicate percentages and probabilities over the psychologically distorting facts of those who may misinterpret or not understand. Your risk of getting disease x is 6 out of 100 if your parents did not have the disease X; if your parents had disease X, your risk is 7 out of 100.
The odds ratio of the above is (7/93)/(6/94) or 1.18
Solution
Communicate and demand you be communicated with precisely. Ask the question: "So that I may better understand, the number you quoted, is that the absolute, or relative risk? What is the expected frequency? The odds ratio?
If you, or they, cannot answer these basic questions, the persuasive utility is at risk.