two_sample_test {statsExpressions}

Two-sample tests

Description

Parametric, non-parametric, robust, and Bayesian two-sample tests.

Usage

two_sample_test(
  data,
  x,
  y,
  subject.id = NULL,
  type = "parametric",
  paired = FALSE,
  alternative = "two.sided",
  digits = 2L,
  conf.level = 0.95,
  effsize.type = "g",
  var.equal = FALSE,
  bf.prior = 0.707,
  tr = 0.2,
  nboot = 100L,
  ...
)

Arguments

data

A data frame (or a tibble) from which variables specified are to be taken. Other data types (e.g., matrix,table, array, etc.) will not be accepted. Additionally, grouped data frames from {dplyr} should be ungrouped before they are entered as data.

x

The grouping (or independent) variable from data. In case of a repeated measures or within-subjects design, if subject.id argument is not available or not explicitly specified, the function assumes that the data has already been sorted by such an id by the user and creates an internal identifier. So if your data is not sorted, the results can be inaccurate when there are more than two levels in x and there are NAs present. The data is expected to be sorted by user in subject-1,subject-2, ..., pattern.

y

The response (or outcome or dependent) variable from data.

subject.id

Relevant in case of a repeated measures or within-subjects design (paired = TRUE, i.e.), it specifies the subject or repeated measures identifier. Important: Note that if this argument is NULL (which is the default), the function assumes that the data has already been sorted by such an id by the user and creates an internal identifier. So if your data is not sorted and you leave this argument unspecified, the results can be inaccurate when there are more than two levels in x and there are NAs present.

type

A character specifying the type of statistical approach:

• "parametric"

• "nonparametric"

• "robust"

• "bayes"

You can specify just the initial letter.

paired

Logical that decides whether the experimental design is repeated measures/within-subjects or between-subjects. The default is FALSE.

alternative

a character string specifying the alternative hypothesis, must be one of "two.sided" (default), "greater" or "less". You can specify just the initial letter.

digits

Number of digits for rounding or significant figures. May also be "signif" to return significant figures or "scientific" to return scientific notation. Control the number of digits by adding the value as suffix, e.g. digits = "scientific4" to have scientific notation with 4 decimal places, or digits = "signif5" for 5 significant figures (see also signif()).

conf.level

Scalar between 0 and 1 (default: ⁠95%⁠ confidence/credible intervals, 0.95). If NULL, no confidence intervals will be computed.

effsize.type

Type of effect size needed for parametric tests. The argument can be "d" (for Cohen's d) or "g" (for Hedge's g).

var.equal

a logical variable indicating whether to treat the two variances as being equal. If TRUE then the pooled variance is used to estimate the variance otherwise the Welch (or Satterthwaite) approximation to the degrees of freedom is used.

bf.prior

A number between 0.5 and 2 (default 0.707), the prior width to use in calculating Bayes factors and posterior estimates. In addition to numeric arguments, several named values are also recognized: "medium", "wide", and "ultrawide", corresponding to r scale values of 1/2, sqrt(2)/2, and 1, respectively. In case of an ANOVA, this value corresponds to scale for fixed effects.

tr

Trim level for the mean when carrying out robust tests. In case of an error, try reducing the value of tr, which is by default set to 0.2. Lowering the value might help.

nboot

Number of bootstrap samples for computing confidence interval for the effect size (Default: 100L).

...

Currently ignored.

Value

The returned tibble data frame can contain some or all of the following columns (the exact columns will depend on the statistical test):

• statistic: the numeric value of a statistic

• df: the numeric value of a parameter being modeled (often degrees of freedom for the test)

• df.error and df: relevant only if the statistic in question has two degrees of freedom (e.g. anova)

• p.value: the two-sided p-value associated with the observed statistic

• method: the name of the inferential statistical test

• estimate: estimated value of the effect size

• conf.low: lower bound for the effect size estimate

• conf.high: upper bound for the effect size estimate

• conf.level: width of the confidence interval

• conf.method: method used to compute confidence interval

• conf.distribution: statistical distribution for the effect

• effectsize: the name of the effect size

• n.obs: number of observations

• expression: pre-formatted expression containing statistical details

For examples, see data frame output vignette.

Two-sample tests

The table below provides summary about:

• statistical test carried out for inferential statistics

• type of effect size estimate and a measure of uncertainty for this estimate

• functions used internally to compute these details

between-subjects

Hypothesis testing

Type	No. of groups	Test	Function used
Parametric	2	Student's or Welch's t-test	stats::t.test()
Non-parametric	2	Mann-Whitney U test	stats::wilcox.test()
Robust	2	Yuen's test for trimmed means	WRS2::yuen()
Bayesian	2	Student's t-test	BayesFactor::ttestBF()

Effect size estimation

Type	No. of groups	Effect size	CI available?	Function used
Parametric	2	Cohen's d, Hedge's g	Yes	effectsize::cohens_d(), effectsize::hedges_g()
Non-parametric	2	r (rank-biserial correlation)	Yes	effectsize::rank_biserial()
Robust	2	Algina-Keselman-Penfield robust standardized difference	Yes	WRS2::akp.effect()
Bayesian	2	difference	Yes	bayestestR::describe_posterior()

within-subjects

Hypothesis testing

Type	No. of groups	Test	Function used
Parametric	2	Student's t-test	stats::t.test()
Non-parametric	2	Wilcoxon signed-rank test	stats::wilcox.test()
Robust	2	Yuen's test on trimmed means for dependent samples	WRS2::yuend()
Bayesian	2	Student's t-test	BayesFactor::ttestBF()

Effect size estimation

Type	No. of groups	Effect size	CI available?	Function used
Parametric	2	Cohen's d, Hedge's g	Yes	effectsize::cohens_d(), effectsize::hedges_g()
Non-parametric	2	r (rank-biserial correlation)	Yes	effectsize::rank_biserial()
Robust	2	Algina-Keselman-Penfield robust standardized difference	Yes	WRS2::wmcpAKP()
Bayesian	2	difference	Yes	bayestestR::describe_posterior()

Examples

# ----------------------- within-subjects -------------------------------------

# data
df <- dplyr::filter(bugs_long, condition %in% c("LDLF", "LDHF"))

# for reproducibility
set.seed(123)

# ----------------------- parametric ---------------------------------------

two_sample_test(df, condition, desire, subject.id = subject, paired = TRUE, type = "parametric")

# ----------------------- non-parametric -----------------------------------

two_sample_test(df, condition, desire, subject.id = subject, paired = TRUE, type = "nonparametric")

# ----------------------- robust --------------------------------------------

two_sample_test(df, condition, desire, subject.id = subject, paired = TRUE, type = "robust")

# ----------------------- Bayesian ---------------------------------------

two_sample_test(df, condition, desire, subject.id = subject, paired = TRUE, type = "bayes")
# ----------------------- between-subjects -------------------------------------

# for reproducibility
set.seed(123)

# ----------------------- parametric ---------------------------------------

# unequal variance
two_sample_test(ToothGrowth, supp, len, type = "parametric")

# equal variance
two_sample_test(ToothGrowth, supp, len, type = "parametric", var.equal = TRUE)

# ----------------------- non-parametric -----------------------------------

two_sample_test(ToothGrowth, supp, len, type = "nonparametric")

# ----------------------- robust --------------------------------------------

two_sample_test(ToothGrowth, supp, len, type = "robust")

# ----------------------- Bayesian ---------------------------------------

two_sample_test(ToothGrowth, supp, len, type = "bayes")