Abstract
BackgroundUsing covariance or mean estimates from previous data introduces randomness into each power value in a power curve. Creating confidence intervals about the power estimates improves study planning by allowing scientists to account for the uncertainty in the power estimates. Driving examples arise in many imaging applications.MethodsWe use both analytical and Monte Carlo simulation methods. Our analytical derivations apply to power for tests with the univariate approach to repeated measures (UNIREP). Approximate confidence intervals and regions for power based on an estimated covariance matrix and fixed means are described. Extensive simulations are used to examine the properties of the approximations.ResultsClosed-form expressions are given for approximate power and confidence intervals and regions. Monte Carlo simulations support the accuracy of the approximations for practical ranges of sample size, rank of the design matrix, error degrees of freedom, and the amount of deviation from sphericity. The new methods provide accurate coverage probabilities for all four UNIREP tests, even for small sample sizes. Accuracy is higher for higher power values than for lower power values, making the methods especially useful in practical research conditions. The new techniques allow the plotting of power confidence regions around an estimated power curve, an approach that has been well received by researchers. Free software makes the new methods readily available.ConclusionsThe new techniques allow a convenient way to account for the uncertainty of using an estimated covariance matrix in choosing a sample size for a repeated measures ANOVA design. Medical imaging and many other types of healthcare research often use repeated measures ANOVA.
Highlights
Using covariance or mean estimates from previous data introduces randomness into each power value in a power curve
Providing confidence intervals to account for the uncertainty inherent in the random power values would be useful for study planning
Simulation overview The accuracy of the new approximate confidence intervals is evaluated for a wide range of conditions
Summary
Using covariance or mean estimates from previous data introduces randomness into each power value in a power curve. Creating confidence intervals about the power estimates improves study planning by allowing scientists to account for the uncertainty in the power estimates. Specifying plausible variance and covariance values usually requires estimates from a previous study. Using data from a previous study to estimate the covariance matrix makes the power value a random variable. Et al [1] noted that if the estimated variance is Providing confidence intervals to account for the uncertainty inherent in the random power values would be useful for study planning. A lower bound for power would allow stating that a test has power of at least “P” to detect an effect, with a specified confidence. A confidence region for a power curve would be even more informative
Sign-in/Register to view highlights & summary 
Published Version (
Free)
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call