Can anyone explain when should I add 0.5 to the z-score?
Why add 0.5 to a z-score?
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statistics
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4Well, if the distribution is symmetric and continuous then $Pr(z\leq 0)=0.5$. – 2011-05-06
2 Answers
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Based on the example you give in your comment above, I think what's being used is that $P(z\lt 0)=0.5$ (and $P(z\gt 0)=0.5$, too), so that $P(z\le 1.35)=P((z\lt0)\text{ or }(0\le z\le 1.35))=0.5+P(0\le z\le 1.35)$.
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0I think Isaac has it right. Some statistics tables give the $z$ score probability corresponding to $P(0 \leq Z \leq z)$, while some give it for $P(Z \leq z)$. I'm guessing OP is looking at one of the former. (See, for example, http://www.mathsisfun.com/data/standard-normal-distribution-table.html) – 2011-05-07
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If your problem involves binomial probabilities, and you wish to use the normal approximation to the binomial, you would add .5 to the z formula (not the score) as a continuity correction factor.