In Schweser, I didn’t understand the concept below: "Decreasing the significance level (probability of a Type I error) from 5% to 1%, for example, will increase the probability of failing to reject a false null (Type II error) and therefore reduce the power of the test. How are these probabilities linked and hence the power of the test?
I will start with saying that this conversation is taking place with a set sample size. A Type I error is when you reject a true null Hypothesis, thus by making alpha smaller (5% to 1%) you decrease the likelihood of making a type I error. A Type II error is when you reject a false null hypothesis (that is then main hypothesis was actually false but you could not find significant statistical evidence to reject the null hypothesis). By requiring more statistical evidence to reject the null hypothesis you decrease the chance of making a type I error, but you increase the chance of making a type II error. The power of the test is defined as 1 - P(making a Type II error) thus by reducing alpha you are making a type II error more likely, therefore you are reducing the “power of the test” Hope it helps.
thanks a bundle
To add to aussie… In type 11 error - it is the fail to reject a false null hypothesis… The power of the test is to correctly rejecting a false null hypothesis…you catch a liar.