4/14/2023 0 Comments Gpower effect size fIf she just wants to detect a small effect in either direction (positive or We specify alternative = "greater" since we She needs to observe about a 1000 students. # approximate correlation power calculation (arctangh transformation) # Conventional effect size from Cohen (1982) It is simply the hypothesized correlation. There is nothing tricky about the effect size argument, r. If you have the ggplot2 package installed, it will create a plot using ggplot. The pwr package provides a generic plot function that allows us to see how power changes as we change our sample size. If we desire a power of 0.90, then we implicitly specify a Type II error tolerance of 0.10. Our tolerance for Type II error is usually 0.20 or lower. This is thinking there is no effect when in fact there is. Type II error, \(\beta\), is the probability of failing to reject the null hypothesis when it is false. Our tolerance for Type I error is usually 0.05 or lower. This is considered the more serious error. This is thinking we have found an effect where none exist. Type I error, \(\alpha\), is the probability of rejecting the null hypothesis when it is true. The alternative argument says we think the alternative is “greater” than the null, not just different. It is sometimes referred to as 1 - \(\beta\), where \(\beta\) is Type II error. This is also sometimes referred to as our tolerance for a Type I error (\(\alpha\)). (More on effect size below.) sig.level is the argument for our desired significance level. The function ES.h is used to calculate a unitless effect size using the arcsine transformation. Our effect size is entered in the h argument. Notice that since we wanted to determine sample size ( n), we left it out of the function. If we're correct that our coin lands heads 75% of the time, we need to flip it at least 23 times to have an 80% chance of correctly rejecting the null hypothesis at the 0.05 significance level. The function tells us we should flip the coin 22.55127 times, which we round up to 23. # proportion power calculation for binomial distribution (arcsine transformation) Here is how we can determine this using the pwr.p.test function. How many times should we flip the coin to have a high probability (or power), say 0.80, of correctly rejecting the null of \(\pi\) = 0.5 if our coin is indeed loaded to land heads 75% of the time?
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