README.md

In varequal: Tests and Measures for Homoscedasticity

varequal

An R package for testing whether group variances are equal.

There are also other nice alternatives such as vartest and other friends.

Installation

You can install the package from CRAN with:

install.packages("varequal")

or the development version from GitHub with:

if (!require("pak")) install.packages("pak")
pak::pak("P10911004-NPUST/varequal")

Quick start

is_var_equal(roGFP[[1]], ro ~ grp)

Benchmark

O_O: observe is homo, predict as homo O_X: observe is homo, predict as hetero X_X: observe is hetero, predict as hetero X_O: observe is hetero, predict as homo Type 1 error: O_X / (O_O + O_X) × 100% Type 2 error: X_O / (X_X + X_O) × 100% Accuracy: (O_O + X_X) / (O_O + O_X + X_X + X_O) × 100%

For normally-distributed, moderate sample size (8 ≤ n ≤ 20), and outliers-free data

| | O_O | O_X | X_X | X_O | Type 1 error (%) | Type 2 error (%) | Accuracy (%) | | :---------- | :---: | :---: | :---: | :---: | :---: | :---: | :---: | | Ansari-Bradley test | 974 | 26 | 749 | 251 | 2.6 | 25.1 | 86.15 | | Bartlett's test | 939 | 61 | 985 | 15 | 6.1 | 1.5 | 96.20 | | Mehrotra-Brown-Forsythe test | 977 | 23 | 767 | 233 | 2.3 | 23.3 | 87.20 | | Brown-Forsythe test | 973 | 27 | 823 | 177 | 2.7 | 17.7 | 89.80 | | Fligner-Killeen test | 976 | 24 | 824 | 176 | 2.4 | 17.6 | 90.00 | | 't Lam's G test | 919 | 81 | 982 | 18 | 8.1 | 1.8 | 95.05 | | Levene's test | 973 | 27 | 864 | 136 | 2.7 | 13.6 | 91.85 | | O'Brien test | 983 | 17 | 625 | 375 | 1.7 | 37.5 | 80.40 | | O'Neill-Mathews test | 983 | 17 | 820 | 180 | 1.7 | 18.0 | 90.15 | |||||||||

For normally-distributed, small sample size (3 ≤ n ≤ 7), and outliers-free data.

| | O_O | O_X | X_X | X_O | Type 1 error (%) | Type 2 error (%) | Accuracy (%) | | :---------- | :---: | :---: | :---: | :---: | :---: | :---: | :---: | | Ansari-Bradley test | 967 | 33 | 104 | 896 | 3.3 | 89.6 | 53.55 | | Bartlett's test | 957 | 43 | 440 | 560 | 4.3 | 56.0 | 69.85 | | Mehrotra-Brown-Forsythe test | 991 | 9 | 61 | 939 | 0.9 | 93.9 | 52.60 | | Brown-Forsythe test | 986 | 14 | 75 | 925 | 1.4 | 92.5 | 53.05 | | Fligner-Killeen test | 978 | 22 | 97 | 903 | 2.2 | 90.3 | 53.75 | | 't Lam's G test | 840 | 160 | 607 | 393 | 16.0 | 39.3 | 72.35 | | Levene's test | 973 | 27 | 121 | 879 | 2.7 | 87.9 | 54.70 | | O'Brien test | 996 | 4 | 30 | 970 | 0.4 | 97.0 | 51.30 | | O'Neill-Mathews test | 994 | 6 | 58 | 942 | 0.6 | 94.2 | 52.60 | |||||||||

For normally-distributed and moderate sample size (8 ≤ n ≤ 20) data, with one or two outliers.

| | O_O | O_X | X_X | X_O | Type 1 error (%) | Type 2 error (%) | Accuracy (%) | | :---------- | :---: | :---: | :---: | :---: | :---: | :---: | :---: | | Ansari-Bradley test | 972 | 28 | 843 | 157 | 2.8 | 15.7 | 90.75 | | Bartlett's test | 0 | 1000 | 1000 | 0 | 100.0 | 0.0 | 50.00 | | Mehrotra-Brown-Forsythe test | 1000 | 0 | 590 | 410 | 0.0 | 41.0 | 79.50 | | Brown-Forsythe test | 1000 | 0 | 745 | 255 | 0.0 | 25.5 | 87.25 | | Fligner-Killeen test | 974 | 26 | 910 | 90 | 2.6 | 9.0 | 94.20 | | 't Lam's G test | 0 | 1000 | 1000 | 0 | 100.0 | 0.0 | 50.00 | | Levene's test | 1000 | 0 | 790 | 210 | 0.0 | 21.0 | 89.50 | | O'Brien test | 1000 | 0 | 101 | 899 | 0.0 | 89.9 | 55.05 | | O'Neill-Mathews test | 1000 | 0 | 713 | 287 | 0.0 | 28.7 | 85.65 | |||||||||

TODO

• [x] Ansari-Bradley test
• Ansari & Bradley, 1960
• [ ] Moses test
• Moses, 1963
• [ ] Miller test
• Miller, 1968
• [x] Bartlett's test
• [x] Brown-Forsythe test
• [x] Cochran G test
• Lam, 2010
• [x] Fligner-Killeen test
• Fligner & Killeen, 1974
• [ ] Hartley's test
• Frey, 2010
• [x] Levene's test

varequal documentation built on Sept. 5, 2026, 5:08 p.m.