Section author: Ravi Selker, Jonathon Love, Damian Dropmann

Independent Samples T-Test (ttestIS)

Description

The Student’s Independent samples t-test (sometimes called a two-samples t-test) is used to test the null hypothesis that two groups have the same mean. A low p-value suggests that the null hypothesis is not true, and therefore the group means are different.

Usage

ttestIS(
  data,
  vars,
  group,
  students = TRUE,
  bf = FALSE,
  bfPrior = 0.707,
  welchs = FALSE,
  mann = FALSE,
  hypothesis = "different",
  norm = FALSE,
  qq = FALSE,
  eqv = FALSE,
  meanDiff = FALSE,
  ci = FALSE,
  ciWidth = 95,
  effectSize = FALSE,
  ciES = FALSE,
  ciWidthES = 95,
  desc = FALSE,
  plots = FALSE,
  miss = "perAnalysis",
  formula
)

Arguments

data	the data as a data frame
vars	the dependent variables (not necessary when using a formula, see the examples)
group	the grouping variable with two levels (not necessary when using a formula, see the examples)
students	TRUE (default) or FALSE, perform Student’s t-tests
bf	TRUE or FALSE (default), provide Bayes factors
bfPrior	a number between 0.5 and 2 (default 0.707), the prior width to use in calculating Bayes factors
welchs	TRUE or FALSE (default), perform Welch’s t-tests
mann	TRUE or FALSE (default), perform Mann-Whitney U tests
hypothesis	'different' (default), 'oneGreater' or 'twoGreater', the alternative hypothesis; group 1 different to group 2, group 1 greater than group 2, and group 2 greater than group 1 respectively
norm	TRUE or FALSE (default), perform Shapiro-Wilk tests of normality
qq	TRUE or FALSE (default), provide Q-Q plots of residuals
eqv	TRUE or FALSE (default), perform Levene’s tests for homogeneity of variances
meanDiff	TRUE or FALSE (default), provide means and standard errors
ci	TRUE or FALSE (default), provide confidence intervals
ciWidth	a number between 50 and 99.9 (default: 95), the width of confidence intervals
effectSize	TRUE or FALSE (default), provide effect sizes
ciES	TRUE or FALSE (default), provide confidence intervals for the effect-sizes
ciWidthES	a number between 50 and 99.9 (default: 95), the width of confidence intervals for the effect sizes
desc	TRUE or FALSE (default), provide descriptive statistics
plots	TRUE or FALSE (default), provide descriptive plots
miss	'perAnalysis' or 'listwise', how to handle missing values; 'perAnalysis' excludes missing values for individual dependent variables, 'listwise' excludes a row from all analyses if one of its entries is missing.
formula	(optional) the formula to use, see the examples

Details

The Student’s independent t-test assumes that the data from each group are from a normal distribution, and that the variances of these groups are equal. If unwilling to assume the groups have equal variances, the Welch’s t-test can be used in it’s place. If one is additionally unwilling to assume the data from each group are from a normal distribution, the non-parametric Mann-Whitney U test can be used instead (However, note that the Mann-Whitney U test has a slightly different null hypothesis; that the distributions of each group is equal).

Output

A results object containing:

results$ttest	a table containing the t-test results
results$assum$norm	a table containing the normality tests
results$assum$eqv	a table containing the homogeneity of variances tests
results$desc	a table containing the group descriptives
results$plots	an array of groups of plots

Tables can be converted to data frames with asDF or as.data.frame(). For example:

results$ttest$asDF

as.data.frame(results$ttest)

Examples

data('ToothGrowth')

ttestIS(formula = len ~ supp, data = ToothGrowth)

#
#  INDEPENDENT SAMPLES T-TEST
#
#  Independent Samples T-Test
#  ----------------------------------------------------
#                          statistic    df      p
#  ----------------------------------------------------
#    len    Student's t         1.92    58.0    0.060
#  ----------------------------------------------------
#