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

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