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A Simple Poverty Scorecard for the Philippines

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from 0.63 to 0.77 (Figure 10), suggesting that <strong>the</strong> indirect measurement of change withscoring is more precise than direct measurement with full-blown income surveys.To illustrate <strong>the</strong> use of (4) to determine sample size <strong>for</strong> estimating changes inpoverty rates across two independent samples, suppose <strong>the</strong> desired confidence level is 90percent (z = 1.64), <strong>the</strong> desired confidence interval is 2 percentage points (c = 0.02), <strong>the</strong>poverty line is <strong>the</strong> national line, <strong>the</strong> baseline is 2004 and <strong>the</strong> follow-up is 2002, α = 0.63(from Figure 10), and pˆ = 0.313 (from Figure 2). Then <strong>the</strong> baseline sample size is21.64n = 0. 63 ⋅ 2 ⋅⎛ ⎞⎜ ⎟ ⋅ 0.313 ⋅ ( 1 − 0.313)= 1,822, and <strong>the</strong> follow-up sample size is also⎝ 0.02 ⎠1,822.8.4 Accuracy <strong>for</strong> estimated change <strong>for</strong> one sample, scored twiceIn general, <strong>the</strong> direct-measurement sample-size <strong>for</strong>mula <strong>for</strong> this case is: 27n2[ pˆ⋅ ( 1 − pˆ) + pˆ⋅ ( 1 − pˆ) + 2 ⋅ pˆ⋅ pˆ]z=⎛ ⎞⎜ ⎟ ⋅1212 212112 21, (5)⎝ c ⎠where z and c are defined as in (1), ˆp12is <strong>the</strong> expected (be<strong>for</strong>e measurement) share ofall sampled cases that move from below <strong>the</strong> poverty line to above it, and ˆp21is <strong>the</strong>expected share of all sampled cases that move from above <strong>the</strong> line to below it.How can a user set ˆp 12and ˆp 21? Be<strong>for</strong>e measurement, a reasonable assumption isthat <strong>the</strong> change in <strong>the</strong> poverty rate is zero. Then ˆp12= ˆp 21= ˆp *and (5) becomes:27See McNemar (1947) and Johnson (2007). John Pezzullo helped find this <strong>for</strong>mula.38

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