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Table 2 Summary of the person selection probability, composite and benchmark weight statistics for each of the frames

From: Developing a weighting strategy to include mobile phone numbers into an ongoing population health survey using an overlapping dual-frame design with limited benchmark information

Group

Phone type

Description

Formula

Sum

Ave

Median

Min

Max

Landline Frame (n = 2171)

Adult and children (n = 2171)

All types (n = 2171)

Interviews divided by universe of phone numbers

t h A T h A

2.68

0.0012

0.0007

0.00017

0.0041

Lines in household divided by eligible persons in household

T jh A N jh

1216.69

0.5699

0.50000

0.11111

3.0000

Person selection probability π ijh A

t h A T h A T jh A N jh

1.59

0.0007

0.0003

0.00003

0.0082

Selection weight w ijh A

1 π ijh A

8939582

4113.94

2864.6

121.31

35214.76

Landline only (n = 383)

Selection weight w ijh A

1 π ijh A

1074321

2805.02

1725.43

121.31

29345.64

Both (n = 1788)

Selection weight w ijh A

1 π ijh A

78765261

4394.00

2911.00

169.30

35214.76

Composite weight w ijh λ (where λ = 0.5)

λ w ijh A

3932630

2197.00

1455.50

84.65

17607.38

Mobile Frame (n = 1207)

Adults (n = 1069)

All types (n = 1069)

Interviews divided by universe of phone numbers

t B T B

0.14

0.0001

0.0001

0.00013

0.0001

Mobile phones for person divided by eligible persons (where N i  = 1)

T i B N i

1168.00

1.0947

1.00000

1.00000

5.0000

Person selection probability π i B

t B T B T i B N i

0.15

0.0001

0.00013

0.00013

0.0007

Selection weight w i B

1 π i B

7819874

7328.84

7655.04

1531.01

7655.04

Mobile only (n = 284)

Selection weight w i B

1 π i B

2071325

7319.17

7655.04

1913.76

7655.04

Both (n = 785)

Selection weight w i B

1 π i B

5748549

7332.33

7655.04

1531.01

7655.04

Composite weight w i λ

1 − λ w i B

2874274

3666.17

3827.52

765.50

3827.52

Children (n = 138)

All types (n = 138)

Parents probability of selection

Ï€ p B

0.02

0.0001

0.0001

0.00013

0.0003

Number of parents divided by eligible children in household

N cp N cj

177.57

1.2867

1.00000

0.33333

2.0000

Person selection probability π cp B

Ï€ p B N cp N cj

0.03

0.0002

0.0001

0.00004

0.0005

Selection weight w cp B

1 π cp B

964534

6989.38

7655.04

1913.76

22965.11

Mobile only (n = 26)

Selection weight w cp B

1 π cp B

158842

6109.31

3827.52

1913.76

15310.07

Both (n = 112)

Selection weight w cp B

1 π cp B

805692

7193.68

7655.04

1913.76

22965.11

Composite weight w cp λ

1 − λ w cp B

402846

3596.84

3827.52

956.88

11482.55

Both frames (n = 3378)

Adults and children (n = 3378)

All types (n = 3378)

Selection weight (composite for both users) -see note (a)

w i U

10514239

3112.56

2934.56

84.65

29345.64

Selection weight (composite for both users) scaled back to the number of respondents

w i U *

3378

1.00000

0.8698

0.04779

10.999

  

Post stratification weight (benchmarked to the population by age × sex × health admin) W i U

N dh N ^ dh w i U *

7272086

2152.78

1634.97

13.54

21807

  1. (a) The weight w i U is the selection weight relevant to the segment of the overall sample from which the respondent was selected. For those respondents accessible through both the landline frame and the mobile phone frame it is the composite weight.