To install and load pwrss:
install.packages("pwrss")
library(pwrss)pwrss R package allows statistical power and minimum required sample size calculations for
(1) testing a proportion (one-sample) against a constant,(2) testing a mean (one-sample) against a constant,(3) testing difference between two proportions (independent samples),(4) testing difference between two means (independent and paired samples),(5) testing a correlation (one-sample) against a constant,(6) testing difference between two correlations (independent samples),(7) testing an R-squared against zero in linear regression(8) testing an R-squared difference against zero in hierarchical regression,(9) testing an eta-squared or f-squared (for main and interaction effects) against zero in analysis of variance (ANOVA) (could be one-way, two-way, and three-way),(10) testing an eta-squared or f-squared (for main and interaction effects) against zero in analysis of covariance (ANCOVA) (could be one-way, two-way, and three-way),(11) testing an eta-squared or f-squared (for between, within, and interaction effects) against zero in one-way repeated measures analysis of variance (RM-ANOVA) (with non-sphericity correction and repeated measures correlation).Alternative hypothesis can be formulated as "not equal", "less", "greater", "non-inferior", "superior", or "equivalent" in (1), (2), (3), and (4); as "not equal", "less", or "greater" in (5) and (6); but always as "greater" in (7), (8), (9), (10), and (11).
If you find the package and related material useful, along with other references, please cite as:
Bulus, M. (2022). pwrss: Power and Sample Size Calculation Tools. R package version 0.1.0. https://CRAN.R-project.org/package=pwrss
Bulus, M., & Polat, C. (2022, November 7). Istatistiksel Guc Analizine Giris [Introduction to Statistical Power Analysis]. https://doi.org/10.35542/osf.io/tfyxq
A Few Snapshots
1. Generic Functions for z, t, and F tests
These generic functions calculate and return statistical power along with optional plots for Type I and Type II error rates (as long as the test statistic and degrees of freedom is known). They can be useful for calculating statistical power after data analysis (ex-post).
power.t.test(ncp = 1.96, df = 99, alpha = 0.05, alternative = "equivalent")
power.z.test(ncp = 1.96, alpha = 0.05, alternative = "equivalent")
power.f.test(ncp = 2, df1 = 2, df2 = 98, alpha = 0.05)
plot() function (S3 method) is a wrapper around the generic functions above.
design1 <- pwrss.t.2means(mu1 = 0.20, margin = -0.05, paired = TRUE,
power = 0.80, alternative = "non-inferior")
plot(design1)
design2 <- pwrss.f.ancova(eta2 = 0.10, n.levels = c(2,3),
power = .80)
plot(design2)
2. Standardizd versus Unstandardized Input for t Test
# it is sufficient to provide standardized difference between two groups for 'mu1'
# e.g. Cohen's d = 0.50 for mu1, because mu2 = 0 by default
pwrss.t.2means(mu1 = 0.50, power = .80)## Difference between two means (independent samples t test)
## H0: mu1 = mu2
## HA: mu1 != mu2
## ------------------------------
## Statistical power = 0.8
## n1 = 64
## n2 = 64
## ------------------------------
## Alternative = "not equal"
## Degrees of freedom = 125.54
## Non-centrality parameter = 2.823
## Type I error rate = 0.05
## Type II error rate = 0.2pwrss.t.2means(mu1 = 0.50, power = .80, paired = TRUE)## Difference between two means (paired samples t test)
## H0: mu1 = mu2
## HA: mu1 != mu2
## ------------------------------
## Statistical power = 0.8
## n = 34
## ------------------------------
## Alternative = "not equal"
## Degrees of freedom = 32.37
## Non-centrality parameter = 2.889
## Type I error rate = 0.05
## Type II error rate = 0.2# it is sufficient to provide pooled standard deviation for sd1
# because sd2 = sd1 by default
pwrss.t.2means(mu1 = 10, mu2 = 5, sd1 = 10, power = .80)## Difference between two means (independent samples t test)
## H0: mu1 = mu2
## HA: mu1 != mu2
## ------------------------------
## Statistical power = 0.8
## n1 = 64
## n2 = 64
## ------------------------------
## Alternative = "not equal"
## Degrees of freedom = 125.54
## Non-centrality parameter = 2.823
## Type I error rate = 0.05
## Type II error rate = 0.23. One-way, Two-way, and Three-way Analysis of Variance (ANOVA) or Analysis of Covariance (ANCOVA)
# one-way ANOVA
pwrss.f.ancova(n.levels = 2, n.covariates = 0,
power = .80, eta2 = 0.10)## One-way Analysis of Variance (ANOVA)
## H0: 'eta2' or 'f2' = 0
## HA: 'eta2' or 'f2' > 0
## ------------------------------------
## Factor A: 2 levels
## ------------------------------------
## Given eta2 = 0.1 or f2 = 0.111
## Total n = 73
## ------------------------------------
## Numerator degrees of freedom = 1
## Denominator degrees of freedom = 70.61
## Non-centrality parameter = 8.07# one-way ANCOVA
pwrss.f.ancova(n.levels = 2, n.covariates = 1,
power = .80, eta2 = 0.08)## One-way Analysis of Covariance (ANCOVA)
## H0: 'eta2' or 'f2' = 0
## HA: 'eta2' or 'f2' > 0
## ------------------------------------
## Factor A: 2 levels
## ------------------------------------
## Given eta2 = 0.08 or f2 = 0.087
## Total n = 93
## ------------------------------------
## Numerator degrees of freedom = 1
## Denominator degrees of freedom = 89.24
## Non-centrality parameter = 8.02# two-way ANOVA
pwrss.f.ancova(n.levels = c(2,3), n.covariates = 0,
power = .80, eta2 = 0.10)## Two-way Analysis of Variance (ANOVA)
## H0: 'eta2' or 'f2' = 0
## HA: 'eta2' or 'f2' > 0
## ------------------------------------
## Factor A: 2 levels
## Factor B: 3 levels
## ------------------------------------
## Given eta2 = 0.1 or f2 = 0.111
## Total n = 73 (for A)
## Total n = 90 (for B)
## Total n = 90 (for A x B)
## ------------------------------------
## Numerator degrees of freedom = 1 2 2
## Denominator degrees of freedom = 66.73 83.89 83.89
## Non-centrality parameter = 8.08 9.99 9.99# two-way ANCOVA
pwrss.f.ancova(n.levels = c(2,3), n.covariates = 1,
power = .80, eta2 = 0.08)## Two-way Analysis of Covariance (ANCOVA)
## H0: 'eta2' or 'f2' = 0
## HA: 'eta2' or 'f2' > 0
## ------------------------------------
## Factor A: 2 levels
## Factor B: 3 levels
## ------------------------------------
## Given eta2 = 0.08 or f2 = 0.087
## Total n = 93 (for A)
## Total n = 114 (for B)
## Total n = 114 (for A x B)
## ------------------------------------
## Numerator degrees of freedom = 1 2 2
## Denominator degrees of freedom = 85.34 106.96 106.96
## Non-centrality parameter = 8.03 9.91 9.91# three-way ANOVA
pwrss.f.ancova(n.levels = c(2,3,2), n.covariates = 0,
power = .80, eta2 = 0.10)## Three-way Analysis of Variance (ANOVA)
## H0: 'eta2' or 'f2' = 0
## HA: 'eta2' or 'f2' > 0
## ------------------------------------
## Factor A: 2 levels
## Factor B: 3 levels
## Factor C: 2 levels
## ------------------------------------
## Given eta2 = 0.1 or f2 = 0.111
## Total n = 73 (for A)
## Total n = 91 (for B)
## Total n = 73 (for C)
## Total n = 91 (for A x B)
## Total n = 73 (for A x C)
## Total n = 91 (for B x C)
## Total n = 91 (for A x B x C)
## ------------------------------------
## Numerator degrees of freedom = 1 2 1 2 1 2 2
## Denominator degrees of freedom = 60.93 78.13 60.93 78.13 60.93 78.13 78.13
## Non-centrality parameter = 8.1 10.01 8.1 10.01 8.1 10.01 10.01# three-way ANCOVA
pwrss.f.ancova(n.levels = c(2,3,2), n.covariates = 1,
power = .80, eta2 = 0.08)## Three-way Analysis of Covariance (ANCOVA)
## H0: 'eta2' or 'f2' = 0
## HA: 'eta2' or 'f2' > 0
## ------------------------------------
## Factor A: 2 levels
## Factor B: 3 levels
## Factor C: 2 levels
## ------------------------------------
## Given eta2 = 0.08 or f2 = 0.087
## Total n = 93 (for A)
## Total n = 115 (for B)
## Total n = 93 (for C)
## Total n = 115 (for A x B)
## Total n = 93 (for A x C)
## Total n = 115 (for B x C)
## Total n = 115 (for A x B x C)
## ------------------------------------
## Numerator degrees of freedom = 1 2 1 2 1 2 2
## Denominator degrees of freedom = 79.49 101.15 79.49 101.15 79.49 101.15 101.15
## Non-centrality parameter = 8.04 9.93 8.04 9.93 8.04 9.93 9.934. One-way Repeated Measures Analysis of Variance (RM-ANOVA)
pwrss.f.rmanova(eta2 = 0.10, n.levels = 2, n.measurements = 3,
repmeasures.r = 0.50, type = "between", power = 0.80)## One-way repeated measures analysis of variance (F test)
## H0: eta2 = 0 (or f2 = 0)
## HA: eta2 > 0 (or f2 > 0)
## ------------------------------
## Number of levels (groups) = 2
## Number of measurement time points = 3
## ------------------------------
## Statistical power = 0.8
## Total n = 50
## ------------------------------
## Type of the effect = "between"
## Numerator degrees of freedom = 1
## Denominator degrees of freedom = 47.09
## Non-centrality parameter = 8.182
## Type I error rate = 0.05
## Type II error rate = 0.2pwrss.f.rmanova(eta2 = 0.10, n.levels = 2, n.measurements = 3,
repmeasures.r = 0.50, epsilon = 1,
type = "within", power = 0.80)## One-way repeated measures analysis of variance (F test)
## H0: eta2 = 0 (or f2 = 0)
## HA: eta2 > 0 (or f2 > 0)
## ------------------------------
## Number of levels (groups) = 2
## Number of measurement time points = 3
## ------------------------------
## Statistical power = 0.8
## Total n = 17
## ------------------------------
## Type of the effect = "within"
## Numerator degrees of freedom = 2
## Denominator degrees of freedom = 28.207
## Non-centrality parameter = 10.736
## Type I error rate = 0.05
## Type II error rate = 0.2pwrss.f.rmanova(eta2 = 0.10, n.levels = 2, n.measurements = 3,
repmeasures.r = 0.50, epsilon = 1,
type = "interaction", power = 0.80)## One-way repeated measures analysis of variance (F test)
## H0: eta2 = 0 (or f2 = 0)
## HA: eta2 > 0 (or f2 > 0)
## ------------------------------
## Number of levels (groups) = 2
## Number of measurement time points = 3
## ------------------------------
## Statistical power = 0.8
## Total n = 17
## ------------------------------
## Type of the effect = "interaction"
## Numerator degrees of freedom = 2
## Denominator degrees of freedom = 28.207
## Non-centrality parameter = 10.736
## Type I error rate = 0.05
## Type II error rate = 0.2--o--