I have good news and bad news he says give me the

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“I have good news and bad news,” he says. “Give me the good news,” Robertson replies. “He didn’t do as well as the law of odds,” says the professor. [Robertson pulls out his handcuffs.] “The bad news is . . .” “he did much worse than can be explained by chance . . .”
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Huh? Robertson wheels to face the professor. “What does it mean?” he snarls. “Beats me,” the professor replies, “that’s your problem.”
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The strange thing is . . . Parapsychologists have done tests of this kind for many decades now, and believe they have documented cases where the outcome is too far from random to be explained by chance. But “psychics” sometimes perform worse than random guessers, so that professional parapsychologists now do two sided tests.
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Accepting and Rejecting In a hypothesis test, after examining the sample data you make a choice: Either you accept the null hypothesis, or You reject the null hypothesis in favor of the alternative. Accepting the null hypothesis means you found no evidence contradicting it; it does not prove that the null is true .
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A useful analogy A hypothesis test is like a jury trial. In a jury trial, the null hypothesis is innocence. “Innocent until proven guilty.” Only if the evidence proves guilt beyond a reasonable doubt do you reject the null and find the defendant guilty. Acquittal (accepting the null) is no guarantee of innocence: it means insufficient evidence to convict. Example: The O. J. Simpson case. The jury acquitted based on doubts about the evidence, not because they were convinced O. J. was innocent.
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This is why . . . Some authors dislike the phrase “accept the null hypothesis” -- it implies the null has been shown to be true. They prefer to say “fail to reject the null” instead. However, since almost everyone uses the phrase “accept the null,” so will I.
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Two Kinds of Errors When you accept or reject a Null, there are two distinct kinds of errors that can be made. Rejecting a true null, or Type I error. Accepting a false null, or Type II error. Ok Type I Reject null Type II Ok Accept null Null False Null True Truth You say
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