Quality Progress - July 2015 - (Page 51)

STATISTICS ROUNDTABLE BY CHRISTOPHER A. SEAMAN, JULIA E. SEAMAN AND I. ELAINE ALLEN The Significance of Power Avoid mistakenly rejecting the null hypothesis in statistical trials THE CONCEPT OF "power" has long been overshadowed in statistical circles Power and statistical significance by its big brother, "significance." Both Null hypothesis should not be rejected parameters, chosen before a test, dictate the sample size and likelihood of making an erroneous conclusion when comparing two groups (see Table 1). The p-value or significance threshold is the first taught / TABLE 1 Null hypothesis should be rejected Reject null hypothesis False positive = α type I error True negative = power Do not reject null hypothesis True positive = confidence interval False negative = β type II error and most commonly used statistic. problems. A higher-power value indicates with budget, time and project logistical mistakenly rejecting the null hypothesis a less likely chance for a false negative. constraints. that both groups are similar when the null The power of a study is directly related to hypothesis is indeed true. This mistaken its sample size and effect size variability. the study setup must reduce the risks result is called a false positive (type I In general, the greater the sample size of being underpowered. If a study is errors or α), and it means you've found a and the lower the variability, the higher a underpowered, the most direct issue that difference between two groups when re- study's power. can arise is to refuse to reject the null Significance sets the threshold for ally they are not different. Both of these study variables, however, As power is a required part of testing, hypothesis when, in fact, it is false. This will increase time and cost. To completely means that there is a real difference in the controlling the complementary testing eliminate any chance for false negatives two groups being compared, but the test is problem to reduce false negatives (type II and for the best study, you must test every unable to detect it. errors or β). Power determines how likely possible option to the absolute physical a test is to reject the null hypothesis when limit of measurement. In reality, therefore, comes in the form of reproducibility of the null hypothesis is false. there is a balancing act between increas- results. One study may find significant ing power through more samples and differences between two groups, but more precise and accurate measurements when others attempt to achieve the same Power, on the other hand, focuses on When a statistical trial is conducted without enough power, it can lead to A more nuanced issue with power results, they do not find a difference. This could be a symptom of underpowered follow-up study. As Figure 1 (p. 52) shows the greater the discrimination between your type I and type II errors, the higher the power and lower the significance level of the study, and the easier it is to discriminate between the null and alternative hypotheses. In the first test (A), there is a high chance for type I and type II errors, as evidenced by the high overlap between the curves. In the second test (B), the study was designed with higher power (increased sample size and lower measurement variability), and there is much less overlap between the two groups. July 2015 * QP 51

Table of Contents for the Digital Edition of Quality Progress - July 2015

Up Front
LogOn
Expert Answers
Keeping Current
Mr. Pareto Head
Open to Change
Passion Project
Turning on the Light Bulb
What‘s Your Theory?
Measure for Measure
Quality in the First Person
Career Corner
Statistics Roundtable
Standards Outlook
ASQ's Continuing Education and Professional Development Directory
QP Toolbox
QP Reviews
One Good Idea
Back to Basics

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