QuantPsyc (version 1.6)

powerF: Power in F distribution

Description

Computes power (1 - beta) to detect an effect with a given effect size, sample size (df) and specified alpha (significance) level.

Usage

powerF(PV, df2, df1 = 1, alpha = 0.05)

Arguments

PV

Percent of variance accounted for by effect.

df2

Denominator Degrees of Freedom for a given model

df1

Numerator Degrees of Freedom for a given model

alpha

Significance level for desired effect

Value

A numeric value representing the power to detect the effect

Warning

It is critical that the user correctly specify the model for which the effect is obtained. For instance, if a single coeficient from a regression model is the object of inquiry (e.g., interaction effect in moderation model), the DF should reflect that effect and not the overall model, which also contains the 'main effects'.

Details

Murphy & Myors (2004) detail the use of a similar function and the notion that most distributions can be converted to F. Therefore, they argue that the F distribution is the most versatile in computing power. Typically, alpha is set at .05 (default). Users will likely find conversions of various distributions to F corresponding to a df1=1 (default). Therefore, users can manipulate df2 based on their model to estiamte sample size needs. Likewise, one may begin with a given sample size (i.e., df2) and manipulate PV (effect size) to iteratively determine what power their study is likely to detect. Conventions maintain that .80 is a sufficient target, and that no study shold be designed with power = .5 or less.

References

Murphy, K. R., & Myors, B. (2004). Statistical power analysis: A simple and general model for traditional and modern hypothesis tests (2nd ed.). Mahwah, NJ: Lawrence Erlbaum Associates.

Examples

# NOT RUN {
# Simulated TRA example
data(tra)
lm1 <- lm (attitudes ~ beliefs*values, tra)
summary(lm1) 
# power to detect the interaction effect, where df1 = 1 and df2 = n-k-1 = 996
# PV = t^2/(t^2+df2) = .1863
powerF(.1863, 996)

# Estimate sample size needed to detect interaction effect with PV = .01 and power = .8
powerF(.01, 200)  # too low
powerF(.01, 1000) # too high
powerF(.01, (800-3-1))  # just right: n=800 - k=3 - 1

# }