wp.t | R Documentation |
A t-test is a statistical hypothesis test in which the test statistic follows a Student's t distribution if the null hypothesis is true and follows a non-central t distribution if the alternative hypothesis is true. The t test can assess the statistical significance of (1) the difference between population mean and a specific value, (2) the difference between two independent populaion means, and (3) difference between means of matched paires.
wp.t(n1 = NULL, n2 = NULL, d = NULL, alpha = 0.05, power = NULL,
type = c("two.sample", "one.sample", "paired", "two.sample.2n"),
alternative = c("two.sided", "less", "greater"),
tol = .Machine$double.eps^0.25)
n1 |
Sample size of the first group. |
n2 |
Sample size of the second group if applicable. |
d |
Effect size. See the book by Cohen (1988) for details. |
alpha |
Significance level chosed for the test. It equals 0.05 by default. |
power |
Statistical power. |
type |
Type of comparison ( |
alternative |
Direction of the alternative hypothesis ( |
tol |
tolerance in root solver. |
An object of the power analysis.
Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd Ed). Hillsdale, NJ: Lawrence Erlbaum Associates.
Zhang, Z., & Yuan, K.-H. (2018). Practical Statistical Power Analysis Using Webpower and R (Eds). Granger, IN: ISDSA Press.
#To calculate the power for one sample t-test given sample size and effect size:
wp.t(n1=150, d=0.2, type="one.sample")
# One-sample t-test
#
# n d alpha power
# 150 0.2 0.05 0.682153
#
# URL: http://psychstat.org/ttest
#To calculate the power for paired t-test given sample size and effect size:
wp.t(n1=40, d=-0.4, type="paired", alternative="less")
# Paired t-test
#
# n d alpha power
# 40 -0.4 0.05 0.7997378
#
# NOTE: n is number of *pairs*
# URL: http://psychstat.org/ttest
#To estimate the required sample size given power and effect size for paired t-test :
wp.t(d=0.4, power=0.8, type="paired", alternative="greater")
# Paired t-test
#
# n d alpha power
# 40.02908 0.4 0.05 0.8
#
# NOTE: n is number of *pairs*
# URL: http://psychstat.org/ttest
#To estimate the power for balanced two-sample t-test given sample size and effect size:
wp.t(n1=70, d=0.3, type="two.sample", alternative="greater")
# Two-sample t-test
#
# n d alpha power
# 70 0.3 0.05 0.5482577
#
# NOTE: n is number in *each* group
# URL: http://psychstat.org/ttest
#To estimate the power for unbalanced two-sample t-test given sample size and effect size:
wp.t(n1=30, n2=40, d=0.356, type="two.sample.2n", alternative="two.sided")
# Unbalanced two-sample t-test
#
# n1 n2 d alpha power
# 30 40 0.356 0.05 0.3064767
#
# NOTE: n1 and n2 are number in *each* group
# URL: http://psychstat.org/ttest2n
#To estimate the power curve for unbalanced two-sample t-test given a sequence of effect sizes:
res <- wp.t(n1=30, n2=40, d=seq(0.2,0.8,0.05), type="two.sample.2n",
alternative="two.sided")
res
# Unbalanced two-sample t-test
#
# n1 n2 d alpha power
# 30 40 0.20 0.05 0.1291567
# 30 40 0.25 0.05 0.1751916
# 30 40 0.30 0.05 0.2317880
# 30 40 0.35 0.05 0.2979681
# 30 40 0.40 0.05 0.3719259
# 30 40 0.45 0.05 0.4510800
# 30 40 0.50 0.05 0.5322896
# 30 40 0.55 0.05 0.6121937
# 30 40 0.60 0.05 0.6876059
# 30 40 0.65 0.05 0.7558815
# 30 40 0.70 0.05 0.8151817
# 30 40 0.75 0.05 0.8645929
# 30 40 0.80 0.05 0.9040910
#
# NOTE: n1 and n2 are number in *each* group
# URL: http://psychstat.org/ttest2n
#To plot a power curve:
plot(res, xvar='d', yvar='power')
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