t-tests
TODO
- link to resamplingPerm
Install required packages
wants <- c("effectsize")
has <- wants %in% rownames(installed.packages())
if(any(!has)) install.packages(wants[!has])One-sample \(t\)-test
Test
set.seed(123)
N <- 100
DV <- rnorm(N, 5, 20)
muH0 <- 0
t.test(DV, alternative="two.sided", mu=muH0)
One Sample t-test
data: DV
t = 3.7292, df = 99, p-value = 0.0003203
alternative hypothesis: true mean is not equal to 0
95 percent confidence interval:
3.185669 10.430568
sample estimates:
mean of x
6.808118 Effect size estimate (Cohen’s \(d\))
library(effectsize)
cohens_d(DV)Cohen's d | 95% CI
------------------------
0.37 | [0.17, 0.57]Two-sample \(t\)-test for independent samples
\(t\)-Test
Nj <- c(18, 21)
DVm <- rnorm(Nj[1], 180, 10)
DVf <- rnorm(Nj[2], 175, 6)
tIndDf <- data.frame(DV=c(DVm, DVf),
IV=factor(rep(c("f", "m"), Nj)))t.test(DVf, DVm, alternative="less", var.equal=TRUE)t.test(DV ~ IV, alternative="greater", var.equal=TRUE, data=tIndDf)
Two Sample t-test
data: DV by IV
t = 1.1137, df = 37, p-value = 0.1363
alternative hypothesis: true difference in means between group f and group m is greater than 0
95 percent confidence interval:
-1.230298 Inf
sample estimates:
mean in group f mean in group m
177.0479 174.6580 Welch \(t\)-Test
t.test(DV ~ IV, alternative="greater", var.equal=FALSE, data=tIndDf)
Welch Two Sample t-test
data: DV by IV
t = 1.1032, df = 34.359, p-value = 0.1388
alternative hypothesis: true difference in means between group f and group m is greater than 0
95 percent confidence interval:
-1.27206 Inf
sample estimates:
mean in group f mean in group m
177.0479 174.6580 Effect size estimate
Cohen’s \(d\) and Hedge’s \(g\)
library(effectsize)
cohens_d(DV ~ IV, data=tIndDf)Cohen's d | 95% CI
-------------------------
0.36 | [-0.28, 0.99]
- Estimated using pooled SD.hedges_g(DV ~ IV, data=tIndDf)Hedges' g | 95% CI
-------------------------
0.35 | [-0.27, 0.97]
- Estimated using pooled SD.Two-sample \(t\)-test for dependent samples
Test
N <- 20
DVpre <- rnorm(N, mean=90, sd=15)
DVpost <- rnorm(N, mean=100, sd=15)
tDepDf <- data.frame(DVpre, DVpost)t.test(Pair(DVpre, DVpost) ~ 1, alternative="less", data=tDepDf)
Paired t-test
data: Pair(DVpre, DVpost)
t = -2.9918, df = 19, p-value = 0.003748
alternative hypothesis: true difference in means is less than 0
95 percent confidence interval:
-Inf -6.739295
sample estimates:
mean of the differences
-15.96821 Equivalent: one-sample t-test for variable built of pair-wise differences
DVdiff <- DVpre - DVpost
t.test(DVdiff, alternative="less")Effect size estimate (Cohen’s \(d\))
cohens_d(DVdiff)Cohen's d | 95% CI
--------------------------
-0.67 | [-1.15, -0.18]Detach (automatically) loaded packages (if possible)
try(detach(package:effectsize))Get the article source from GitHub
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