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METHODS: Perfect Relationship


When the 'Effect Size' Is 1.00

One way to think of effect size is to consider how well one characteristic of a person allows us to predict the another characteristic. For example, if we know a person is a woman, we can predict that she's more likely to be an Abolitionist than a man. However, since the effect size is small, we would not make very accurate predictions about abolitionist status simply by knowing a person's gender. 

The drawing illustrates a situation where knowing one characteristic (temperature in degrees Celsius) allows us to perfectly predict the temperature in degrees Fahrenheit.

In fact, the mathematical formula in the diagram allows us to 'predict' degrees Fahrenheit exactly. A scientist would say that degrees Celsius accounts for 100% of the variance in degrees Fahrenheit.* 

In the social sciences, we use mathematical formulas like the one shown in the diagram (using a tool called regression analysis) to predict one characteristic by using one or more predictors. In real life, these formulas never make perfect predictions, like the temperature conversion formula in the diagram. Eta Squared is a tool for estimating how much 'strength' or 'power' one characteristic has in predicting another—realizing that 'perfect' prediction is highly unlikely.



*This example is for purposes of illustration only. Celsius and Fahrenheit are two yardsticks for measuring the same thing, not measures of two different things where one might 'influence' the other.

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