Chapter 6. Select the Client Sample
Chapter 6 in PDF format
The Toolkit contains a Sample Size Calculator to help agencies determine the number of service recipients out of the population of interest that need to complete a survey instrument (see
Table 61). The sample size needs to be large enough to provide sufficient accuracy for results that can be generalized to the entire population. The sample size program is based upon a common method used by statisticians to determine a sample size, yet is easy enough for anyone to use. (Please note: The confidence interval calculation procedure below applies only to percentage estimates and not to means.)
Instructions for Using the Sample Size Calculator
Sample Size Calculator
Confidence Level: An indicator of how often the true percentage of the population would pick an answer lying within the confidence interval. For example, 95 percent confidence level means you can be 95 percent certain. Most researchers use the 95 percent confidence level.
Population Size: The exact number of people in the population that you are studying and from which the sample will be drawn.
Margin of Error: Indicates the desired degree of precision attached to an estimate computed from the survey. It indicates the range into which the estimate would fall if the entire population was surveyed. For example, if a 5 percent margin of error is acceptable to the researcher and the survey estimate of the measured characteristic is 48 percent, then if the entire population were surveyed, one would expect the true value of the characteristic of interest to lie between 43 percent and 53 percent.
Estimated Response Rate: This is an estimate of the percent of the sample that will complete the survey and is usually based on previous experience. For example, 95 percent response rate assumes that 5 percent of the people in the sample will not complete the survey because they refused or couldn’t be located or for other reasons.
Population Proportion:This is an estimate of the percentage of your sample that will pick a particular response. For example, based on previous experience 40 percent will respond “Yes” and 60 percent will answer “No” to the question. It is best to assume the worst case percentage (50 percent) when determining a sample size.
Table 61 illustrates the increase in the variability of the estimates as the population proportion estimate approaches 50 percent. For example, for a sample of size 1,000, for a target characteristic of around 10 percent, the confidence interval (CI) would be the estimate 2.12 percent. For a sample of size 1,000, for a target characteristic of 50 percent, the CI would be the estimate 3.53 percent.
Table 61. Halfwidths of 95 percent confidence intervals (or margins of error) by various sample sizes and estimates of target characteristics (computed for a twostage design with a design effect of 1.30)
Sample size 
Estimates of Target Characteristics 
10 percent 
20 percent 
30 percent 
40 percent 
50 percent 
1,000 
2.12 
2.83 
3.24 
3.46 
3.53 
750 
2.45 
3.26 
3.74 
4.00 
4.08 
500 
3.00 
4.00 
4.58 
4.90 
5.00 
400 
3.35 
4.47 
5.12 
5.47 
5.59 
300 
3.87 
5.16 
5.91 
6.32 
6.45 
250 
4.24 
5.65 
6.48 
6.92 
7.07 
200 
4.74 
6.32 
7.24 
7.74 
7.90 
100 
6.70 
8.94 
10.24 
10.95 
11.17 
Sample Size: This is the number of people out of the entire population of interest that will be selected for the administration of the survey. It is NOT the number of completed surveys to be gathered. Depending on the response rate selected, the sample size estimate includes the number of completed surveys and a percentage of refusals or no contacts.
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