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# 27 - hypothesis • If you insist on higher power(such as...

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If our sample is too small, even large effects in the population will often fail to give statistically significant results. To decide how many observations we need: Significance level. How much protection do we want against getting a significant result from our sample when there really is no effect in the population? Effect size. How large an effect in the population is important in practice? Power. How confident do we want to be that our study will detect an effect of the size we think is important? Power: The test's ability to detect an alternative hypothesis. The power against a specific alternative is the probability that the test will reject H0 when the alternative is true. If you insist on a smaller significance level (such as 1% rather than 5%), you will need a larger sample. A smaller significance level requires stronger evidence to reject the null
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Unformatted text preview: hypothesis. • If you insist on higher power (such as 99% rather than 90%), you will need a larger sample. Higher power gives a better chance of detecting an effect when it is really there. • At any significance level and desired power, a two-sided alternative requires a larger sample than a one-sided alternative. • At any significance level and desired power, detecting a small effect requires a larger sample than detecting a large effect. The significance level of a test is the probability of reaching the wrong conclusion when the null hypothesis is true. The power for a specific alternative is the probability of reaching the right conclusion when that alternative is true....
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