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 5 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) 0.05 0.1 0.15 0.2 0.25
0.01 1825 3457 4898 6147 7203
0.02 456 864 1225 1537 1801
0.03 203 384 544 683 800
0.04 114 216 306 384 450
0.05 73 138 196 246 288

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