Table 7. Open in new tab Results of...

Data	〈t_i〉	μ_i	\|$s_i/\sqrt{N_i}$\|	t ₀	N _i	p-value
Main group (63 stars)
Fourier	–104	–103	18.9	–0.053	63	.958
Fourier	–104	–75	18.9	–1.534	63	.130
Fourier	–104	–51	18.9	–2.804	63	.007
Fourier	–104	+103	18.9	+10.952	63	<.001
χ²	–107	–103	15.9	–0.252	63	.802
χ²	–107	–75	15.9	–2.013	63	.048
χ²	–107	–51	15.9	–3.522	63	.0008
χ²	–107	+103	15.9	–13.208	63	<.001
Determinative stars (25 stars)
Fourier	–53	–103	28.6	+1.748	25	.093
Fourier	–53	–75	28.6	+0.769	25	.449
Fourier	–53	–51	28.6	–0.070	25	.945
Fourier	–53	+103	28.6	–5.455	25	<.001
χ²	–64	–103	27.7	+1.408	25	.172
χ²	–64	–75	27.7	+0.397	25	.695
χ²	–64	–51	27.7	–0.469	25	.643
χ²	–64	+103	27.7	–6.029	25	<.001
Group A (6 outliers and two determinative stars)
	–200	–201	45	0.022	8	.983
	–200	–103	45	–2.156	8	.068
	–200	–75	45	–2.778	8	.027
	–200	–51	45	–3.311	8	.013
	–200	+103	45	–6.733	8	<.001
Group B (12 outliers and one determinative star)
	+100	–103	35	+5.8	13	<.001
	+100	–75	35	+5.0	13	<.001
	+100	–51	35	+4.3	13	.001
	+100	+103	35	–0.09	13	.930

Data

〈t_i〉

μ_i

|$s_i/\sqrt{N_i}$|

t ₀

N _i

p-value

Main group (63 stars)

Fourier

–104

–103

18.9

–0.053

.958

Fourier

–104

–75

18.9

–1.534

.130

Fourier

–104

–51

18.9

–2.804

.007

Fourier

–104

+103

18.9

+10.952

<.001

χ²

–107

–103

15.9

–0.252

.802

χ²

–107

–75

15.9

–2.013

.048

χ²

–107

–51

15.9

–3.522

.0008

χ²

–107

+103

15.9

–13.208

<.001

Determinative stars (25 stars)

Fourier

–53

–103

28.6

+1.748

.093

Fourier

–53

–75

28.6

+0.769

.449

Fourier

–53

–51

28.6

–0.070

.945

Fourier

–53

+103

28.6

–5.455

<.001

χ²

–64

–103

27.7

+1.408

.172

χ²

–64

–75

27.7

+0.397

.695

χ²

–64

–51

27.7

–0.469

.643

χ²

–64

+103

27.7

–6.029

<.001

Group A (6 outliers and two determinative stars)

–200

–201

0.022

.983

–200

–103

–2.156

.068

–200

–75

–2.778

.027

–200

–51

–3.311

.013

–200

+103

–6.733

<.001

Group B (12 outliers and one determinative star)

+100

–103

+5.8

<.001

+100

–75

+5.0

<.001

+100

–51

+4.3

.001

+100

+103

–0.09

.930

Data	〈t_i〉	μ_i	\|$s_i/\sqrt{N_i}$\|	t ₀	N _i	p-value
Main group (63 stars)
Fourier	–104	–103	18.9	–0.053	63	.958
Fourier	–104	–75	18.9	–1.534	63	.130
Fourier	–104	–51	18.9	–2.804	63	.007
Fourier	–104	+103	18.9	+10.952	63	<.001
χ²	–107	–103	15.9	–0.252	63	.802
χ²	–107	–75	15.9	–2.013	63	.048
χ²	–107	–51	15.9	–3.522	63	.0008
χ²	–107	+103	15.9	–13.208	63	<.001
Determinative stars (25 stars)
Fourier	–53	–103	28.6	+1.748	25	.093
Fourier	–53	–75	28.6	+0.769	25	.449
Fourier	–53	–51	28.6	–0.070	25	.945
Fourier	–53	+103	28.6	–5.455	25	<.001
χ²	–64	–103	27.7	+1.408	25	.172
χ²	–64	–75	27.7	+0.397	25	.695
χ²	–64	–51	27.7	–0.469	25	.643
χ²	–64	+103	27.7	–6.029	25	<.001
Group A (6 outliers and two determinative stars)
	–200	–201	45	0.022	8	.983
	–200	–103	45	–2.156	8	.068
	–200	–75	45	–2.778	8	.027
	–200	–51	45	–3.311	8	.013
	–200	+103	45	–6.733	8	<.001
Group B (12 outliers and one determinative star)
	+100	–103	35	+5.8	13	<.001
	+100	–75	35	+5.0	13	<.001
	+100	–51	35	+4.3	13	.001
	+100	+103	35	–0.09	13	.930

Table 7.

Open in new tab

Results of hypothesis tests if each group of stars in SSXJ was measured at an occasion recorded in history.*

Data	〈t_i〉	μ_i	\|$s_i/\sqrt{N_i}$\|	t ₀	N _i	p-value
Main group (63 stars)
Fourier	–104	–103	18.9	–0.053	63	.958
Fourier	–104	–75	18.9	–1.534	63	.130
Fourier	–104	–51	18.9	–2.804	63	.007
Fourier	–104	+103	18.9	+10.952	63	<.001
χ²	–107	–103	15.9	–0.252	63	.802
χ²	–107	–75	15.9	–2.013	63	.048
χ²	–107	–51	15.9	–3.522	63	.0008
χ²	–107	+103	15.9	–13.208	63	<.001
Determinative stars (25 stars)
Fourier	–53	–103	28.6	+1.748	25	.093
Fourier	–53	–75	28.6	+0.769	25	.449
Fourier	–53	–51	28.6	–0.070	25	.945
Fourier	–53	+103	28.6	–5.455	25	<.001
χ²	–64	–103	27.7	+1.408	25	.172
χ²	–64	–75	27.7	+0.397	25	.695
χ²	–64	–51	27.7	–0.469	25	.643
χ²	–64	+103	27.7	–6.029	25	<.001
Group A (6 outliers and two determinative stars)
	–200	–201	45	0.022	8	.983
	–200	–103	45	–2.156	8	.068
	–200	–75	45	–2.778	8	.027
	–200	–51	45	–3.311	8	.013
	–200	+103	45	–6.733	8	<.001
Group B (12 outliers and one determinative star)
	+100	–103	35	+5.8	13	<.001
	+100	–75	35	+5.0	13	<.001
	+100	–51	35	+4.3	13	.001
	+100	+103	35	–0.09	13	.930

Data	〈t_i〉	μ_i	\|$s_i/\sqrt{N_i}$\|	t ₀	N _i	p-value
Main group (63 stars)
Fourier	–104	–103	18.9	–0.053	63	.958
Fourier	–104	–75	18.9	–1.534	63	.130
Fourier	–104	–51	18.9	–2.804	63	.007
Fourier	–104	+103	18.9	+10.952	63	<.001
χ²	–107	–103	15.9	–0.252	63	.802
χ²	–107	–75	15.9	–2.013	63	.048
χ²	–107	–51	15.9	–3.522	63	.0008
χ²	–107	+103	15.9	–13.208	63	<.001
Determinative stars (25 stars)
Fourier	–53	–103	28.6	+1.748	25	.093
Fourier	–53	–75	28.6	+0.769	25	.449
Fourier	–53	–51	28.6	–0.070	25	.945
Fourier	–53	+103	28.6	–5.455	25	<.001
χ²	–64	–103	27.7	+1.408	25	.172
χ²	–64	–75	27.7	+0.397	25	.695
χ²	–64	–51	27.7	–0.469	25	.643
χ²	–64	+103	27.7	–6.029	25	<.001
Group A (6 outliers and two determinative stars)
	–200	–201	45	0.022	8	.983
	–200	–103	45	–2.156	8	.068
	–200	–75	45	–2.778	8	.027
	–200	–51	45	–3.311	8	.013
	–200	+103	45	–6.733	8	<.001
Group B (12 outliers and one determinative star)
	+100	–103	35	+5.8	13	<.001
	+100	–75	35	+5.0	13	<.001
	+100	–51	35	+4.3	13	.001
	+100	+103	35	–0.09	13	.930

According to “Han Shu” (the history of the Han dynasty) there were at least four observational campaigns, in 104 BCE, 78–76 BCE, 52 BCE, and 103 CE. In addition, we consider the establishment of the Han dynasty in 202 BCE.

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