This is based on a t-distribution with df = 38 degrees of freedom (total sample size N = 40 - 2). We expect p = 0.023 so we expect to reject H 0. Compute t-test for expected sample sizes, means and SD's in Excel
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So let's for a moment pretend that we'll find exactly these and enter them into a t-test calculator. However, we do know the most likely outcomes: they're our population estimates. Obviously, nobody knows the outcomes for this study until it's finished. Or -alternatively- what's the probability of rejecting H 0 that the mean blood pressure is equal between treated and untreated populations?
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the average blood pressure in some untreated population is 160 mmHg.Power Calculation ExampleĪ pharmaceutical company wants to demonstrate that their medicine against high blood pressure actually works. But before taking a look at factors affecting power, let's first try and understand how a power calculation actually works. This results in the 4 scenarios outlined below.Ĭorrect decision Probability = (1 - β) = powerĪs you probably guess, we usually want the power for our tests to be as high as possible. Type I and Type II ErrorsĪny null hypothesis may be true or false and we may or may not reject it. Not rejecting a false H 0 is known as a committing a type II error. So even though H 0 is false, we've little power to actually reject it. The probability of finding this is only 0.058. If a population correlation ρ = 0.10 and we sample N = 10 respondents, then we need to find an absolute sample correlation of |r| > 0.63 for rejecting H 0 at α = 0.05. For the aforementioned example, (1 - β) is only 0.058 (roughly 6%) as shown below. This probability is known as power and denoted as (1 - β) in statistics. What's the probability of correctly rejecting the null hypothesis? Now, given a sample size of N = 10 and a population correlation ρ = 0.10, Since p > 0.05, his chosen alpha level, he does not reject his (false) null hypothesis that ρ = 0.The significance level for this test, p = 0.68.
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He tests the (false) null hypothesis H 0 that ρ = 0.A scientist examines a sample of N = 10 people and finds a sample correlation r = 0.15.In some country, IQ and salary have a population correlation ρ = 0.10.