Table 1 Open in new tab The approximate...

n	Statistic	BD	BH	QA	Permutation	Confidence interval
50	t					7.044	6.312	6.915	6.243	(6.835, 7.316)	(6.034, 6.539)
	U					6.968	6.245	9.264	8.088	(9.120, 10.001)	(7.738, 8.597)
	\|${\chi}^2$\|					7.279	6.557	9.264	8.088	(9.120, 10.001)	(7.738, 8.597)
	p	7.000	6.301	6.997	6.288	7.316	6.538	6.915	6.243	(6.835, 7.316)	(6.034, 6.539)
100	t					6.998	6.271	6.934	6.245	(6.738, 7.004)	(6.067, 6.561)
	U					6.963	6.239	7.969	7.063	(7.709, 8.063)	(6.834, 7.475)
	\|${\chi}^2$\|					7.274	6.551	7.969	7.063	(7.709, 8.063)	(6.834, 7.475)
	p	7.000	6.301	6.998	6.287	7.003	6.560	6.934	6.245	(6.738, 7.004)	(6.067, 6.561)
200	t					6.977	6.252	6.837	6.284	(6.775, 7.204)	(6.104, 6.487)
	U					6.960	6.236	7.309	6.677	(7.237, 7.733)	(6.472, 6.907)
	\|${\chi}^2$\|					7.271	6.548	7.309	6.677	(7.237, 7.733)	(6.472, 6.907)
	p	7.000	6.301	6.998	6.286	7.329	6.607	6.837	6.284	(6.775, 7.204)	(6.104, 6.487)
500	U					7.247	6.245	7.521	6.372	(7.265, 7.710)	(6.245, 6.607)
	\|${\chi}^2$\|					7.269	6.547	7.521	6.372	(7.265, 7.710)	(6.245, 6.607)
	p	7.000	6.301	6.995	6.288	7.329	6.445	7.311	6.224	(7.070, 7.489)	(6.102, 6.446)
1000	U					6.958	6.323	7.046	6.468	(6.874, 7.655)	(6.319, 6.776)
	\|${\chi}^2$\|					7.269	6.546	7.046	6.468	(6.874, 7.655)	(6.319, 6.776)
	p	7.000	6.301	6.997	6.281	7.329	6.607	6.953	6.391	(6.786, 7.544)	(6.245, 6.691)
2000	U					6.958	6.234	7.066	6.403	(6.925, 7.274)	(6.171, 6.637)
	\|${\chi}^2$\|					7.268	6.546	7.066	6.403	(6.925, 7.274)	(6.171, 6.637)
	p	7.000	6.301	6.997	6.290	7.231	6.499	7.004	6.175	(6.913, 7.232)	(6.042, 6.500)

Statistic

Permutation

Confidence interval

0.01

0.05

0.01

0.05

0.01

0.05

0.01

0.05

0.01

0.05

7.044

6.312

6.915

6.243

(6.835, 7.316)

(6.034, 6.539)

6.968

6.245

9.264

8.088

(9.120, 10.001)

(7.738, 8.597)

|${\chi}^2$|

7.279

6.557

9.264

8.088

(9.120, 10.001)

(7.738, 8.597)

7.000

6.301

6.997

6.288

7.316

6.538

6.915

6.243

(6.835, 7.316)

(6.034, 6.539)

100

6.998

6.271

6.934

6.245

(6.738, 7.004)

(6.067, 6.561)

6.963

6.239

7.969

7.063

(7.709, 8.063)

(6.834, 7.475)

|${\chi}^2$|

7.274

6.551

7.969

7.063

(7.709, 8.063)

(6.834, 7.475)

7.000

6.301

6.998

6.287

7.003

6.560

6.934

6.245

(6.738, 7.004)

(6.067, 6.561)

200

6.977

6.252

6.837

6.284

(6.775, 7.204)

(6.104, 6.487)

6.960

6.236

7.309

6.677

(7.237, 7.733)

(6.472, 6.907)

|${\chi}^2$|

7.271

6.548

7.309

6.677

(7.237, 7.733)

(6.472, 6.907)

7.000

6.301

6.998

6.286

7.329

6.607

6.837

6.284

(6.775, 7.204)

(6.104, 6.487)

500

7.247

6.245

7.521

6.372

(7.265, 7.710)

(6.245, 6.607)

|${\chi}^2$|

7.269

6.547

7.521

6.372

(7.265, 7.710)

(6.245, 6.607)

7.000

6.301

6.995

6.288

7.329

6.445

7.311

6.224

(7.070, 7.489)

(6.102, 6.446)

1000

6.958

6.323

7.046

6.468

(6.874, 7.655)

(6.319, 6.776)

|${\chi}^2$|

7.269

6.546

7.046

6.468

(6.874, 7.655)

(6.319, 6.776)

7.000

6.301

6.997

6.281

7.329

6.607

6.953

6.391

(6.786, 7.544)

(6.245, 6.691)

2000

6.958

6.234

7.066

6.403

(6.925, 7.274)

(6.171, 6.637)

|${\chi}^2$|

7.268

6.546

7.066

6.403

(6.925, 7.274)

(6.171, 6.637)

7.000

6.301

6.997

6.290

7.231

6.499

7.004

6.175

(6.913, 7.232)

(6.042, 6.500)

n	Statistic	BD	BH	QA	Permutation	Confidence interval
50	t					7.044	6.312	6.915	6.243	(6.835, 7.316)	(6.034, 6.539)
	U					6.968	6.245	9.264	8.088	(9.120, 10.001)	(7.738, 8.597)
	\|${\chi}^2$\|					7.279	6.557	9.264	8.088	(9.120, 10.001)	(7.738, 8.597)
	p	7.000	6.301	6.997	6.288	7.316	6.538	6.915	6.243	(6.835, 7.316)	(6.034, 6.539)
100	t					6.998	6.271	6.934	6.245	(6.738, 7.004)	(6.067, 6.561)
	U					6.963	6.239	7.969	7.063	(7.709, 8.063)	(6.834, 7.475)
	\|${\chi}^2$\|					7.274	6.551	7.969	7.063	(7.709, 8.063)	(6.834, 7.475)
	p	7.000	6.301	6.998	6.287	7.003	6.560	6.934	6.245	(6.738, 7.004)	(6.067, 6.561)
200	t					6.977	6.252	6.837	6.284	(6.775, 7.204)	(6.104, 6.487)
	U					6.960	6.236	7.309	6.677	(7.237, 7.733)	(6.472, 6.907)
	\|${\chi}^2$\|					7.271	6.548	7.309	6.677	(7.237, 7.733)	(6.472, 6.907)
	p	7.000	6.301	6.998	6.286	7.329	6.607	6.837	6.284	(6.775, 7.204)	(6.104, 6.487)
500	U					7.247	6.245	7.521	6.372	(7.265, 7.710)	(6.245, 6.607)
	\|${\chi}^2$\|					7.269	6.547	7.521	6.372	(7.265, 7.710)	(6.245, 6.607)
	p	7.000	6.301	6.995	6.288	7.329	6.445	7.311	6.224	(7.070, 7.489)	(6.102, 6.446)
1000	U					6.958	6.323	7.046	6.468	(6.874, 7.655)	(6.319, 6.776)
	\|${\chi}^2$\|					7.269	6.546	7.046	6.468	(6.874, 7.655)	(6.319, 6.776)
	p	7.000	6.301	6.997	6.281	7.329	6.607	6.953	6.391	(6.786, 7.544)	(6.245, 6.691)
2000	U					6.958	6.234	7.066	6.403	(6.925, 7.274)	(6.171, 6.637)
	\|${\chi}^2$\|					7.268	6.546	7.066	6.403	(6.925, 7.274)	(6.171, 6.637)
	p	7.000	6.301	6.997	6.290	7.231	6.499	7.004	6.175	(6.913, 7.232)	(6.042, 6.500)

Table 1

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The approximate and accurate threshold values of –log₁₀(p) simulated for different population sizes

n	Statistic	BD		BH		QA		Permutation		Confidence interval
		0.01	0.05	0.01	0.05	0.01	0.05	0.01	0.05	0.01	0.05
50	t					7.044	6.312	6.915	6.243	(6.835, 7.316)	(6.034, 6.539)
	U					6.968	6.245	9.264	8.088	(9.120, 10.001)	(7.738, 8.597)
	\|${\chi}^2$\|					7.279	6.557	9.264	8.088	(9.120, 10.001)	(7.738, 8.597)
	p	7.000	6.301	6.997	6.288	7.316	6.538	6.915	6.243	(6.835, 7.316)	(6.034, 6.539)
100	t					6.998	6.271	6.934	6.245	(6.738, 7.004)	(6.067, 6.561)
	U					6.963	6.239	7.969	7.063	(7.709, 8.063)	(6.834, 7.475)
	\|${\chi}^2$\|					7.274	6.551	7.969	7.063	(7.709, 8.063)	(6.834, 7.475)
	p	7.000	6.301	6.998	6.287	7.003	6.560	6.934	6.245	(6.738, 7.004)	(6.067, 6.561)
200	t					6.977	6.252	6.837	6.284	(6.775, 7.204)	(6.104, 6.487)
	U					6.960	6.236	7.309	6.677	(7.237, 7.733)	(6.472, 6.907)
	\|${\chi}^2$\|					7.271	6.548	7.309	6.677	(7.237, 7.733)	(6.472, 6.907)
	p	7.000	6.301	6.998	6.286	7.329	6.607	6.837	6.284	(6.775, 7.204)	(6.104, 6.487)
500	U					7.247	6.245	7.521	6.372	(7.265, 7.710)	(6.245, 6.607)
	\|${\chi}^2$\|					7.269	6.547	7.521	6.372	(7.265, 7.710)	(6.245, 6.607)
	p	7.000	6.301	6.995	6.288	7.329	6.445	7.311	6.224	(7.070, 7.489)	(6.102, 6.446)
1000	U					6.958	6.323	7.046	6.468	(6.874, 7.655)	(6.319, 6.776)
	\|${\chi}^2$\|					7.269	6.546	7.046	6.468	(6.874, 7.655)	(6.319, 6.776)
	p	7.000	6.301	6.997	6.281	7.329	6.607	6.953	6.391	(6.786, 7.544)	(6.245, 6.691)
2000	U					6.958	6.234	7.066	6.403	(6.925, 7.274)	(6.171, 6.637)
	\|${\chi}^2$\|					7.268	6.546	7.066	6.403	(6.925, 7.274)	(6.171, 6.637)
	p	7.000	6.301	6.997	6.290	7.231	6.499	7.004	6.175	(6.913, 7.232)	(6.042, 6.500)

n	Statistic	BD		BH		QA		Permutation		Confidence interval
		0.01	0.05	0.01	0.05	0.01	0.05	0.01	0.05	0.01	0.05
50	t					7.044	6.312	6.915	6.243	(6.835, 7.316)	(6.034, 6.539)
	U					6.968	6.245	9.264	8.088	(9.120, 10.001)	(7.738, 8.597)
	\|${\chi}^2$\|					7.279	6.557	9.264	8.088	(9.120, 10.001)	(7.738, 8.597)
	p	7.000	6.301	6.997	6.288	7.316	6.538	6.915	6.243	(6.835, 7.316)	(6.034, 6.539)
100	t					6.998	6.271	6.934	6.245	(6.738, 7.004)	(6.067, 6.561)
	U					6.963	6.239	7.969	7.063	(7.709, 8.063)	(6.834, 7.475)
	\|${\chi}^2$\|					7.274	6.551	7.969	7.063	(7.709, 8.063)	(6.834, 7.475)
	p	7.000	6.301	6.998	6.287	7.003	6.560	6.934	6.245	(6.738, 7.004)	(6.067, 6.561)
200	t					6.977	6.252	6.837	6.284	(6.775, 7.204)	(6.104, 6.487)
	U					6.960	6.236	7.309	6.677	(7.237, 7.733)	(6.472, 6.907)
	\|${\chi}^2$\|					7.271	6.548	7.309	6.677	(7.237, 7.733)	(6.472, 6.907)
	p	7.000	6.301	6.998	6.286	7.329	6.607	6.837	6.284	(6.775, 7.204)	(6.104, 6.487)
500	U					7.247	6.245	7.521	6.372	(7.265, 7.710)	(6.245, 6.607)
	\|${\chi}^2$\|					7.269	6.547	7.521	6.372	(7.265, 7.710)	(6.245, 6.607)
	p	7.000	6.301	6.995	6.288	7.329	6.445	7.311	6.224	(7.070, 7.489)	(6.102, 6.446)
1000	U					6.958	6.323	7.046	6.468	(6.874, 7.655)	(6.319, 6.776)
	\|${\chi}^2$\|					7.269	6.546	7.046	6.468	(6.874, 7.655)	(6.319, 6.776)
	p	7.000	6.301	6.997	6.281	7.329	6.607	6.953	6.391	(6.786, 7.544)	(6.245, 6.691)
2000	U					6.958	6.234	7.066	6.403	(6.925, 7.274)	(6.171, 6.637)
	\|${\chi}^2$\|					7.268	6.546	7.066	6.403	(6.925, 7.274)	(6.171, 6.637)
	p	7.000	6.301	6.997	6.290	7.231	6.499	7.004	6.175	(6.913, 7.232)	(6.042, 6.500)

n is population size; BD represents Bonferroni step-down adjustment, BH controlling FDR and QA quick approximation methods.

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