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Will G Hopkins Sport and Recreation AUT University Auckland NZ Clinically or Practically Decisive Sample Sizes General Principles Sample vs population Ethics Effects of effect magnitude, design, validity, reliability Approaches to Sample-Size Estimation What others have used Statistical significance Precision of estimation Clinical decisiveness
General Principles We study an effect in a sample, but we want to know about the effect in the population. The larger the sample, the closer we get to the population. Too large is unethical, because it's wasteful. Too small is unethical, because the effect won't be clear. And you are less likely to get your study published. But meta-analysis of several such studies leads to a clear outcome, so small-scale studies should be published. The bigger the effect, the smaller the sample you need to get a clear effect. So start with a smallish sample, then add more if necessary. But this approach may overestimate the effect.
More General Principles Sample size depends on the design. Cross-sectional studies (case-control, correlational) usually need hundreds of subjects. Controlled-trial interventions usually need scores of subjects. Crossover interventions usually need 10 or so subjects. Sample size depends on the validity (for cross-sectional studies) and reliability (for trials). Different approaches to estimation of sample size give different estimates of sample size. Traditional approach #1: what others have used. Traditional approach #2: statistical significance. Newer approach: acceptable precision of estimation. Newest approach: clinical decisiveness.
Traditional Approach #1: Use What Others Have Used No-one will believe your study in isolation, no matter what the sample size. A meta-analyst will combine your study with others, so... You might as well use the sample size that others have used, because… If the journal editors accepted their studies, they should accept yours. But your measurements need to be comparable to what others have used. Example: if your measure is less reliable, your outcome will be less clear unless you use more subjects.
Traditional Approach #2: Statistical Significance You need enough subjects to "detect" (get statistical significance for) the smallest important effect most of the time. You set a Type I error rate = chance of detecting null effect (5%) and a Type II error rate = chance of missing smallest effect (20%) or power = chance of detecting smallest effect = % = 80%. Problem: statistical non/significance is easy to misinterpret. Problem: this approach leads to large sample sizes. Example: ~800 subjects for case-control study to detect a standardized (Cohen) effect size of 0.2 or a correlation of 0.1. Samples are even larger if you keep the overall p<0.05 for multiple effects (the problem of inflation of Type 1 error). Smaller samples give clinically or practically decisive outcomes in our discipline.
The Type I error rate (5%) defines a critical value of the statistic. If observed value > critical value, the effect is significant. SIGNIFICANT NON-SIG Statistical Significance: How It Works area = 2.5% area = 20% When true value = smallest important value, the Type II error rate (20%) = chance of observing non-significant values. Solve for the sample size (via the critical value). probability value of effect statistic 0 positivenegative distribution of observed values, if true value = smallest important value distribution of observed values, if true value = 0 critical value smallest important value
Newer Approach: Acceptable Precision of Estimation Many researchers now report precision of estimation using confidence limits. Confidence limits define a range within which the true value of the effect is likely to be. Therefore they should justify sample size in terms of achieving acceptable confidence limits. My rationale: if you observe a zero effect, the range shouldn't include substantial positive (or beneficial) and substantial negative (or harmful) values. Gives half traditional sample sizes, for 95% confidence limits. But why 95%? 90% can be acceptable and leads to one-third the traditional sample size. The calculations are simple–I won't explain here. This approach is appropriate for studies of mechanisms.
Newest Approach: Clinical Decisiveness You do a study to decide whether an effect is clinically or practically useful or important. You can make two kinds of clinical error with your decision: Type 1: you decide to use an effect that in reality is harmful. Type 2: you decide not to use an effect that in reality is beneficial. You need a big enough sample to keep rates of these errors acceptably low. Acceptably low will depend on how good the benefit is and how bad the harm is. Default: 1% for Type 1 and 20% for Type 2. Leads to sample sizes a bit less than one-third those based on statistical significance.
The Type 1 and 2 error rates are defined by a decision value. If true value = smallest harmful value, and observed value > decision value, you will use the effect in error (rate=1%, say). HARMFULTRIVIALBENEFICIAL Clinical Decisiveness: How It Works, Version 1 If true value = smallest beneficial value, and observed value < decision value, you will not use the effect in error (rate=20%, say). Now solve for the sample size (and the decision value). probability value of effect statistic 0 positivenegative smallest harmful value distribution of observed values, if true value = smallest harmful value distribution of observed values, if true value = smallest beneficial value area = 20% area = 1% decision value smallest beneficial value
How it Works, Version 2 This approach may be easier to understand, because it doesn't involve "if the true value is the smallest worthwhile…". Instead, it's just "worst-case scenario is chances of Type 1 and 2 errors of 1% and 20% (say), which occurs when the observed value is the decision value." Put the observed value on the decision value. Work out the chances that the true effect is harmful and beneficial. You want these to be 1% and 20%. You need to draw a different diagram for this scenario. Solve for the sample size (and the decision value). This approach gives the same answer, of course. Work at it until you understand it!
Conclusions You can justify sample size using adequate precision or acceptable rates of clinical errors. Both make more sense than sample size based on statistical significance and lead to smaller samples. HOWEVER… These sample sizes are for the population mean effect. If there are substantial individual responses, precision or clinical error rates for an individual will be different: Very unlikely may become unlikely or even possible. Your decision for the individual will therefore change. So you need a sample size large enough to characterize individual responses adequately. I'm thinking about it.
This presentation was downloaded from: See Sportscience 10, 2006