BS1.7: Sample Size Calculations

OBJECTIVES
At the end of this section you should understand the concept of sample size calculations.

DETERMINING SAMPLE SIZE:

In the planning stage of the study you need to have some idea of an appropriate sample size for investigation. If a sample is too small it may be impossible to obtain statistical significance or estimate the population measures with sufficient confidence.

To determine the minimum sample size for estimating a proportion, the following are required:

  1. Estimated population proportion (p).
  2. Confidence level (95%).
  3. Absolute precision required on either side of the proportion (d).
Example:

A researcher wishes to estimate the prevalence of tuberculosis among municipal workers.

How many workers should be included in the sample so that the prevalence may be estimated within 3 percent of the true value with 95% confidence, if it is known that the true rate is unlikely to exceed 15%.

Estimated population proportion (p) = 15%

Absolute precision (d) = 3%

The table below shows that for p = 0.15 and d = 0.03 a sample size of 544 would be needed.

>
Sample size determination for estimating a proportion with 95% confidence interval
  Estimated proportion (p)
Precision (d) 0.1 0.15 0.2 0.25 0.30 0.35 0.40 0.50 0.60
0.01 3457 4898 6147 7203 8067 8740 9220 9604 9220
0.02 864 1225 1537 1801 2017 2185 2305 2401 2305
0.03 384 544 683 800 896 971 1024 1067 1024
0.04 216 306 384 450 504 546 576 600 576
0.05 138 196 246 288 323 350 369 384 369
0.06 96 136 171 200 224 243 256 267 256
0.07 71 100 125 147 165 178 188 196 188
0.08 54 77 96 113 126 137 144 150 144
0.09 43 60 76 89 100 108 114 119 114
0.10 35 49 61 72 81 87 92 96 92

Interactive Examples**

The Examples listed below have been included in order to illustrate the concepts discussed in this Section.
Question 1 Question 5 Question 9
Question 2 Question 6 Question 10  
Question 3 Question 7  
Question 4 Question 8  

**These examples work on Internet Explorer




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General Introduction to Occupational Health: Occupational Hygiene, Epidemiology & Biostatistics by Prof Jonny Myers is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 2.5 South Africa License
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