slides_12_inferfinite

# A one sided p value is easily obtained from a two

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A one-sided p -value is easily obtained from a two-sided p -value by dividing the latter by two, but only if the estimate is in the direction of the stated one-sided alternative. 56

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EXAMPLE : We can compute exact p -values in some cases without a normal population. Consider the plebiscite example, where the null is H 0 : .5, which is operationally the same as H 0 : .5, against the alternative H 1 : .5. In the sample n 500, we obtained 241 yes votes, so x ̄ .482. Let Y Binomial 500,.5 – the distribution of the number of yes votes if .5. Then the p -value against .5 is P Y 241 . di binomial(500,241,.5) .22356475 57
This p -value is probably not small enough to overturn the election because it would entail a chance of Type I error of greater than 22%. There is substantially more evidence against the dictator’s claim that the population vote was 52.6%. . di binomial(500,241,.526) .02715266 So we would reject H 0 : .526 against H 1 : .526 at the 5% level but not at the 2.5% level. If the dictator cheated, he would arouse less suspicion by reporting a percentage just a little higher than 50%. 58

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