2007, vol. 3 (2), p. 43-50 | Carmen R. Wilson VanVoorhis and Betsy L. Morgan
This article discusses the concept of statistical power and its relationship to Type I and Type II errors. Power is the probability of correctly rejecting a false null hypothesis. It is crucial for researchers to consider power during the design phase of a study to ensure sufficient sample size for detecting differences, associations, chi-square, and factor analyses. Researchers often struggle with Type II errors, which occur when the null hypothesis is false but not rejected. Power is influenced by sample size, effect size, and the significance level (α). Larger sample sizes increase power, as do larger effect sizes. However, practical constraints often limit sample size, so researchers must balance these factors.
The article provides rules of thumb for determining appropriate sample sizes for various statistical tests. For tests designed to detect differences (e.g., t-tests, ANOVA), a sample size of 30 per cell is generally sufficient for 80% power with a medium effect size. For correlation and regression analyses, a minimum of 50 participants is recommended, with more needed for larger numbers of independent variables. For chi-square tests, no expected frequency should drop below 5, and for factor analysis, a minimum of 300 cases is suggested.
The article also discusses how error variance and the choice of α level affect power. Increasing α can increase power, but it also increases the risk of Type I errors. Researchers should be aware of these trade-offs and consider the context of their study when determining sample size. The article concludes that proper attention to power is essential for reliable research, and that guidelines for sample size are increasingly important in research protocols and manuscripts.This article discusses the concept of statistical power and its relationship to Type I and Type II errors. Power is the probability of correctly rejecting a false null hypothesis. It is crucial for researchers to consider power during the design phase of a study to ensure sufficient sample size for detecting differences, associations, chi-square, and factor analyses. Researchers often struggle with Type II errors, which occur when the null hypothesis is false but not rejected. Power is influenced by sample size, effect size, and the significance level (α). Larger sample sizes increase power, as do larger effect sizes. However, practical constraints often limit sample size, so researchers must balance these factors.
The article provides rules of thumb for determining appropriate sample sizes for various statistical tests. For tests designed to detect differences (e.g., t-tests, ANOVA), a sample size of 30 per cell is generally sufficient for 80% power with a medium effect size. For correlation and regression analyses, a minimum of 50 participants is recommended, with more needed for larger numbers of independent variables. For chi-square tests, no expected frequency should drop below 5, and for factor analysis, a minimum of 300 cases is suggested.
The article also discusses how error variance and the choice of α level affect power. Increasing α can increase power, but it also increases the risk of Type I errors. Researchers should be aware of these trade-offs and consider the context of their study when determining sample size. The article concludes that proper attention to power is essential for reliable research, and that guidelines for sample size are increasingly important in research protocols and manuscripts.