| Title: | Basic Functions for Power Analysis |
|---|---|
| Description: | Power analysis functions along the lines of Cohen (1988). |
| Authors: | Stephane Champely [aut], Claus Ekstrom [ctb], Peter Dalgaard [ctb], Jeffrey Gill [ctb], Stephan Weibelzahl [ctb], Aditya Anandkumar [ctb], Clay Ford [ctb], Robert Volcic [ctb], Helios De Rosario [cre] |
| Maintainer: | Helios De Rosario <[email protected]> |
| License: | GPL (>= 3) |
| Version: | 1.3-0 |
| Built: | 2024-08-30 04:07:06 UTC |
| Source: | https://github.com/heliosdrm/pwr |
Power calculations along the lines of Cohen (1988) using in particular the same notations for effect sizes. Examples from the book are given.
| Package: | pwr |
| Type: | Package |
| Version: | 1.3-0 |
| Date: | 2020-03-16 |
| License: | GPL (>= 3) |
This package contains functions for basic power calculations using effect sizes and notations from Cohen (1988) : pwr.p.test: test for one proportion (ES=h) pwr.2p.test: test for two proportions (ES=h) pwr.2p2n.test: test for two proportions (ES=h, unequal sample sizes) pwr.t.test: one sample and two samples (equal sizes) t tests for means (ES=d) pwr.t2n.test: two samples (different sizes) t test for means (ES=d) pwr.anova.test: test for one-way balanced anova (ES=f) pwr.r.test: correlation test (ES=r) pwr.chisq.test: chi-squared test (ES=w) pwr.f2.test: test for the general linear model (ES=f2) ES.h: computing effect size h for proportions tests ES.w1: computing effect size w for the goodness of fit chi-squared test ES.w2: computing effect size w for the association chi-squared test cohen.ES: computing effect sizes for all the previous tests corresponding to conventional effect sizes (small, medium, large)
Stephane Champely, based on previous works by Claus Ekstrom and Peter Dalgaard, with contributions of Jeffrey Gill, Stephan Weibelzahl, Clay Ford, Aditya Anandkumar and Robert Volcic.
Maintainer: Helios De Rosario-Martinez <[email protected]>
Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Hillsdale,NJ: Lawrence Erlbaum.
power.t.test,power.prop.test,power.anova.test
## Exercise 8.1 P. 357 from Cohen (1988) pwr.anova.test(f=0.28,k=4,n=20,sig.level=0.05) ## Exercise 6.1 p. 198 from Cohen (1988) pwr.2p.test(h=0.3,n=80,sig.level=0.05,alternative="greater") ## Exercise 7.3 p. 251 pwr.chisq.test(w=0.346,df=(2-1)*(3-1),N=140,sig.level=0.01) ## Exercise 6.5 p. 203 from Cohen (1988) pwr.p.test(h=0.2,n=60,sig.level=0.05,alternative="two.sided")## Exercise 8.1 P. 357 from Cohen (1988) pwr.anova.test(f=0.28,k=4,n=20,sig.level=0.05) ## Exercise 6.1 p. 198 from Cohen (1988) pwr.2p.test(h=0.3,n=80,sig.level=0.05,alternative="greater") ## Exercise 7.3 p. 251 pwr.chisq.test(w=0.346,df=(2-1)*(3-1),N=140,sig.level=0.01) ## Exercise 6.5 p. 203 from Cohen (1988) pwr.p.test(h=0.2,n=60,sig.level=0.05,alternative="two.sided")
Give the conventional effect size (small, medium, large) for the tests available in this package
cohen.ES(test = c("p", "t", "r", "anov", "chisq", "f2"), size = c("small", "medium", "large"))cohen.ES(test = c("p", "t", "r", "anov", "chisq", "f2"), size = c("small", "medium", "large"))
test |
The statistical test of interest |
size |
The ES : small, medium of large? |
The corresponding effect size
Stephane CHAMPELY
Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Hillsdale,NJ: Lawrence Erlbaum.
## medium effect size for the correlation test cohen.ES(test="r", size="medium") ## sample size for a medium size effect in the two-sided correlation test ## using the conventional power of 0.80 pwr.r.test(r=cohen.ES(test="r",size="medium")$effect.size, power=0.80, sig.level=0.05, alternative="two.sided")## medium effect size for the correlation test cohen.ES(test="r", size="medium") ## sample size for a medium size effect in the two-sided correlation test ## using the conventional power of 0.80 pwr.r.test(r=cohen.ES(test="r",size="medium")$effect.size, power=0.80, sig.level=0.05, alternative="two.sided")
Compute effect size h for two proportions
ES.h(p1, p2)ES.h(p1, p2)
p1 |
First proportion |
p2 |
Second proportion |
The effect size is 2*asin(sqrt(p1))-2*asin(sqrt(p2))
The corresponding effect size
Stephane CHAMPELY
Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Hillsdale,NJ: Lawrence Erlbaum.
pwr.p.test, pwr.2p.test, pwr.2p2n.test, power.prop.test
## Exercise 6.5 p. 203 from Cohen h<-ES.h(0.5,0.4) h pwr.p.test(h=h,n=60,sig.level=0.05,alternative="two.sided")## Exercise 6.5 p. 203 from Cohen h<-ES.h(0.5,0.4) h pwr.p.test(h=h,n=60,sig.level=0.05,alternative="two.sided")
Compute effect size w for two sets of k probabilities P0 (null hypothesis) and P1 (alternative hypothesis)
ES.w1(P0, P1)ES.w1(P0, P1)
P0 |
First set of k probabilities (null hypothesis) |
P1 |
Second set of k probabilities (alternative hypothesis) |
The corresponding effect size w
Stephane CHAMPELY
Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Hillsdale,NJ: Lawrence Erlbaum.
pwr.chisq.test
## Exercise 7.1 p. 249 from Cohen P0<-rep(1/4,4) P1<-c(0.375,rep((1-0.375)/3,3)) ES.w1(P0,P1) pwr.chisq.test(w=ES.w1(P0,P1),N=100,df=(4-1))## Exercise 7.1 p. 249 from Cohen P0<-rep(1/4,4) P1<-c(0.375,rep((1-0.375)/3,3)) ES.w1(P0,P1) pwr.chisq.test(w=ES.w1(P0,P1),N=100,df=(4-1))
Compute effect size w for a two-way probability table corresponding to the alternative hypothesis in the chi-squared test of association in two-way contingency tables
ES.w2(P)ES.w2(P)
P |
A two-way probability table (alternative hypothesis) |
The corresponding effect size w
Stephane CHAMPELY
Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Hillsdale,NJ: Lawrence Erlbaum.
pwr.chisq.test
prob<-matrix(c(0.225,0.125,0.125,0.125,0.16,0.16,0.04,0.04),nrow=2,byrow=TRUE) prob ES.w2(prob) pwr.chisq.test(w=ES.w2(prob),df=(2-1)*(4-1),N=200)prob<-matrix(c(0.225,0.125,0.125,0.125,0.16,0.16,0.04,0.04),nrow=2,byrow=TRUE) prob ES.w2(prob) pwr.chisq.test(w=ES.w2(prob),df=(2-1)*(4-1),N=200)
Plot a diagram to illustrate the relationship of sample size and test power for a given set of parameters.
## S3 method for class 'power.htest' plot(x, ...)## S3 method for class 'power.htest' plot(x, ...)
x |
object of class power.htest usually created by one of the power calculation functions, e.g., pwr.t.test() |
... |
Arguments to be passed to |
Power calculations for the following tests are supported: t-test (pwr.t.test(), pwr.t2n.test()), chi squared test (pwr.chisq.test()), one-way ANOVA (pwr.anova.test(), standard normal distribution (pwr.norm.test()), Pearson correlation (pwr.r.test()), proportions (pwr.p.test(), pwr.2p.test(), pwr.2p2n.test()))
These functions are invoked for their side effect of drawing on the active graphics device.
By default it attempts to use the plotting tools of ggplot2 and scales. If they are not installed, it will use the basic R plotting tools.
Stephan Weibelzahl <[email protected]>
pwr.t.test, pwr.p.test, pwr.2p.test,
pwr.2p2n.test, pwr.r.test, pwr.chisq.test,
pwr.anova.test, pwr.t2n.test
## Two-sample t-test p.t.two <- pwr.t.test(d=0.3, power=0.8, type="two.sample", alternative="two.sided") plot(p.t.two) plot(p.t.two, xlab="sample size per group")## Two-sample t-test p.t.two <- pwr.t.test(d=0.3, power=0.8, type="two.sample", alternative="two.sided") plot(p.t.two) plot(p.t.two, xlab="sample size per group")
Compute power of test, or determine parameters to obtain target power (similar to power.prop.test).
pwr.2p.test(h = NULL, n = NULL, sig.level = 0.05, power = NULL, alternative = c("two.sided","less","greater"))pwr.2p.test(h = NULL, n = NULL, sig.level = 0.05, power = NULL, alternative = c("two.sided","less","greater"))
h |
Effect size |
n |
Number of observations (per sample) |
sig.level |
Significance level (Type I error probability) |
power |
Power of test (1 minus Type II error probability) |
alternative |
a character string specifying the alternative hypothesis, must be one of "two.sided" (default), "greater" or "less" |
Exactly one of the parameters 'h','n', 'power' and 'sig.level' must be passed as NULL, and that parameter is determined from the others. Notice that the last one has non-NULL default so NULL must be explicitly passed if you want to compute it.
Object of class '"power.htest"', a list of the arguments (including the computed one) augmented with 'method' and 'note' elements.
'uniroot' is used to solve power equation for unknowns, so you may see errors from it, notably about inability to bracket the root when invalid arguments are given.
Stephane Champely <[email protected]> but this is a mere copy of Peter Dalgaard work (power.t.test)
Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Hillsdale,NJ: Lawrence Erlbaum.
ES.h, pwr.2p2n.test, power.prop.test
## Exercise 6.1 p. 198 from Cohen (1988) pwr.2p.test(h=0.3,n=80,sig.level=0.05,alternative="greater")## Exercise 6.1 p. 198 from Cohen (1988) pwr.2p.test(h=0.3,n=80,sig.level=0.05,alternative="greater")
Compute power of test, or determine parameters to obtain target power.
pwr.2p2n.test(h = NULL, n1 = NULL, n2 = NULL, sig.level = 0.05, power = NULL, alternative = c("two.sided", "less","greater"))pwr.2p2n.test(h = NULL, n1 = NULL, n2 = NULL, sig.level = 0.05, power = NULL, alternative = c("two.sided", "less","greater"))
h |
Effect size |
n1 |
Number of observations in the first sample |
n2 |
Number of observations in the second sample |
sig.level |
Significance level (Type I error probability) |
power |
Power of test (1 minus Type II error probability) |
alternative |
a character string specifying the alternative hypothesis, must be one of "two.sided" (default), "greater" or "less" |
Exactly one of the parameters 'h','n1', 'n2', 'power' and 'sig.level' must be passed as NULL, and that parameter is determined from the others. Notice that the last one has non-NULL default so NULL must be explicitly passed if you want to compute it.
Object of class '"power.htest"', a list of the arguments (including the computed one) augmented with 'method' and 'note' elements.
'uniroot' is used to solve power equation for unknowns, so you may see errors from it, notably about inability to bracket the root when invalid arguments are given.
Stephane Champely <[email protected]> but this is a mere copy of Peter Dalgaard work (power.t.test)
Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Hillsdale,NJ: Lawrence Erlbaum.
ES.h, pwr.2p.test, power.prop.test
## Exercise 6.3 P. 200 from Cohen (1988) pwr.2p2n.test(h=0.30,n1=80,n2=245,sig.level=0.05,alternative="greater") ## Exercise 6.7 p. 207 from Cohen (1988) pwr.2p2n.test(h=0.20,n1=1600,power=0.9,sig.level=0.01,alternative="two.sided")## Exercise 6.3 P. 200 from Cohen (1988) pwr.2p2n.test(h=0.30,n1=80,n2=245,sig.level=0.05,alternative="greater") ## Exercise 6.7 p. 207 from Cohen (1988) pwr.2p2n.test(h=0.20,n1=1600,power=0.9,sig.level=0.01,alternative="two.sided")
Compute power of test or determine parameters to obtain target power (same as power.anova.test).
pwr.anova.test(k = NULL, n = NULL, f = NULL, sig.level = 0.05, power = NULL)pwr.anova.test(k = NULL, n = NULL, f = NULL, sig.level = 0.05, power = NULL)
k |
Number of groups |
n |
Number of observations (per group) |
f |
Effect size |
sig.level |
Significance level (Type I error probability) |
power |
Power of test (1 minus Type II error probability) |
Exactly one of the parameters 'k','n','f','power' and 'sig.level' must be passed as NULL, and that parameter is determined from the others. Notice that the last one has non-NULL default so NULL must be explicitly passed if you want to compute it.
Object of class '"power.htest"', a list of the arguments (including the computed one) augmented with 'method' and 'note' elements.
'uniroot' is used to solve power equation for unknowns, so you may see errors from it, notably about inability to bracket the root when invalid arguments are given.
Stephane Champely <[email protected]> but this is a mere copy of Peter Dalgaard work (power.t.test)
Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Hillsdale,NJ: Lawrence Erlbaum.
power.anova.test
## Exercise 8.1 P. 357 from Cohen (1988) pwr.anova.test(f=0.28,k=4,n=20,sig.level=0.05) ## Exercise 8.10 p. 391 pwr.anova.test(f=0.28,k=4,power=0.80,sig.level=0.05)## Exercise 8.1 P. 357 from Cohen (1988) pwr.anova.test(f=0.28,k=4,n=20,sig.level=0.05) ## Exercise 8.10 p. 391 pwr.anova.test(f=0.28,k=4,power=0.80,sig.level=0.05)
Compute power of test or determine parameters to obtain target power (same as power.anova.test).
pwr.chisq.test(w = NULL, N = NULL, df = NULL, sig.level = 0.05, power = NULL)pwr.chisq.test(w = NULL, N = NULL, df = NULL, sig.level = 0.05, power = NULL)
w |
Effect size |
N |
Total number of observations |
df |
degree of freedom (depends on the chosen test) |
sig.level |
Significance level (Type I error probability) |
power |
Power of test (1 minus Type II error probability) |
Exactly one of the parameters 'w','N','power' and 'sig.level' must be passed as NULL, and that parameter is determined from the others. Notice that the last one has non-NULL default so NULL must be explicitly passed if you want to compute it.
Object of class '"power.htest"', a list of the arguments (including the computed one) augmented with 'method' and 'note' elements.
'uniroot' is used to solve power equation for unknowns, so you may see errors from it, notably about inability to bracket the root when invalid arguments are given.
Stephane Champely <[email protected]> but this is a mere copy of Peter Dalgaard work (power.t.test)
Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Hillsdale,NJ: Lawrence Erlbaum.
ES.w1,ES.w2
## Exercise 7.1 P. 249 from Cohen (1988) pwr.chisq.test(w=0.289,df=(4-1),N=100,sig.level=0.05) ## Exercise 7.3 p. 251 pwr.chisq.test(w=0.346,df=(2-1)*(3-1),N=140,sig.level=0.01) ## Exercise 7.8 p. 270 pwr.chisq.test(w=0.1,df=(5-1)*(6-1),power=0.80,sig.level=0.05)## Exercise 7.1 P. 249 from Cohen (1988) pwr.chisq.test(w=0.289,df=(4-1),N=100,sig.level=0.05) ## Exercise 7.3 p. 251 pwr.chisq.test(w=0.346,df=(2-1)*(3-1),N=140,sig.level=0.01) ## Exercise 7.8 p. 270 pwr.chisq.test(w=0.1,df=(5-1)*(6-1),power=0.80,sig.level=0.05)
Compute power of test or determine parameters to obtain target power (same as power.anova.test).
pwr.f2.test(u = NULL, v = NULL, f2 = NULL, sig.level = 0.05, power = NULL)pwr.f2.test(u = NULL, v = NULL, f2 = NULL, sig.level = 0.05, power = NULL)
u |
degrees of freedom for numerator |
v |
degrees of freedom for denominator |
f2 |
effect size |
sig.level |
Significance level (Type I error probability) |
power |
Power of test (1 minus Type II error probability) |
Exactly one of the parameters 'u','v','f2','power' and 'sig.level' must be passed as NULL, and that parameter is determined from the others. Notice that the last one has non-NULL default so NULL must be explicitly passed if you want to compute it.
Object of class '"power.htest"', a list of the arguments (including the computed one) augmented with 'method' and 'note' elements.
'uniroot' is used to solve power equation for unknowns, so you may see errors from it, notably about inability to bracket the root when invalid arguments are given.
Stephane Champely <[email protected]> but this is a mere copy of Peter Dalgaard work (power.t.test)
Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Hillsdale,NJ: Lawrence Erlbaum.
## Exercise 9.1 P. 424 from Cohen (1988) pwr.f2.test(u=5,v=89,f2=0.1/(1-0.1),sig.level=0.05)## Exercise 9.1 P. 424 from Cohen (1988) pwr.f2.test(u=5,v=89,f2=0.1/(1-0.1),sig.level=0.05)
Compute power of test or determine parameters to obtain target power (same as power.anova.test).
pwr.norm.test(d = NULL, n = NULL, sig.level = 0.05, power = NULL, alternative = c("two.sided","less","greater"))pwr.norm.test(d = NULL, n = NULL, sig.level = 0.05, power = NULL, alternative = c("two.sided","less","greater"))
d |
Effect size d=mu-mu0 |
n |
Number of observations |
sig.level |
Significance level (Type I error probability) |
power |
Power of test (1 minus Type II error probability) |
alternative |
a character string specifying the alternative hypothesis, must be one of "two.sided" (default), "greater" or "less" |
Exactly one of the parameters 'd','n','power' and 'sig.level' must be passed as NULL, and that parameter is determined from the others. Notice that the last one has non-NULL default so NULL must be explicitly passed if you want to compute it.
Object of class '"power.htest"', a list of the arguments (including the computed one) augmented with 'method' and 'note' elements.
'uniroot' is used to solve power equation for unknowns, so you may see errors from it, notably about inability to bracket the root when invalid arguments are given.
Stephane Champely <[email protected]> but this is a mere copy of Peter Dalgaard work (power.t.test)
Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Hillsdale,NJ: Lawrence Erlbaum.
## Power at mu=105 for H0:mu=100 vs. H1:mu>100 (sigma=15) 20 obs. (alpha=0.05) sigma<-15 c<-100 mu<-105 d<-(mu-c)/sigma pwr.norm.test(d=d,n=20,sig.level=0.05,alternative="greater") ## Sample size of the test for power=0.80 pwr.norm.test(d=d,power=0.8,sig.level=0.05,alternative="greater") ## Power function of the same test mu<-seq(95,125,l=100) d<-(mu-c)/sigma plot(d,pwr.norm.test(d=d,n=20,sig.level=0.05,alternative="greater")$power, type="l",ylim=c(0,1)) abline(h=0.05) abline(h=0.80) ## Power function for the two-sided alternative plot(d,pwr.norm.test(d=d,n=20,sig.level=0.05,alternative="two.sided")$power, type="l",ylim=c(0,1)) abline(h=0.05) abline(h=0.80)## Power at mu=105 for H0:mu=100 vs. H1:mu>100 (sigma=15) 20 obs. (alpha=0.05) sigma<-15 c<-100 mu<-105 d<-(mu-c)/sigma pwr.norm.test(d=d,n=20,sig.level=0.05,alternative="greater") ## Sample size of the test for power=0.80 pwr.norm.test(d=d,power=0.8,sig.level=0.05,alternative="greater") ## Power function of the same test mu<-seq(95,125,l=100) d<-(mu-c)/sigma plot(d,pwr.norm.test(d=d,n=20,sig.level=0.05,alternative="greater")$power, type="l",ylim=c(0,1)) abline(h=0.05) abline(h=0.80) ## Power function for the two-sided alternative plot(d,pwr.norm.test(d=d,n=20,sig.level=0.05,alternative="two.sided")$power, type="l",ylim=c(0,1)) abline(h=0.05) abline(h=0.80)
Compute power of test or determine parameters to obtain target power (same as power.anova.test).
pwr.p.test(h = NULL, n = NULL, sig.level = 0.05, power = NULL, alternative = c("two.sided","less","greater"))pwr.p.test(h = NULL, n = NULL, sig.level = 0.05, power = NULL, alternative = c("two.sided","less","greater"))
h |
Effect size |
n |
Number of observations |
sig.level |
Significance level (Type I error probability) |
power |
Power of test (1 minus Type II error probability) |
alternative |
a character string specifying the alternative hypothesis, must be one of "two.sided" (default), "greater" or "less" |
These calculations use arcsine transformation of the proportion (see Cohen (1988))
Exactly one of the parameters 'h','n','power' and 'sig.level' must be passed as NULL, and that parameter is determined from the others. Notice that the last one has non-NULL default so NULL must be explicitly passed if you want to compute it.
Object of class '"power.htest"', a list of the arguments (including the computed one) augmented with 'method' and 'note' elements.
'uniroot' is used to solve power equation for unknowns, so you may see errors from it, notably about inability to bracket the root when invalid arguments are given.
Stephane Champely <[email protected]> but this is a mere copy of Peter Dalgaard work (power.t.test)
Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Hillsdale,NJ: Lawrence Erlbaum.
ES.h
## Exercise 6.5 p. 203 from Cohen h<-ES.h(0.5,0.4) h pwr.p.test(h=h,n=60,sig.level=0.05,alternative="two.sided") ## Exercise 6.8 p. 208 pwr.p.test(h=0.2,power=0.95,sig.level=0.05,alternative="two.sided")## Exercise 6.5 p. 203 from Cohen h<-ES.h(0.5,0.4) h pwr.p.test(h=h,n=60,sig.level=0.05,alternative="two.sided") ## Exercise 6.8 p. 208 pwr.p.test(h=0.2,power=0.95,sig.level=0.05,alternative="two.sided")
Compute power of test or determine parameters to obtain target power (same as power.anova.test).
pwr.r.test(n = NULL, r = NULL, sig.level = 0.05, power = NULL, alternative = c("two.sided", "less","greater"))pwr.r.test(n = NULL, r = NULL, sig.level = 0.05, power = NULL, alternative = c("two.sided", "less","greater"))
n |
Number of observations |
r |
Linear correlation coefficient |
sig.level |
Significance level (Type I error probability) |
power |
Power of test (1 minus Type II error probability) |
alternative |
a character string specifying the alternative hypothesis, must be one of "two.sided" (default), "greater" or "less" |
These calculations use the Z' transformation of correlation coefficient : Z'=arctanh(r) and a bias correction is applied. Note that contrary to Cohen (1988) p.546, where zp' = arctanh(rp) + rp/(2*(n-1)) and zc' = arctanh(rc) + rc/(2*(n-1)), we only use here zp' = arctanh(rp) + rp/(2*(n-1)) and zc' = arctanh(rc).
Exactly one of the parameters 'r','n','power' and 'sig.level' must be passed as NULL, and that parameter is determined from the others. Notice that the last one has non-NULL default so NULL must be explicitly passed if you want to compute it.
Object of class '"power.htest"', a list of the arguments (including the computed one) augmented with 'method' and 'note' elements.
'uniroot' is used to solve power equation for unknowns, so you may see errors from it, notably about inability to bracket the root when invalid arguments are given.
Stephane Champely <[email protected]> but this is a mere copy of Peter Dalgaard work (power.t.test). The modified bias correction is contributed by Jeffrey Gill.
Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Hillsdale,NJ: Lawrence Erlbaum.
## Exercise 3.1 p. 96 from Cohen (1988) pwr.r.test(r=0.3,n=50,sig.level=0.05,alternative="two.sided") pwr.r.test(r=0.3,n=50,sig.level=0.05,alternative="greater") ## Exercise 3.4 p. 208 pwr.r.test(r=0.3,power=0.80,sig.level=0.05,alternative="two.sided") pwr.r.test(r=0.5,power=0.80,sig.level=0.05,alternative="two.sided") pwr.r.test(r=0.1,power=0.80,sig.level=0.05,alternative="two.sided")## Exercise 3.1 p. 96 from Cohen (1988) pwr.r.test(r=0.3,n=50,sig.level=0.05,alternative="two.sided") pwr.r.test(r=0.3,n=50,sig.level=0.05,alternative="greater") ## Exercise 3.4 p. 208 pwr.r.test(r=0.3,power=0.80,sig.level=0.05,alternative="two.sided") pwr.r.test(r=0.5,power=0.80,sig.level=0.05,alternative="two.sided") pwr.r.test(r=0.1,power=0.80,sig.level=0.05,alternative="two.sided")
Compute power of tests or determine parameters to obtain target power (similar to power.t.test).
pwr.t.test(n = NULL, d = NULL, sig.level = 0.05, power = NULL, type = c("two.sample", "one.sample", "paired"), alternative = c("two.sided", "less", "greater"))pwr.t.test(n = NULL, d = NULL, sig.level = 0.05, power = NULL, type = c("two.sample", "one.sample", "paired"), alternative = c("two.sided", "less", "greater"))
n |
Number of observations (per sample) |
d |
Effect size (Cohen's d) - difference between the means divided by the pooled standard deviation |
sig.level |
Significance level (Type I error probability) |
power |
Power of test (1 minus Type II error probability) |
type |
Type of t test : one- two- or paired-samples |
alternative |
a character string specifying the alternative hypothesis, must be one of "two.sided" (default), "greater" or "less" |
Exactly one of the parameters 'd','n','power' and 'sig.level' must be passed as NULL, and that parameter is determined from the others. Notice that the last one has non-NULL default so NULL must be explicitly passed if you want to compute it.
Object of class '"power.htest"', a list of the arguments (including the computed one) augmented with 'method' and 'note' elements.
'uniroot' is used to solve power equation for unknowns, so you may see errors from it, notably about inability to bracket the root when invalid arguments are given.
Stephane Champely <[email protected]> but this is a mere copy of Peter Dalgaard work (power.t.test)
Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Hillsdale,NJ: Lawrence Erlbaum.
power.prop.test
## One sample (power) ## Exercise 2.5 p. 47 from Cohen (1988) pwr.t.test(d=0.2,n=60,sig.level=0.10,type="one.sample",alternative="two.sided") ## Paired samples (power) ## Exercise p. 50 from Cohen (1988) d<-8/(16*sqrt(2*(1-0.6))) pwr.t.test(d=d,n=40,sig.level=0.05,type="paired",alternative="two.sided") ## Two independent samples (power) ## Exercise 2.1 p. 40 from Cohen (1988) d<-2/2.8 pwr.t.test(d=d,n=30,sig.level=0.05,type="two.sample",alternative="two.sided") ## Two independent samples (sample size) ## Exercise 2.10 p. 59 pwr.t.test(d=0.3,power=0.75,sig.level=0.05,type="two.sample",alternative="greater")## One sample (power) ## Exercise 2.5 p. 47 from Cohen (1988) pwr.t.test(d=0.2,n=60,sig.level=0.10,type="one.sample",alternative="two.sided") ## Paired samples (power) ## Exercise p. 50 from Cohen (1988) d<-8/(16*sqrt(2*(1-0.6))) pwr.t.test(d=d,n=40,sig.level=0.05,type="paired",alternative="two.sided") ## Two independent samples (power) ## Exercise 2.1 p. 40 from Cohen (1988) d<-2/2.8 pwr.t.test(d=d,n=30,sig.level=0.05,type="two.sample",alternative="two.sided") ## Two independent samples (sample size) ## Exercise 2.10 p. 59 pwr.t.test(d=0.3,power=0.75,sig.level=0.05,type="two.sample",alternative="greater")
Compute power of tests or determine parameters to obtain target power (similar to as power.t.test).
pwr.t2n.test(n1 = NULL, n2= NULL, d = NULL, sig.level = 0.05, power = NULL, alternative = c("two.sided", "less","greater"))pwr.t2n.test(n1 = NULL, n2= NULL, d = NULL, sig.level = 0.05, power = NULL, alternative = c("two.sided", "less","greater"))
n1 |
Number of observations in the first sample |
n2 |
Number of observations in the second sample |
d |
Effect size |
sig.level |
Significance level (Type I error probability) |
power |
Power of test (1 minus Type II error probability) |
alternative |
a character string specifying the alternative hypothesis, must be one of "two.sided" (default), "greater" or "less" |
Exactly one of the parameters 'd','n1','n2','power' and 'sig.level' must be passed as NULL, and that parameter is determined from the others. Notice that the last one has non-NULL default so NULL must be explicitly passed if you want to compute it.
Object of class '"power.htest"', a list of the arguments (including the computed one) augmented with 'method' and 'note' elements.
'uniroot' is used to solve power equation for unknowns, so you may see errors from it, notably about inability to bracket the root when invalid arguments are given.
Stephane Champely <[email protected]> but this is a mere copy of Peter Dalgaard work (power.t.test)
Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Hillsdale,NJ: Lawrence Erlbaum.
## Exercise 2.3 p. 437 from Cohen (1988) pwr.t2n.test(d=0.6,n1=90,n2=60,alternative="greater")## Exercise 2.3 p. 437 from Cohen (1988) pwr.t2n.test(d=0.6,n1=90,n2=60,alternative="greater")