Table 4 Open in new tab Correlation...

Flux density (mJy)	1.0	2.0	3.0	4.0	5.0	6.0	7.0	8.0	9.0	10.0	11.0	σ_{N(> S)} (deg⁻²)
	Statistical errors only
1.0	1.00											74
2.0	0.77	1.00										32
3.0	0.47	0.83	1.00									17
4.0	0.31	0.59	0.87	1.00								11
5.0	0.19	0.40	0.64	0.88	1.00							6.7
6.0	0.11	0.24	0.43	0.66	0.90	1.00						4.5
7.0	0.06	0.15	0.28	0.48	0.72	0.92	1.00					3.2
8.0	0.04	0.10	0.21	0.36	0.57	0.78	0.94	1.00				2.4
9.0	0.03	0.07	0.15	0.27	0.44	0.63	0.80	0.93	1.00			1.8
10.0	0.02	0.05	0.11	0.21	0.34	0.49	0.65	0.80	0.95	1.00		1.4
11.0	0.02	0.04	0.08	0.16	0.26	0.38	0.52	0.66	0.84	0.95	1.00	1.1
	Including systematic uncertainties from cosmic variance
1.0	1.00											100
2.0	0.90	1.00										43
3.0	0.74	0.91	1.00									21
4.0	0.61	0.76	0.91	1.00								12
5.0	0.46	0.58	0.73	0.90	1.00							7.2
6.0	0.32	0.41	0.53	0.70	0.90	1.00						4.7
7.0	0.23	0.29	0.38	0.52	0.73	0.92	1.00					3.3
8.0	0.17	0.21	0.28	0.40	0.58	0.79	0.95	1.00				2.5
9.0	0.13	0.16	0.21	0.30	0.45	0.63	0.80	0.93	1.00			1.9
10.0	0.10	0.12	0.16	0.23	0.35	0.49	0.65	0.80	0.95	1.00		1.4
11.0	0.07	0.09	0.13	0.18	0.27	0.39	0.51	0.66	0.83	0.95	1.00	1.1
	Including systematic uncertainties from flux calibration
1.0	1.00											90
2.0	0.75	1.00										35
3.0	0.46	0.83	1.00									24
4.0	0.30	0.59	0.87	1.00								18
5.0	0.19	0.39	0.63	0.88	1.00							12
6.0	0.11	0.25	0.43	0.65	0.89	1.00						7.1
7.0	0.07	0.16	0.29	0.47	0.71	0.92	1.00					4.5
8.0	0.05	0.11	0.21	0.36	0.57	0.78	0.94	1.00				3.1
9.0	0.03	0.08	0.16	0.27	0.42	0.60	0.78	0.93	1.00			2.2
10.0	0.03	0.07	0.12	0.20	0.32	0.47	0.63	0.80	0.95	1.00		1.6
11.0	0.02	0.05	0.10	0.16	0.25	0.37	0.50	0.66	0.83	0.95	1.00	1.2
	Including systematic uncertainties from cosmic variance and flux calibration
1.0	1.00											120
2.0	0.89	1.00										45
3.0	0.74	0.91	1.00									27
4.0	0.60	0.75	0.91	1.00								19
5.0	0.46	0.57	0.72	0.90	1.00							12
6.0	0.32	0.40	0.52	0.69	0.90	1.00						7.2
7.0	0.23	0.28	0.37	0.52	0.73	0.92	1.00					4.5
8.0	0.18	0.23	0.29	0.41	0.59	0.79	0.94	1.00				3.1
9.0	0.14	0.18	0.23	0.31	0.46	0.62	0.78	0.93	1.00			2.2
10.0	0.12	0.14	0.18	0.24	0.35	0.48	0.63	0.81	0.95	1.00		1.6
11.0	0.09	0.12	0.14	0.19	0.28	0.38	0.50	0.66	0.83	0.96	1.00	1.3

Flux density (mJy)

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

9.0

10.0

11.0

σ_{N(> S)} (deg⁻²)

Statistical errors only

1.0

1.00

2.0

0.77

1.00

3.0

0.47

0.83

1.00

4.0

0.31

0.59

0.87

1.00

5.0

0.19

0.40

0.64

0.88

1.00

6.7

6.0

0.11

0.24

0.43

0.66

0.90

1.00

4.5

7.0

0.06

0.15

0.28

0.48

0.72

0.92

1.00

3.2

8.0

0.04

0.10

0.21

0.36

0.57

0.78

0.94

1.00

2.4

9.0

0.03

0.07

0.15

0.27

0.44

0.63

0.80

0.93

1.00

1.8

10.0

0.02

0.05

0.11

0.21

0.34

0.49

0.65

0.80

0.95

1.00

1.4

11.0

0.02

0.04

0.08

0.16

0.26

0.38

0.52

0.66

0.84

0.95

1.00

1.1

Including systematic uncertainties from cosmic variance

1.0

1.00

100

2.0

0.90

1.00

3.0

0.74

0.91

1.00

4.0

0.61

0.76

0.91

1.00

5.0

0.46

0.58

0.73

0.90

1.00

7.2

6.0

0.32

0.41

0.53

0.70

0.90

1.00

4.7

7.0

0.23

0.29

0.38

0.52

0.73

0.92

1.00

3.3

8.0

0.17

0.21

0.28

0.40

0.58

0.79

0.95

1.00

2.5

9.0

0.13

0.16

0.21

0.30

0.45

0.63

0.80

0.93

1.00

1.9

10.0

0.10

0.12

0.16

0.23

0.35

0.49

0.65

0.80

0.95

1.00

1.4

11.0

0.07

0.09

0.13

0.18

0.27

0.39

0.51

0.66

0.83

0.95

1.00

1.1

Including systematic uncertainties from flux calibration

1.0

1.00

2.0

0.75

1.00

3.0

0.46

0.83

1.00

4.0

0.30

0.59

0.87

1.00

5.0

0.19

0.39

0.63

0.88

1.00

6.0

0.11

0.25

0.43

0.65

0.89

1.00

7.1

7.0

0.07

0.16

0.29

0.47

0.71

0.92

1.00

4.5

8.0

0.05

0.11

0.21

0.36

0.57

0.78

0.94

1.00

3.1

9.0

0.03

0.08

0.16

0.27

0.42

0.60

0.78

0.93

1.00

2.2

10.0

0.03

0.07

0.12

0.20

0.32

0.47

0.63

0.80

0.95

1.00

1.6

11.0

0.02

0.05

0.10

0.16

0.25

0.37

0.50

0.66

0.83

0.95

1.00

1.2

Including systematic uncertainties from cosmic variance and flux calibration

1.0

1.00

120

2.0

0.89

1.00

3.0

0.74

0.91

1.00

4.0

0.60

0.75

0.91

1.00

5.0

0.46

0.57

0.72

0.90

1.00

6.0

0.32

0.40

0.52

0.69

0.90

1.00

7.2

7.0

0.23

0.28

0.37

0.52

0.73

0.92

1.00

4.5

8.0

0.18

0.23

0.29

0.41

0.59

0.79

0.94

1.00

3.1

9.0

0.14

0.18

0.23

0.31

0.46

0.62

0.78

0.93

1.00

2.2

10.0

0.12

0.14

0.18

0.24

0.35

0.48

0.63

0.81

0.95

1.00

1.6

11.0

0.09

0.12

0.14

0.19

0.28

0.38

0.50

0.66

0.83

0.96

1.00

1.3

Flux density (mJy)	1.0	2.0	3.0	4.0	5.0	6.0	7.0	8.0	9.0	10.0	11.0	σ_{N(> S)} (deg⁻²)
	Statistical errors only
1.0	1.00											74
2.0	0.77	1.00										32
3.0	0.47	0.83	1.00									17
4.0	0.31	0.59	0.87	1.00								11
5.0	0.19	0.40	0.64	0.88	1.00							6.7
6.0	0.11	0.24	0.43	0.66	0.90	1.00						4.5
7.0	0.06	0.15	0.28	0.48	0.72	0.92	1.00					3.2
8.0	0.04	0.10	0.21	0.36	0.57	0.78	0.94	1.00				2.4
9.0	0.03	0.07	0.15	0.27	0.44	0.63	0.80	0.93	1.00			1.8
10.0	0.02	0.05	0.11	0.21	0.34	0.49	0.65	0.80	0.95	1.00		1.4
11.0	0.02	0.04	0.08	0.16	0.26	0.38	0.52	0.66	0.84	0.95	1.00	1.1
	Including systematic uncertainties from cosmic variance
1.0	1.00											100
2.0	0.90	1.00										43
3.0	0.74	0.91	1.00									21
4.0	0.61	0.76	0.91	1.00								12
5.0	0.46	0.58	0.73	0.90	1.00							7.2
6.0	0.32	0.41	0.53	0.70	0.90	1.00						4.7
7.0	0.23	0.29	0.38	0.52	0.73	0.92	1.00					3.3
8.0	0.17	0.21	0.28	0.40	0.58	0.79	0.95	1.00				2.5
9.0	0.13	0.16	0.21	0.30	0.45	0.63	0.80	0.93	1.00			1.9
10.0	0.10	0.12	0.16	0.23	0.35	0.49	0.65	0.80	0.95	1.00		1.4
11.0	0.07	0.09	0.13	0.18	0.27	0.39	0.51	0.66	0.83	0.95	1.00	1.1
	Including systematic uncertainties from flux calibration
1.0	1.00											90
2.0	0.75	1.00										35
3.0	0.46	0.83	1.00									24
4.0	0.30	0.59	0.87	1.00								18
5.0	0.19	0.39	0.63	0.88	1.00							12
6.0	0.11	0.25	0.43	0.65	0.89	1.00						7.1
7.0	0.07	0.16	0.29	0.47	0.71	0.92	1.00					4.5
8.0	0.05	0.11	0.21	0.36	0.57	0.78	0.94	1.00				3.1
9.0	0.03	0.08	0.16	0.27	0.42	0.60	0.78	0.93	1.00			2.2
10.0	0.03	0.07	0.12	0.20	0.32	0.47	0.63	0.80	0.95	1.00		1.6
11.0	0.02	0.05	0.10	0.16	0.25	0.37	0.50	0.66	0.83	0.95	1.00	1.2
	Including systematic uncertainties from cosmic variance and flux calibration
1.0	1.00											120
2.0	0.89	1.00										45
3.0	0.74	0.91	1.00									27
4.0	0.60	0.75	0.91	1.00								19
5.0	0.46	0.57	0.72	0.90	1.00							12
6.0	0.32	0.40	0.52	0.69	0.90	1.00						7.2
7.0	0.23	0.28	0.37	0.52	0.73	0.92	1.00					4.5
8.0	0.18	0.23	0.29	0.41	0.59	0.79	0.94	1.00				3.1
9.0	0.14	0.18	0.23	0.31	0.46	0.62	0.78	0.93	1.00			2.2
10.0	0.12	0.14	0.18	0.24	0.35	0.48	0.63	0.81	0.95	1.00		1.6
11.0	0.09	0.12	0.14	0.19	0.28	0.38	0.50	0.66	0.83	0.96	1.00	1.3

Table 4

Open in new tab

Correlation matrix for the cumulative counts derived from the combined AzTEC blank-field surveys. The first set shows the bin-to-bin correlations when considering only statistical errors from the bootstrap sampling method (Section 3.1); these represent the actual correlations between bins in the data themselves. The second, third and fourth sets show the correlations when systematic uncertainties from cosmic variance (Section 3.3), flux calibration (Section 3.4) and both are included, respectively. The last column in all four cases shows the standard deviation on the cumulative counts for each flux bin, and can be used to compute the covariance matrix from these correlations.

Flux density (mJy)	1.0	2.0	3.0	4.0	5.0	6.0	7.0	8.0	9.0	10.0	11.0	σ_{N(> S)} (deg⁻²)
	Statistical errors only
1.0	1.00											74
2.0	0.77	1.00										32
3.0	0.47	0.83	1.00									17
4.0	0.31	0.59	0.87	1.00								11
5.0	0.19	0.40	0.64	0.88	1.00							6.7
6.0	0.11	0.24	0.43	0.66	0.90	1.00						4.5
7.0	0.06	0.15	0.28	0.48	0.72	0.92	1.00					3.2
8.0	0.04	0.10	0.21	0.36	0.57	0.78	0.94	1.00				2.4
9.0	0.03	0.07	0.15	0.27	0.44	0.63	0.80	0.93	1.00			1.8
10.0	0.02	0.05	0.11	0.21	0.34	0.49	0.65	0.80	0.95	1.00		1.4
11.0	0.02	0.04	0.08	0.16	0.26	0.38	0.52	0.66	0.84	0.95	1.00	1.1
	Including systematic uncertainties from cosmic variance
1.0	1.00											100
2.0	0.90	1.00										43
3.0	0.74	0.91	1.00									21
4.0	0.61	0.76	0.91	1.00								12
5.0	0.46	0.58	0.73	0.90	1.00							7.2
6.0	0.32	0.41	0.53	0.70	0.90	1.00						4.7
7.0	0.23	0.29	0.38	0.52	0.73	0.92	1.00					3.3
8.0	0.17	0.21	0.28	0.40	0.58	0.79	0.95	1.00				2.5
9.0	0.13	0.16	0.21	0.30	0.45	0.63	0.80	0.93	1.00			1.9
10.0	0.10	0.12	0.16	0.23	0.35	0.49	0.65	0.80	0.95	1.00		1.4
11.0	0.07	0.09	0.13	0.18	0.27	0.39	0.51	0.66	0.83	0.95	1.00	1.1
	Including systematic uncertainties from flux calibration
1.0	1.00											90
2.0	0.75	1.00										35
3.0	0.46	0.83	1.00									24
4.0	0.30	0.59	0.87	1.00								18
5.0	0.19	0.39	0.63	0.88	1.00							12
6.0	0.11	0.25	0.43	0.65	0.89	1.00						7.1
7.0	0.07	0.16	0.29	0.47	0.71	0.92	1.00					4.5
8.0	0.05	0.11	0.21	0.36	0.57	0.78	0.94	1.00				3.1
9.0	0.03	0.08	0.16	0.27	0.42	0.60	0.78	0.93	1.00			2.2
10.0	0.03	0.07	0.12	0.20	0.32	0.47	0.63	0.80	0.95	1.00		1.6
11.0	0.02	0.05	0.10	0.16	0.25	0.37	0.50	0.66	0.83	0.95	1.00	1.2
	Including systematic uncertainties from cosmic variance and flux calibration
1.0	1.00											120
2.0	0.89	1.00										45
3.0	0.74	0.91	1.00									27
4.0	0.60	0.75	0.91	1.00								19
5.0	0.46	0.57	0.72	0.90	1.00							12
6.0	0.32	0.40	0.52	0.69	0.90	1.00						7.2
7.0	0.23	0.28	0.37	0.52	0.73	0.92	1.00					4.5
8.0	0.18	0.23	0.29	0.41	0.59	0.79	0.94	1.00				3.1
9.0	0.14	0.18	0.23	0.31	0.46	0.62	0.78	0.93	1.00			2.2
10.0	0.12	0.14	0.18	0.24	0.35	0.48	0.63	0.81	0.95	1.00		1.6
11.0	0.09	0.12	0.14	0.19	0.28	0.38	0.50	0.66	0.83	0.96	1.00	1.3

Flux density (mJy)	1.0	2.0	3.0	4.0	5.0	6.0	7.0	8.0	9.0	10.0	11.0	σ_{N(> S)} (deg⁻²)
	Statistical errors only
1.0	1.00											74
2.0	0.77	1.00										32
3.0	0.47	0.83	1.00									17
4.0	0.31	0.59	0.87	1.00								11
5.0	0.19	0.40	0.64	0.88	1.00							6.7
6.0	0.11	0.24	0.43	0.66	0.90	1.00						4.5
7.0	0.06	0.15	0.28	0.48	0.72	0.92	1.00					3.2
8.0	0.04	0.10	0.21	0.36	0.57	0.78	0.94	1.00				2.4
9.0	0.03	0.07	0.15	0.27	0.44	0.63	0.80	0.93	1.00			1.8
10.0	0.02	0.05	0.11	0.21	0.34	0.49	0.65	0.80	0.95	1.00		1.4
11.0	0.02	0.04	0.08	0.16	0.26	0.38	0.52	0.66	0.84	0.95	1.00	1.1
	Including systematic uncertainties from cosmic variance
1.0	1.00											100
2.0	0.90	1.00										43
3.0	0.74	0.91	1.00									21
4.0	0.61	0.76	0.91	1.00								12
5.0	0.46	0.58	0.73	0.90	1.00							7.2
6.0	0.32	0.41	0.53	0.70	0.90	1.00						4.7
7.0	0.23	0.29	0.38	0.52	0.73	0.92	1.00					3.3
8.0	0.17	0.21	0.28	0.40	0.58	0.79	0.95	1.00				2.5
9.0	0.13	0.16	0.21	0.30	0.45	0.63	0.80	0.93	1.00			1.9
10.0	0.10	0.12	0.16	0.23	0.35	0.49	0.65	0.80	0.95	1.00		1.4
11.0	0.07	0.09	0.13	0.18	0.27	0.39	0.51	0.66	0.83	0.95	1.00	1.1
	Including systematic uncertainties from flux calibration
1.0	1.00											90
2.0	0.75	1.00										35
3.0	0.46	0.83	1.00									24
4.0	0.30	0.59	0.87	1.00								18
5.0	0.19	0.39	0.63	0.88	1.00							12
6.0	0.11	0.25	0.43	0.65	0.89	1.00						7.1
7.0	0.07	0.16	0.29	0.47	0.71	0.92	1.00					4.5
8.0	0.05	0.11	0.21	0.36	0.57	0.78	0.94	1.00				3.1
9.0	0.03	0.08	0.16	0.27	0.42	0.60	0.78	0.93	1.00			2.2
10.0	0.03	0.07	0.12	0.20	0.32	0.47	0.63	0.80	0.95	1.00		1.6
11.0	0.02	0.05	0.10	0.16	0.25	0.37	0.50	0.66	0.83	0.95	1.00	1.2
	Including systematic uncertainties from cosmic variance and flux calibration
1.0	1.00											120
2.0	0.89	1.00										45
3.0	0.74	0.91	1.00									27
4.0	0.60	0.75	0.91	1.00								19
5.0	0.46	0.57	0.72	0.90	1.00							12
6.0	0.32	0.40	0.52	0.69	0.90	1.00						7.2
7.0	0.23	0.28	0.37	0.52	0.73	0.92	1.00					4.5
8.0	0.18	0.23	0.29	0.41	0.59	0.79	0.94	1.00				3.1
9.0	0.14	0.18	0.23	0.31	0.46	0.62	0.78	0.93	1.00			2.2
10.0	0.12	0.14	0.18	0.24	0.35	0.48	0.63	0.81	0.95	1.00		1.6
11.0	0.09	0.12	0.14	0.19	0.28	0.38	0.50	0.66	0.83	0.96	1.00	1.3

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