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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 π 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 π 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.