A group of researchers is designing a study to investigate the role of a new diet in treating patients with mild hypertension. The researchers are using the following parameters to calculate the sample size required for the study: Expected change (decrease) in systolic blood pressure (SBP) with the new diet: 8 mm HgExpected standard deviation for SBP in the population: 10 mm HgValue for α: 0.01Power: 0.85
Based on these parameters, they estimate the minimum sample size required for a 2-tailed test to be 21. In which of the following situations would a sample size 21 be needed to appropriately address the research question?
A)If actual decrease in systolic blood pressure with the new diet is 5 mm Hg rather than 8 mm Hg
B)If actual standard deviation for systolic blood pressure is 7 mm Hg rather than 10 mm Hg
C)If α is set at 0.05 rather than at 0.01
D)If power is set at 0.75 rather than at 0.85
E)If the 2-tailed test is replaced by a 1-tailed test

Question

A group of researchers is designing a study to investigate the role of a new diet in treating patients with mild hypertension.  The researchers are using the following parameters to calculate the sample size required for the study: Expected change (decrease) in systolic blood pressure (SBP) with the new diet:  8 mm HgExpected standard deviation for SBP in the population:  10 mm HgValue for α:  0.01Power:  0.85
Based on these parameters, they estimate the minimum sample size required for a 2-tailed test to be 21.  In which of the following situations would a sample size >21 be needed to appropriately address the research question?
A)If actual decrease in systolic blood pressure with the new diet is 5 mm Hg rather than 8 mm Hg
B)If actual standard deviation for systolic blood pressure is 7 mm Hg rather than 10 mm Hg
C)If α is set at 0.05 rather than at 0.01
D)If power is set at 0.75 rather than at 0.85
E)If the 2-tailed test is replaced by a 1-tailed test

Quizplus · Accepted Answer

Explanation: 11ec2b69_c0f7_d2e8_8f63_0dbf00f908c2_MD0005_00 Sample size is related to statistical power, which is the ability to detect a significant effect in a study (eg, difference between groups) when an effect really exists. In general, larger sample sizes have higher statistical power than smaller sample sizes. However, sample size and statistical power are affected by a number of parameters, including the magnitude of the expected effect size (size of expected difference between the groups) and the level of statistical significance adopted in the study. In this example, researchers have estimated that a sample size of 21 is required for 85% (0.85) statistical power in detecting an average decrease in systolic blood pressure (SBP) of 8 mm Hg (effect size). If the actual effect size is smaller than initially expected (eg, 5 mm Hg rather than 8 mm Hg), the study might not have adequate power to detect the effect due to a reduction in statistical power (ie, <85%). In other words, more study subjects (ie, n >21) will be needed to increase the power of the study so as to detect a smaller effect size. (Choice B) A smaller than expected standard deviation in the population means that observations are more homogeneous than expected. As a result, differences between groups can be detected more easily due to increased power. Therefore, the estimated sample size (n = 21) should have sufficient power to address the research question. (Choice C) Increasing the significance level from 0.01 to 0.05 means accepting a less stringent cutoff for statistical significance (5% rather 1%). As a result, even with the same sample size (n = 21), there will be a greater probability of detecting differences between groups with a less stringent cutoff. (Choice D) The sample size of 21 was estimated to have 85% statistical power for detecting a specific effect size. A higher level of power requires larger sample sizes; if a lower power (eg, 75%) is considered, a sample size of 21 would be more than enough to detect the same effect size. (Choice E) In contrast to 2-tailed tests, 1-tailed tests have more statistical power as they look only for an effect in 1 direction (eg, looking for an increase only rather than either an increase or a decrease). Conducting a 1-tailed test (eg, assessing whether there is a statistically significant SBP decrease with diet) would require fewer subjects as the study would naturally have more power. Educational objective: The sample size and power of a study are interdependent and affected by a number of parameters. In general, larger sample sizes are needed when a higher level of power is required or when differences between groups are small.

A Group of Researchers Is Designing a Study to Investigate