In the context of a randomised control trial comparing a trial drug with placebo:
a) briefly explain the following terms:
b) List the factors that influence sample size.
Type 1 error
The null hypothesis is incorrectly rejected. Type 1 errors may result in the implementation of therapy that is in fact ineffective or a false positive test result.
Type 2 error
The null hypothesis is incorrectly accepted. Type 2 errors may result in rejection of effective treatment strategies or a false negative test result.
Power is equal to 1-β. Thus if β = 0.2, the power is 0.8 and the study has 80% probability of detecting a difference if one exists
Effect size (∆) is the clinically significant difference the investigator wants to detect between the study groups. This is arbitrary but needs to be reasonable and accepted by peers. It is harder to detect a small difference than a large difference. The effect size helps us to know whether the difference observed is a difference that matters.
Factors influencing sample size
• Selected values for significance level, α, power β and effect size ∆ (smaller values mean larger sample size)
• Variance /SD in the underlying population (larger variance means larger sample size)
The college presents a concise and effective answer to this question, which should serve as a model. Below is a non-model answer overgrown with the unnecessary fat of references and digressions.
Type 1 error: The incorrect rejection of a null hypothesis.
Type 2 error: the incorrect rejection of the alternative hypothesis.
Study power: The probability that the study correctly rejects the null hypothesis, when the null hypothesis is false.
Effect size: a quantitative reflection of the magnitude of a phenomenon; in this case, the magnitude of the positive effects of a drug on the study population.
Factors which influence sample size:
There is a good article on this in Radiology (2003)
There is an online Handbook of Biological Statistics which has an excellent overview of power analysis.
Kelley, Ken, and Kristopher J. Preacher. "On effect size." Psychological methods 17.2 (2012): 137.
Moher, David, Corinne S. Dulberg, and George A. Wells. "Statistical power, sample size, and their reporting in randomized controlled trials." Jama 272.2 (1994): 122-124.
Cohen, Jacob. "A power primer." Psychological bulletin 112.1 (1992): 155.
Dupont, William D., and Walton D. Plummer Jr. "Power and sample size calculations: a review and computer program." Controlled clinical trials 11.2 (1990): 116-128.
Eng, John. "Sample Size Estimation: How Many Individuals Should Be Studied? 1." Radiology 227.2 (2003): 309-313.