WebPower (version 0.6)

wp.anova: Statistical Power Analysis for One-way ANOVA

Description

One-way analysis of variance (one-way ANOVA) is a technique used to compare means of two or more groups (e.g., Maxwell & Delaney, 2003). The ANOVA tests the null hypothesis that samples in two or more groups are drawn from populations with the same mean values. The ANOVA analysis typically produces an F-statistic, the ratio of the bewteen-group variance to the within-group variance.

Usage

wp.anova(k = NULL, n = NULL, f = NULL, alpha = 0.05, power = NULL,
  type = c("overall", "two.sided", "greater", "less"))

Arguments

k

Number of groups.

n

Sample size.

f

Effect size. We use the statistic f as the measure of effect size for one-way ANOVA as in Cohen (1988). Cohen defined the size of effect as: small 0.1, medium 0.25, and large 0.4.

alpha

Significance level chosed for the test. It equals 0.05 by default.

power

Statistical power.

type

Type of test ("overall" or "two.sided" or "greater" or "less"). The default is "two.sided". The option "overall" is for the overall test of anova; "two.sided" is for a contrast anova; "greater" is testing the between-group vairance greater than the within-group, while "less" is vis versus.

Value

An object of the power analysis.

References

Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd Ed). Hillsdale, NJ: Lawrence Erlbaum Associates.

Maxwell, S. E., & Delaney, H. D. (2004). Designing experiments and analyzing data: A model comparison perspective (Vol. 1). Psychology Press.

Zhang, Z., & Yuan, K.-H. (2018). Practical Statistical Power Analysis Using Webpower and R (Eds). Granger, IN: ISDSA Press.

Examples

# NOT RUN {
#To calculate the statistical power for the overall test of one-way ANOVA:
wp.anova(f=0.25,k=4, n=100, alpha=0.05)
#  Power for One-way ANOVA
#
#    k   n    f alpha     power
#    4 100 0.25  0.05 0.5181755
#
#  NOTE: n is the total sample size (overall)
#  URL: http://psychstat.org/anova

#To calculate the power curve with a sequence of sample sizes:
res <- wp.anova(f=0.25, k=4, n=seq(100,200,10), alpha=0.05)
res
#  Power for One-way ANOVA
#
#    k   n    f alpha     power
#    4 100 0.25  0.05 0.5181755
#    4 110 0.25  0.05 0.5636701
#    4 120 0.25  0.05 0.6065228
#    4 130 0.25  0.05 0.6465721
#    4 140 0.25  0.05 0.6837365
#    4 150 0.25  0.05 0.7180010
#    4 160 0.25  0.05 0.7494045
#    4 170 0.25  0.05 0.7780286
#    4 180 0.25  0.05 0.8039869
#    4 190 0.25  0.05 0.8274169
#    4 200 0.25  0.05 0.8484718
#
#  NOTE: n is the total sample size (overall)
#  URL: http://psychstat.org/anova

#To plot the power curve:
plot(res, type='b')

#To estimate the sample size with a given power:
wp.anova(f=0.25,k=4, n=NULL, alpha=0.05, power=0.8)
#  Power for One-way ANOVA
#
#    k        n    f alpha power
#    4 178.3971 0.25  0.05   0.8
#
#  NOTE: n is the total sample size (overall)
#  URL: http://psychstat.org/anova

#To estimate the minimum detectable effect size with a given power:
wp.anova(f=NULL,k=4, n=100, alpha=0.05, power=0.8)
#  Power for One-way ANOVA
#
#    k   n         f alpha power
#    4 100 0.3369881  0.05   0.8
#
#  NOTE: n is the total sample size (overall)
#  URL: http://psychstat.org/anova

#To conduct power analysis for a contrast one-way ANOVA:
wp.anova(f=0.25,k=4, n=100, alpha=0.05, type='two.sided')
#  Power for One-way ANOVA
#
#    k   n    f alpha     power
#    4 100 0.25  0.05 0.6967142
#
#  NOTE: n is the total sample size (contrast, two.sided)
#  URL: http://psychstat.org/anova

#To calculate the power curve with a sequence of sample sizes:
res <- wp.anova(f=seq(0.1, 0.8, 0.1), k=4, n=100, alpha=0.05)
res
#  Power for One-way ANOVA
#
#    k   n   f alpha     power
#    4 100 0.1  0.05 0.1128198
#    4 100 0.2  0.05 0.3452612
#    4 100 0.3  0.05 0.6915962
#    4 100 0.4  0.05 0.9235525
#    4 100 0.5  0.05 0.9911867
#    4 100 0.6  0.05 0.9995595
#    4 100 0.7  0.05 0.9999908
#    4 100 0.8  0.05 0.9999999
#
#  NOTE: n is the total sample size (overall)
#  URL: http://psychstat.org/anova
# }