Package {TH}

TH: Hypothesis Tests in R

Description

The TH package provides educational functions for teaching and performing Z, Student and Welch t, F, and Pearson chi-square hypothesis tests in R. Every function returns an htest-compatible object and can optionally draw a step-by-step educational graph.

Tests for means

tz1(), tz2(), tt1(), tt2i(), tt2d(), and tt2p().

Test for variances

tf2().

Tests for frequencies

tq2a(), tq2i(), and tq2h().

Author(s)

Maintainer: Willian Silva Barros willian.barros@ufpel.edu.br [copyright holder]

Authors:

• Willian Silva Barros willian.barros@ufpel.edu.br [copyright holder]

F Test for Two Variances

Description

Performs an F test for comparing two population variances.

Usage

tf2(
  dadosX = NULL,
  dadosY = NULL,
  alfa = 0.05,
  Ha = 1,
  s2X = NULL,
  nX = NULL,
  s2Y = NULL,
  nY = NULL,
  plot = TRUE
)

Arguments

Details

Raw-data and summary-statistics modes are mutually exclusive. The function accepts raw data or the sample variances and sample sizes.

Main assumptions:

• independent samples;

• normal populations;

Value

Invisibly returns an object of classes th_test and htest containing the test statistic, degrees of freedom when applicable, p-value, estimates, critical values, significance level, and decision. When plot = TRUE, the educational graph is produced as a side effect.

Author(s)

Willian Silva Barros

Examples

X <- c(8, 12, 16, 20, 24, 28)
Y <- c(14, 15, 14, 15, 14, 15)
tf2(X, Y, alfa = 0.05, Ha = 2, plot = FALSE)

Chi-Square Goodness-of-Fit Test

Description

Compares observed frequencies with a specified categorical distribution.

Usage

tq2a(
  dadosX = NULL,
  p = NULL,
  FO = NULL,
  FE = NULL,
  alfa = 0.05,
  Ha = 2,
  r = 0,
  plot = TRUE
)

Arguments

Details

Input modes are mutually exclusive: use raw categories with p, FO with p, or FO with FE. Named p and FE vectors are aligned to named observed categories. The standard omnibus chi-square goodness-of-fit test has an upper-tail rejection region.

Main assumptions:

• mutually exclusive categories;

• independent observations;

• adequately large expected frequencies;

Value

Invisibly returns an object of classes th_test and htest containing the statistic, degrees of freedom, p-value, critical value, decision, observed frequencies, and expected frequencies. When plot = TRUE, an educational graph is produced as a side effect.

Author(s)

Willian Silva Barros

See Also

tq2i(), tq2h()

Examples

categories <- c(rep("A", 50), rep("B", 30), rep("C", 20))
tq2a(categories, p = c(1, 1, 1), alfa = 0.05, Ha = 2, r = 0, plot = FALSE)

Chi-Square Test of Homogeneity

Description

Compares categorical distributions across groups or populations.

Usage

tq2h(
  dadosX = NULL,
  dadosY = NULL,
  FO = NULL,
  alfa = 0.05,
  Ha = 2,
  r = 0,
  plot = TRUE
)

Arguments

Details

The function accepts individual categorical observations or an observed frequency matrix. The standard omnibus chi-square homogeneity test has an upper-tail rejection region.

Main assumptions:

• independent samples or groups;

• mutually exclusive categories;

• adequately large expected frequencies;

Value

Invisibly returns an object of classes th_test and htest containing the statistic, degrees of freedom, p-value, critical value, decision, observed frequencies, and expected frequencies. When plot = TRUE, an educational graph is produced as a side effect.

Author(s)

Willian Silva Barros

See Also

tq2a(), tq2i()

Examples

FO <- matrix(c(30, 15, 5, 10, 25, 15, 20, 20, 10), nrow = 3, byrow = TRUE)
tq2h(NULL, NULL, FO = FO, alfa = 0.05, Ha = 2, r = 0, plot = FALSE)

Chi-Square Test of Independence

Description

Assesses association between two categorical variables.

Usage

tq2i(
  dadosX = NULL,
  dadosY = NULL,
  FO = NULL,
  alfa = 0.05,
  Ha = 2,
  r = 0,
  plot = TRUE
)

Arguments

Details

The function accepts two categorical variables recorded at the observation level or an observed contingency table. The standard omnibus chi-square test of independence has an upper-tail rejection region.

Main assumptions:

• independent observations;

• mutually exclusive categories;

• adequately large expected frequencies;

Value

Invisibly returns an object of classes th_test and htest containing the statistic, degrees of freedom, p-value, critical value, decision, observed frequencies, and expected frequencies. When plot = TRUE, an educational graph is produced as a side effect.

Author(s)

Willian Silva Barros

See Also

tq2a(), tq2h()

Examples

FO <- matrix(c(30, 10, 5, 10, 25, 20), nrow = 2, byrow = TRUE)
tq2i(NULL, NULL, FO = FO, alfa = 0.05, Ha = 2, r = 0, plot = FALSE)

One-Sample t Test

Description

Performs Student's t test for one population mean when the population variance is unknown.

Usage

tt1(
  dadosX = NULL,
  mp,
  alfa = 0.05,
  Ha = 1,
  unidade = NULL,
  media = NULL,
  s2 = NULL,
  n = NULL,
  plot = TRUE
)

Arguments

Details

Raw-data and summary-statistics modes are mutually exclusive. The function can be run using raw observations or the sample mean, sample variance, and sample size.

Main assumptions:

• random sampling and independent observations;

• approximately normal population, particularly for small samples;

Value

Invisibly returns an object of classes th_test and htest containing the test statistic, degrees of freedom when applicable, p-value, estimates, critical values, significance level, and decision. When plot = TRUE, the educational graph is produced as a side effect.

Author(s)

Willian Silva Barros

Examples

X <- c(11, 12, 13, 12, 14, 13, 12, 15)
tt1(X, mp = 10, alfa = 0.05, Ha = 2, unidade = " units", plot = FALSE)

Two-Sample t Test with Unequal Variances

Description

Compares two independent population means without assuming equal population variances.

Usage

tt2d(
  dadosX = NULL,
  dadosY = NULL,
  alfa = 0.05,
  Ha = 1,
  mX = NULL,
  s2X = NULL,
  nX = NULL,
  mY = NULL,
  s2Y = NULL,
  nY = NULL,
  plot = TRUE
)

Arguments

Details

Raw-data and summary-statistics modes are mutually exclusive. The function accepts raw data or summary statistics and uses Welch's standard error with Welch-Satterthwaite fractional degrees of freedom.

Main assumptions:

• independent samples;

• approximately normal populations;

Value

Invisibly returns an object of classes th_test and htest containing the test statistic, degrees of freedom when applicable, p-value, estimates, critical values, significance level, and decision. When plot = TRUE, the educational graph is produced as a side effect.

Author(s)

Willian Silva Barros

Examples

X <- c(20, 21, 19, 22, 18, 20)
Y <- c(10, 15, 5, 20, 0, 10)
tt2d(X, Y, alfa = 0.05, Ha = 2, plot = FALSE)

Two-Sample t Test with Equal Variances

Description

Compares two independent population means under the assumption of equal population variances.

Usage

tt2i(
  dadosX = NULL,
  dadosY = NULL,
  alfa = 0.05,
  Ha = 1,
  mX = NULL,
  s2X = NULL,
  nX = NULL,
  mY = NULL,
  s2Y = NULL,
  nY = NULL,
  plot = TRUE
)

Arguments

Details

Raw-data and summary-statistics modes are mutually exclusive. The function accepts raw data or summary statistics and uses the pooled variance of the two samples.

Main assumptions:

• independent samples;

• approximately normal populations;

• equal population variances;

Value

Invisibly returns an object of classes th_test and htest containing the test statistic, degrees of freedom when applicable, p-value, estimates, critical values, significance level, and decision. When plot = TRUE, the educational graph is produced as a side effect.

Author(s)

Willian Silva Barros

Examples

X <- c(18, 20, 19, 21, 22, 20)
Y <- c(14, 15, 16, 15, 14, 16)
tt2i(X, Y, alfa = 0.05, Ha = 1, plot = FALSE)

Paired t Test

Description

Performs a t test for two dependent or paired measurements.

Usage

tt2p(
  dadosX1 = NULL,
  dadosX2 = NULL,
  mpD = 0,
  alfa = 0.05,
  Ha = 1,
  unidade = NULL,
  mD = NULL,
  s2D = NULL,
  nD = NULL,
  plot = TRUE
)

Arguments

Details

Raw paired data and summary statistics for the differences are mutually exclusive. In raw-data mode, the difference is calculated as dadosX2 - dadosX1.

Main assumptions:

• correct pairing of the observations;

• independence among pairs;

• approximately normal distribution of the paired differences;

Value

Invisibly returns an object of classes th_test and htest containing the test statistic, degrees of freedom when applicable, p-value, estimates, critical values, significance level, and decision. When plot = TRUE, the educational graph is produced as a side effect.

Author(s)

Willian Silva Barros

Examples

before <- c(70, 72, 68, 75, 74, 71, 69, 73)
after <- c(66, 69, 65, 71, 70, 68, 66, 69)
tt2p(before, after, mpD = 0, alfa = 0.05, Ha = 3, unidade = " units", plot = FALSE)

One-Sample Z Test

Description

Performs a Z test for one population mean when the population variance is known.

Usage

tz1(
  dadosX = NULL,
  mp,
  vp,
  alfa = 0.05,
  Ha = 1,
  unidade = NULL,
  media = NULL,
  n = NULL,
  plot = TRUE
)

Arguments

Details

Raw-data and summary-statistics modes are mutually exclusive. The function accepts either raw observations or the sample mean and sample size. It produces a graphical representation of the main stages of the test.

Main assumptions:

• random sampling and independent observations;

• known population variance;

• normal population or an adequately large sample;

Value

Invisibly returns an object of classes th_test and htest containing the test statistic, degrees of freedom when applicable, p-value, estimates, critical values, significance level, and decision. When plot = TRUE, the educational graph is produced as a side effect.

Author(s)

Willian Silva Barros

Examples

X <- c(52, 49, 51, 50, 53, 54, 48, 52, 51, 50)
tz1(X, mp = 50, vp = 4, alfa = 0.05, Ha = 1, unidade = " units", plot = FALSE)

Two-Sample Z Test

Description

Performs a Z test for comparing two population means when both population variances are known.

Usage

tz2(
  dadosX = NULL,
  dadosY = NULL,
  vpX,
  vpY,
  alfa = 0.05,
  Ha = 1,
  mX = NULL,
  nX = NULL,
  mY = NULL,
  nY = NULL,
  plot = TRUE
)

Arguments

Details

Raw-data and summary-statistics modes are mutually exclusive. The function accepts raw data or summary statistics for two samples and displays the hypothesis test graphically.

Main assumptions:

• independent samples;

• known population variances;

• normal populations or adequately large samples;

Value

Invisibly returns an object of classes th_test and htest containing the test statistic, degrees of freedom when applicable, p-value, estimates, critical values, significance level, and decision. When plot = TRUE, the educational graph is produced as a side effect.

Author(s)

Willian Silva Barros

Examples

X <- c(15, 16, 14, 17, 15, 16, 14, 15)
Y <- c(11, 12, 13, 10, 12, 11, 13, 12)
tz2(X, Y, vpX = 4, vpY = 4, alfa = 0.05, Ha = 2, plot = FALSE)