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Problems of a significance test with a low power.

Reproducible research findings are a cornerstone of the scientific method. However, studies have shown that results of published research can be difficult to replicate when only statistically significant results are published, particularly when the statistical significance tests are conducted with small sample sizes (hence with low statistical power). Let’s consider a one sample t-test with Problems of a significance test with a low power. Reproducible research findings are a cornerstone...-10Problems of a significance test with a low power. Reproducible research findings are a cornerstone...-2 versus Problems of a significance test with a low power. Reproducible research findings are a cornerstone...-1aProblems of a significance test with a low power. Reproducible research findings are a cornerstone...-4

(a) If the population standard deviation is 0.5, what is the power of the test when the effect size is δ = 0.1 and sample size is Problems of a significance test with a low power. Reproducible research findings are a cornerstone...-51 = 10?

(b) In order to reject the null hypothesis, how large must the sample mean Problems of a significance test with a low power. Reproducible research findings are a cornerstone...-6 be?

(c) If you rejected the null using data from one experiment, how likely can the statistically significant result be verified if you repeat the same experiment?

(d) Suppose that you realized that the test has a low power and you decided to repeat the experiment with a much larger sample size (e.g., Problems of a significance test with a low power. Reproducible research findings are a cornerstone...-52 = 100). What is the power of the new test?

(e) Assuming δ = 0.1, how likely is it that you will obtain a sample mean as large as the statistically significant result from the experiment with Problems of a significance test with a low power. Reproducible research findings are a cornerstone...-51 = 10?

 
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