Statistical hypotheses are compared with data, often collected in carefully designed experiments. Evidence may lead us tentatively to accept or reject hypotheses. Evidence can be good or bad; it can be more, or less, convincing. When is it significant? What are the underlying ideas about accepting and rejecting hypotheses? This chapter introduces two fundamentally different ways of thinking about these issues, both of which are deeply entrenched in statistical practice. One idea is that of significance tests. Another is the power of a test to discriminate false hypotheses.
ASTROLOGY
Four members of this class went for coffee after the first meeting. Two of them had the same astrological sign (of the zodiac). There are 12 signs of the zodiac. Is this significant? Were they fated to meet?
We need to consider plausible models and ask, how likely is it, that this phenomenon would occur by chance alone?
Theoretical probability model: each person is assigned a sign by a chance setup with equal probability for each sign–just as if you drew your sign from a pack of twelve different cards, say a pack of all the clubs except the ace.
Think of a deck of cards with the aces removed, leaving 4 suits of 12 different cards each (analogous to the 12 signs and the 4 people). If we select at random a card from each suit, what is the probability that we get at least two cards that match in value?
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