Behavioural Surveillance Surveys - The Wisdom of Whores

Table 5 : Values of Z 1-α
and Z 1-β
α Z 1-α
Z 1-α
/2 β Z 1-β
To measure One-sided Test Two-sided Test
change in one
to measure change
direction
in two directions
0.10 1.282 1.645 0.30 0.53
0.05 1.645 1.960 0.20 0.83
0.025 1.960 2.240 0.10 1.282
0.01 2.326 2.576 0.05 1.645
0.025 1.960
0.01 2.326
Figure 4 : sample size calculations
Example 1
Suppose you wanted to detect an increase of 10 percentage points in the proportion of
commercial sex workers who always used a condom with clients, and be 90 percent confident
that if an increase of this magnitude did occur, you would catch it (i.e., you want 90 percent
power). Furthermore, you want to be 95 percent sure that if you do observe an increase of
10 percentage points or more, you are not seeing something that is the result of chance
fluctuations in the data (i.e., you want your results to be significant at the 95 percent level).
At the time of the first survey, it is thought that about 30 percent of sex workers always use
condoms with clients. Thus, you wish to be able to detect when the proportion of sex workers
who always use condoms exceeds 40 percent. Set P 1
= .30 and P 2
= .40, and use the
one-tailed z-score value for Z 1-α
= 95% (1.645) and the z-score value for Z 1-β
= 90% (1.282).
Inserting these values into the formula, we obtain:
n = 2 [1.645 √ 2(.35)(.65)+1.282 √ (.3)(.7)+(.4)(.6)] 2 /(.4-.3) 2
= 2 [(1.1096+.8600) 2 /.01] = 776 FSW’s in each survey round.
Example 2
Suppose you wanted to detect an decrease of 15 percentage points in the proportion of
male vocational students who had unprotected sex in the past 12 months. Levels of
significance of 95 percent and power of 80 percent are desired. On the basis of earlier survey
data, it is thought that the appropriate “baseline” value on the indicator would be 55 percent.
Thus, we set P 1
= .55 and P 2
= .40, and use z-score values of Z 1-α
=1.645 (95% significance level
for a one-sided test) and Z 1-β
=0.84 (corresponding to 80% power) and obtain:
n = 2 [1.645 √2(.475)(.525)+0.84 √(.4)(.6)+(.55)(.45)] 2 /(.40-.55) 2
= 2 [(1.1617+.5865) 2 /.0225] = 271 vocational students in each survey round.
*Note: Sample Sizes assume a design effect of 2.
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C H A PTER 4 B EHAV I OR A L S U R V EI L L A NC E S U R V EY S