METHODS: No Influence
When the 'Effect Size' Is 0.00
In the Death Penalty Study, researchers asked 800 people if the punishment for murder should be the death penalty or life imprisonment with absolutely no possibility of parole. Of the 800, 49% favored the death penalty while 51% favored life in prison.
In this example, imagine that researchers flipped a coin for each of these 800 people before they completed the questionnaire. If the coin came up heads (which it would roughly half the time), that person would be assigned to the heads group. If tails, that person would be assigned to the tails group. So each person is randomly assigned by the coin tosses to one group or the other. How much 'influence' does the coin toss exert on a person's subsequent support for the death penalty? The answer is no influence.* Since 49% of the 800 people favor the death penalty, we would expect about 49% of the people in the heads group and 49% of the people in the tails group to also favor the death penalty.
Of course, in reality, there might be slight differences between people favoring the death penalty in the heads group and those in the tails group. If we had only 8 people instead of 800, we might see a big percentage difference between the two groups by chance alone. But as the number of people increases, differences in randomly assigned groups become tiny. In other words, knowing whether a person is in the heads group or the tails group does not help us 'predict' whether a person supports the death penalty over life in prison. Eta Squared is .00.
*There is no logical connection between a coin landing heads or tails and a person's support for the death penalty.