Nice test! I have trouble wrapping my head around the suggested answer (b) to Question 4. How can we try assessing the test power *given that H0 is true*? And why should the power equal the significance level? Could you perhaps elaborate on that a little?
The power curve shows the probability of rejecting the null. In the one special case where the null is true, the power is clearly then the significance level (the probability of a Type I error). In all other cases, the power is the probability of rejecting the null when it is actually false. It's one minus the probability of a Type II error.
Thanks! I was confused because I am used to the definition of test power with a condition that the null hypothesis is false, like here: http://en.wikipedia.org/wiki/Statistical_power. I now see that you define test power in a different way. Of course, your answer makes sense then.
Very good, excellent test. thank you for share.
ReplyDeleteNice test! I have trouble wrapping my head around the suggested answer (b) to Question 4. How can we try assessing the test power *given that H0 is true*? And why should the power equal the significance level? Could you perhaps elaborate on that a little?
ReplyDeleteThe power curve shows the probability of rejecting the null. In the one special case where the null is true, the power is clearly then the significance level (the probability of a Type I error). In all other cases, the power is the probability of rejecting the null when it is actually false. It's one minus the probability of a Type II error.
DeleteThanks! I was confused because I am used to the definition of test power with a condition that the null hypothesis is false, like here: http://en.wikipedia.org/wiki/Statistical_power. I now see that you define test power in a different way. Of course, your answer makes sense then.
DeleteGlad that helped.
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