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Table 1 Example of application of the LQAS methodology

From: Three methods to monitor utilization of healthcare services by the poor

Sample size No. in the sample non-poor Probability of detecting health facilities with 80% poor as adequate Probability of detecting health facilities with 50% poor as inadequate Provider Risk Consumer Risk Total classification error
(n) (d) (a) (b) (1-a) (1-b) (1-a)+(1-b)
8 0 0.17 1 0.83 0 0.83
  1 0.50 0.96 0.50 0.04 0.54
  2 0.79 0.83 0.21 0.17 0.38*
  3 0.94 0.64 0.06 0.36 0.42
12 0 0.07 1.00 0.93 0.00 0.93
  1 0.28 1.00 0.73 0.00 0.73
  2 0.56 0.98 0.46 0.02 0.48
  3 0.80 0.93 0.21 0.07 0.28
  4 0.93 0.81 0.07 0.19 0.27*
  5 0.98 0.61 0.02 0.39 0.41
14 0 0.04 1 0.96 0 0.96
  1 0.20 1 0.80 0 0.80
  2 0.45 0.99 0.55 0.01 0.56
  3 0.70 0.97 0.30 0.03 0.33
  4 0.87 0.91 0.13 0.09 0.22*
  5 0.96 0.79 0.04 0.21 0.25
19 0 0.01 1 0.99 0 0.99
  1 0.08 1 0.92 0 0.92
  2 0.24 1 0.76 0 0.76
  3 0.46 1 0.54 0 0.55
  4 0.67 0.99 0.33 0.01 0.34
  5 0.84 0.97 0.17 0.03 0.20
  6 0.93 0.92 0.07 0.08 0.15*
  7 0.98 0.82 0.02 0.18 0.20
28 5 0.50 1 0.50 0 0.50
  6 0.68 1 0.32 0 0.32
  7 0.81 0.99 0.19 0.01 0.20
  8 0.91 0.98 0.09 0.02 0.11
  9 0.96 0.96 0.04 0.04 0.08*
  10 0.99 0.90 0.01 0.10 0.11
  1. * - Optimal decision rule for a sample size.
  2. Source: Adopted from Valadez 1991, p:73.