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Understanding Power and Sample Size Terminology in Statistical Analysis

This guide provides an overview of key terminology related to power and sample size in statistical analysis. Power refers to the likelihood of correctly rejecting a false null hypothesis and should approach one. It discusses sample sizes (N1, N2), the significance level (alpha), and the probability of Type II error (beta), emphasizing their importance in study design. It also covers means, proportions, standard deviations, and various statistical tools (e.g., SPSS, SigmaStat, PASS) that assist in power analysis. Essential for optimizing resource allocation in research.

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Understanding Power and Sample Size Terminology in Statistical Analysis

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  1. Week 5 POWER AND SAMPLE SIZE

  2. Terminology: Normal Samples • Power is the probability of rejecting a false null hypothesis. Power should be close to one. • N1 and N2 are the number of items sampled from each population. To conserve resources, they should be small. • Alpha is the probability of rejecting a true null hypothesis. It should be small. • Beta is the probability of accepting a false null hypothesis. It should be small. • Mean1 is the mean of populations 1 and 2 under the null hypothesis of equality. • Mean2 is the mean of population 2 under the alternative hypothesis. The mean of population 1 is unchanged. • S1 and S2 are the population standard deviations. They represent the variability in the populations.

  3. Terminology: Counts/Proportions • Power is the probability of rejecting a false null hypothesis. It should be close to one. • Ni is the size of the sample drawn from the ith population. • Allocation Ratio is N2/N1 so that N2 = N1 x R. • Alpha is the probability of rejecting a true null hypothesis. It should be small. • Beta is the probability of accepting a false null hypothesis. It should be small. • P1 is the proportion for group one. • P2 is the proportion for group two under the alternative hypothesis. • Odds Ratio is [P2/(1-P2)] / [P1/(1-P1)].

  4. SPSS module SAMPLEPOWER • SigmaStat (SPSS product) • PASS (NCSS product) • SPLUS (Insightful product) SPSS: • www.spss.com/spssbi/samplepower/ • www.spssscience.com/SigmaStat/index.cfm NCSS: www.ncss.com/pass.html INSIGHTFUL: www.insightful.com/products/

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