Statistical Power Analysis for One-way ANOVA
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.
wp.anova(k = NULL, n = NULL, f = NULL, alpha = 0.05, power = NULL,
type = c("overall", "two.sided", "greater", "less"))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 ( |
An object of the power analysis.
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.
#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
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