Section_6.3_How_Testing_Works[1]

# Section_6.3_How_Testing_Works[1] - How Testing Works - and...

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How Testing Works - and Doesn’t 1. The value of P depends on the size of the effect. Example: In example 16 of section 6.2 the average score of the 500 seniors was drivers was 461. This supports the claim that μ > 450 P = .0069 But suppose the500 seniors had only scored a little more than 450. For example, suppose they had only scored an average of 452. The smaller difference would make P larger. Here is the calculation of P: P = 1 - .6736 = .3264 z = - 452 450 100 500 45 . Moral: Bigger effects lead to smaller values of P. So we are more likely to support the claim if the effect is a big one. This is reasonable. 2. The value of P depends on the sample size. This is because smaller samples are naturally more variable than big ones, so it is harder to tell whether the observed effect is due to chance or not. Example: Suppose in the same example the sample consisted of only 100 seniors instead of 500. If there were 100 drivers then z would be and P would be 1 - .8643 = .1359. z = - 461 450 100 100 110 . So if there had been only 100 drivers in the sample, P would have been more than 5%, and we could not reject the null hypothesis. Moral: Larger samples result in smaller values of P. So you can not judge how big the effect is just by seeing P. 3. Statistical significance/ practical significance. In everyday speech, something that is significant has some practical importance. But an effect can be statistically significant even if the effect is so small that it does not matter to anyone - if the sample is large enough. (Of course, people can also do statistical tests of questions that no one cares about.) 4. Type I Error:

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## This note was uploaded on 09/23/2011 for the course MATH 324 taught by Professor Staff during the Spring '08 term at S.F. State.

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Section_6.3_How_Testing_Works[1] - How Testing Works - and...

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