2.1: Anthropometric Indicators Measurement Guide - Linkages Project

Figure A3.2. Values of Z alpha (Z∞) and Z beta (Zß)
alpha ∞
.90
.95
.975
.99
One-tailed test
1.282
1.645
1.960
2.326
Two-tailed test
1.645
1.960
2.240
2.576
beta ß
.80
.90
.95
.975
.999
Z beta Z ß
0.840
1.282
1.645
1.960
2.320
Figure A3.3. Illustrative sample size calculations for indicators expressed as proportions
Example 1
Suppose that it were desired to measure a decrease in the prevalence of underweight (weight-for-age) of 10
percentage points. At the time of the first survey, it is thought that about 40 percent of children between 12
and 36 months were underweight. Thus, P1 = .40 and P2 = .30. Using ‘standard’ parameters of 95 percent level
of significance and 80 percent power, values from Figure A5.2 of alpha (∞) = 1.645 (for a one-tailed test - see
below for further discussion) and beta (ß) = 0.840 are chosen. Inserting these values into the above formula,
we obtain:
n = 2 [(1.645 + 0.840) 2 * ((.3)(.7) + (.6)(.4))] / (.3 - .4) 2
= 2 [(6.175 * 0.45)] / .01
= 2 * [2.77875] / .01 = 2 (277.875) = 555.75
or 556 households per survey round.
Figure A3.4 provides a "lookup" table based upon the above formula to permit sample sizes to be chosen
without having to perform calculations. The table provides sample sizes needed to measure changes/differences
in a given indicator of specified magnitudes P two minus P one (P2 - P1) for different initial levels of the
indicator (P1). The table is for values of alpha (∞) = 0.95 and beta (ß) = 0.80.
Figure A3.4. Sample sizes required for selected combinations of P one (P1) and changes
or comparison-group differences to be detected (for alpha (∞) = .95 and beta (ß) = .80)
Change/difference to be detected (P2 - P1) (P two minus P one)
P one
P1
.05
.10
.15
.20
.25
.30
.10
.15
.20
.25
.30
.35
.40
.45
.50
1,075
1,420
1,176
1,964
2,161
2,310
2,408
2,458
2,458
309
389
457
513
556
587
606
611
606
152
185
213
235
251
262
268
268
262
93
110
124
134
142
147
148
147
142
63
73
81
57
90
92
92
90
87
45
52
56
60
62
62
62
60
56
9.
Note: sample sizes shown assume a design effect of 2.0 and one-tailed tests. In a study of population-based cluster surveys to
determine the design effects Katz (AJCN, 1995 Jan; 61(1):155-60) found the design effect range from 0.44 to 2.59. The use of
D=2.0, therefore is conservative. For values of P one (P1) greater than .50, use the value in the table that differs from .50 by
the same amount. For example, for P one (P1 ) = .60, use the value for P one (P1 ) = .40; for P one (P1 ) = .70, use the value for
P one (P1 ) = .30.
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