README

Overview

Visualise the results of F test to compare two variances, Student’s t-test, test of equal or given proportions, Pearson’s chi-squared test for count data and test for association/correlation between paired samples.

Installation

# CRAN installation:
install.packages("gginference")

# Or the development version from GitHub:
# install.packages("devtools")
devtools::install_github("okgreece/gginference")

Usage

One sample

One sample t-test with normal population and σ2 unknown

The rejection regions for one sample t-test with normal population and σ2 unknown are calculated using ggttest function. The following table shows the rejection regions which is calculated with gginference depending the specified parameters in t.test.

H0 H1 Rejection Region of gginference Parameters of t.test
μ = μ0 μ < μ0 R = {z <  − za}
  • x = vector of sample data,
  • mu = μ0,
  • alternative = “less”
μ > μ0 R = {z > za}
  • x = vector of sample data,
  • mu = μ0,
  • alternative = “greater”
μ ≠ μ0 R = {|z| > za/2}
  • x = vector of sample data,
  • mu = μ0,
  • alternative = “two.sided”

where

One sample t-test with normal population and n < 30 and σ2 unknown

ggttest is also used to calculate rejection region for one sample t-test with normal population and n < 30 and σ2 unknown.

H0 H1 Rejection Region of gginference Parameters of t.test
μ = μ0 μ < μ0 R = {t <  − tn − 1, a}
  • x = vector of sample data,
  • mu = μ0,
  • alternative = “less”
μ > μ0 R = {t > tn − 1, a}
  • x = vector of sample data,
  • mu = μ0,
  • alternative = “greater”
μ ≠ μ0 R = {|t| > tn − 1, a/2}
  • x = vector of sample data,
  • mu = μ0,
  • alternative = “two.sided”

where

Two samples

Two independent samples t-test with normal populations and σ12 = σ22 unknown

Next table shows the rejection regions of two independent samples t-test with normal populations and σ12 = σ22. ggttest is also used to visualize this test.

H0 H1 Rejection Region of gginference Parameters of t.test
μ1 − μ2 = d0 μ1 − μ2 < d0 R = {t <  − tn1 + n2 − 2, a}
  • x = vector of sample 1 data,
  • y = vector of sample 2 data,
  • paired = FALSE,
  • var.equal = TRUE,
  • alternative = “less”
μ1 − μ2 > d0 R = {t > tn1 + n2 − 2, a}
  • x = vector of sample 1 data,
  • y = vector of sample 2 data,
  • paired = FALSE,
  • var.equal = TRUE,
  • alternative = “greater”
μ1 − μ2 ≠ d0 R = {|t| > tn1 + n2 − 2, a/2}
  • x = vector of sample 1 data,
  • y = vector of sample 2 data,
  • paired = FALSE,
  • var.equal = TRUE,
  • alternative = “two.sided”

where

Two independent samples t-test with normal populations and σ12 σ22

ggttest is used to visualize two independent samples t-test with normal populations and σ12 σ22. The following table shows the rejection regions of this test.

H0 H1 Rejection Region of gginference Parameters of t.test
μ1 − μ2 = d0 μ1 − μ2 < d0 R = {t <  − tν, a}
  • x = vector of sample 1 data,
  • y = vector of sample 2 data,
  • paired = FALSE,
  • var.equal = FALSE,
  • alternative = “less”
μ1 − μ2 > d0 R = {t > tν, a}
  • x = vector of sample 1 data,
  • y = vector of sample 2 data,
  • paired = FALSE,
  • var.equal = FALSE,
  • alternative = “greater”
μ1 − μ2 ≠ d0 R = {|t| > tν, a/2}
  • x = vector of sample 1 data,
  • y = vector of sample 2 data,
  • paired = FALSE,
  • var.equal = FALSE,
  • alternative = “two.sided”

where

and ν degrees of freedom with

Paired samples with normal population

ggttest is used also to visualize the results of the paired sample Student’s t-test. Next table shows th rejection region of this test.

H0 H1 Rejection Region of gginference Parameters of t.test
μ1 − μ2 = d0 μ1 − μ2 < d0 R = {t <  − tn − 1, a}
  • x = vector of sample 1 data,
  • y = vector of sample 2 data,
  • paired = FALSE,
  • var.equal = FALSE,
  • alternative = “less”
μ1 − μ2 > d0 R = {t > tn − 1, a}
  • x = vector of sample 1 data,
  • y = vector of sample 2 data,
  • paired = FALSE,
  • var.equal = FALSE,
  • alternative = “greater”
μ1 − μ2 ≠ d0 R = {|t| > tn − 1, a/2}
  • x = vector of sample 1 data,
  • y = vector of sample 2 data,
  • paired = FALSE,
  • var.equal = FALSE,
  • alternative = “two.sided”

where

Proportion test

One-proportion z-test

ggproptest() is used to visualize one-proportion z-test. The rejection regions are shown below.

H0 H1 Rejection Region of gginference Parameters of prop.test()
p = p0 p < p0 R = {z <  − za}
  • x = vector of sample data,
  • mu = μ0,
  • alternative = “less”
p > p0 R = {z > za}
  • x = vector of sample data,
  • mu = μ0,
  • alternative = “greater”
p ≠ p0 R = {|z| > za/2}
  • x = vector of sample data,
  • mu = μ0,
  • alternative = “two.sided”

where

Two-proportion z-test

The results of two-proportion z-test are visualized using ggproptest() and next table shows the rejection regions.

H0 H1 Rejection Region of gginference Parameters of prop.test()
p1 − p2 = d0 p1 − p2 < d0 R = {z <  − za}
  • x = vector of sample 1 data,
  • y = vector of sample 2 data,
  • paired = FALSE,
  • var.equal = FALSE,
  • alternative = “less”
p1 − p2 > d0 R = {z > za}
  • x = vector of sample 1 data,
  • y = vector of sample 2 data,
  • paired = FALSE,
  • var.equal = FALSE,
  • alternative = “greater”
p1 − p2 ≠ d0 R = {|z| > za/2}
  • x = vector of sample 1 data,
  • y = vector of sample 2 data,
  • paired = FALSE,
  • var.equal = FALSE,
  • alternative = “two.sided”

where

Two-sample F test for equality of variances

ggvartest is used to visualize the results of the paired sample Student’s t-test. The rejection region that is used in this test is shown below.

H0 H1 Rejection Region of gginference Parameters of var.test
σ12 / σ22 = 1 σ12 / σ22 < 1 R = {F > Fn1 − 1, n2 − 1, 1 − a}
  • x = vector of sample 1 data,
  • y = vector of sample 2 data,
  • ratio = 1
  • alternative = “less”
σ12 / σ22 > 1 R = {F > Fn1 − 1, n2 − 1, a}
  • x = vector of sample data,
  • mu = μ0,
  • ratio = 1
  • alternative = “greater”
σ12 / σ22≠ 1 R = {F > Fn1 − 1, n2 − 1, a/2}
  • x = vector of sample data,
  • mu = μ0,
  • ratio = 1
  • alternative = “two.sided”

where

Test for Correlation Between Paired Samples

ggcortest is usesd to visualize the results of test for correlation between paired samples. The following table shows the rejection region of this test.

H0 H1 Rejection Region of gginference Parameters of cor.test
𝜚 = 0 𝜚 ≠ 0 R = {|t| > tn − 2, a/2}
  • x = vector of sample 1 data
  • y = vector of sample 2 data,
  • alternative = “two.sided”

where

Chi-squared Test of Independence

The results of Pearson’s chi-squared test for count data are visulized using ggchisqtest. Next table shows the rejection region of this test.

H0 H1 Rejection Region of gginference Parameters of chisq.test
Two variables are independent Two variables are not independent R = {X2 > χa/22}
  • x = 2-dimensional contingency table

where

ANOVA F-test

ggaov is used to visualize the results of ANOVA F-test. Table below shows rejection region of Anova F-stest.

H0 H1 Rejection Region of gginference Parameters of aov
H0 : μ1 = μ2= … = μk Not all three population means are equal R = {F > Fk − 1, n − k, a}
  • formula = formula specifying the model
  • data = data frame with the variables specified in the formula

where

Getting help

If you encounter a bug, please feel free to open an issue with a minimal reproducible example.