Do you every watch a basketball game and think that a player has a “hot hand,” by making a lot of baskets consecutively? Do you ever play on slot machines and think that you are having a “streak” of good, or bad, luck? People often tend to see patterns in random events that are not really there.
But there’s a bit more to it than that. Are the odds of heads after flipping a coin always 50/50? Sure. That’s the basis for knowing that random assignment leads to equal probabilities of selection for each condition in an experiment. But what is the answer to the question: What are the odds of heads after flipping a coin when you have just obtained a head on the prior toss?
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Does the logic of sampling on the basis of chance make sense to you as a way to achieve a representative sample?
Is it possible to do “better than chance” when choosing individuals in order to create two or more equivalent groups in an experiment?