TTEST {bruceR}  R Documentation 
Onesample, independentsamples, and pairedsamples ttest.
Description
Onesample, independentsamples, and pairedsamples ttest,
with both Frequentist and Bayesian approaches.
The output includes descriptives, t statistics,
mean difference with 95% CI, Cohen's d with 95% CI,
and Bayes factor (BF10; BayesFactor
package needs to be installed).
It also tests the assumption of homogeneity of variance
and allows users to determine whether variances are equal or not.
Users can simultaneously test multiple dependent and/or independent variables. The results of one pair of YX would be summarized in one row in the output. Key results can be saved in APA format to MS Word.
Usage
TTEST(
data,
y,
x = NULL,
paired = FALSE,
paired.d.type = "dz",
var.equal = TRUE,
mean.diff = TRUE,
test.value = 0,
test.sided = c("=", "<", ">"),
factor.rev = TRUE,
bayes.prior = "medium",
digits = 2,
file = NULL
)
Arguments
data 
Data frame (wideformat only, i.e., one case in one row). 
y 
Dependent variable(s).
Multiple variables should be included in a character vector For pairedsamples ttest, the number of variables should be 2, 4, 6, etc. 
x 
Independent variable(s).
Multiple variables should be included in a character vector Only necessary for independentsamples ttest. 
paired 
For pairedsamples ttest, set it as 
paired.d.type 
Type of Cohen's d for pairedsamples ttest (see Lakens, 2013). Defaults to

var.equal 
If Levene's test indicates a violation of the homogeneity of variance,
then you should better set this argument as 
mean.diff 
Whether to display results of mean difference and its 95% CI. Defaults to 
test.value 
The true value of the mean (or difference in means for a twosamples test). Defaults to 
test.sided 
Any of 
factor.rev 
Whether to reverse the levels of factor (X)
such that the test compares higher vs. lower level. Defaults to 
bayes.prior 
Prior scale in Bayesian ttest. Defaults to 0.707.
See details in 
digits 
Number of decimal places of output. Defaults to 
file 
File name of MS Word ( 
Details
Note that the point estimate of Cohen's d is computed using
the common method "Cohen's d = mean difference / (pooled) standard deviation", which is
consistent with results from other R packages (e.g., effectsize
) and software (e.g., jamovi
).
The 95% CI of Cohen's d is estimated based on the 95% CI of mean difference
(i.e., also divided by the pooled standard deviation).
However, different packages and software diverge greatly on the estimate of the 95% CI of Cohen's d.
R packages such as psych
and effectsize
, R software jamovi
,
and several online statistical tools for estimating effect sizes
indeed produce surprisingly inconsistent results on the 95% CI of Cohen's d.
See an illustration of this issue in the section "Examples".
References
Lakens, D. (2013). Calculating and reporting effect sizes to facilitate cumulative science: A practical primer for ttests and ANOVAs. Frontiers in Psychology, 4, Article 863.
See Also
Examples
## Demo data ##
d1 = between.3
d1$Y1 = d1$SCORE # shorter name for convenience
d1$Y2 = rnorm(32) # random variable
d1$B = factor(d1$B, levels=1:2, labels=c("Low", "High"))
d1$C = factor(d1$C, levels=1:2, labels=c("M", "F"))
d2 = within.1
## Onesample ttest ##
TTEST(d1, "SCORE")
TTEST(d1, "SCORE", test.value=5)
## Independentsamples ttest ##
TTEST(d1, "SCORE", x="A")
TTEST(d1, "SCORE", x="A", var.equal=FALSE)
TTEST(d1, y="Y1", x=c("A", "B", "C"))
TTEST(d1, y=c("Y1", "Y2"), x=c("A", "B", "C"),
mean.diff=FALSE, # remove to save space
file="tresult.doc")
unlink("tresult.doc") # delete file for code check
## Pairedsamples ttest ##
TTEST(d2, y=c("A1", "A2"), paired=TRUE)
TTEST(d2, y=c("A1", "A2", "A3", "A4"), paired=TRUE)
## Not run:
## Illustration for the issue stated in "Details"
# Inconsistency in the 95% CI of Cohen's d between R packages:
# In this example, the true point estimate of Cohen's d = 3.00
# and its 95% CI should be equal to 95% CI of mean difference.
data = data.frame(X=rep(1:2, each=3), Y=1:6)
data # simple demo data
TTEST(data, y="Y", x="X")
# d = 3.00 [0.73, 5.27] (estimated based on 95% CI of mean difference)
MANOVA(data, dv="Y", between="X") %>%
EMMEANS("X")
# d = 3.00 [0.73, 5.27] (the same as TTEST)
psych::cohen.d(x=data, group="X")
# d = 3.67 [0.04, 7.35] (strange)
psych::d.ci(d=3.00, n1=3, n2=3)
# d = 3.00 [0.15, 6.12] (significance inconsistent with ttest)
# jamovi uses psych::d.ci() to compute 95% CI
# so its results are also: 3.00 [0.15, 6.12]
effectsize::cohens_d(Y ~ rev(X), data=data)
# d = 3.00 [0.38, 5.50] (using the noncentrality parameter method)
effectsize::t_to_d(t=t.test(Y ~ rev(X), data=data, var.equal=TRUE)$statistic,
df_error=4)
# d = 3.67 [0.47, 6.74] (merely an approximate estimate, often overestimated)
# see ?effectsize::t_to_d
# https://www.psychometrica.de/effect_size.html
# d = 3.00 [0.67, 5.33] (slightly different from TTEST)
# https://www.campbellcollaboration.org/escalc/
# d = 3.00 [0.67, 5.33] (slightly different from TTEST)
# Conclusion:
# TTEST() provides a reasonable estimate of Cohen's d and its 95% CI,
# and effectsize::cohens_d() offers another method to compute the CI.
## End(Not run)