# Sample Size Determination

3.4.1  Sample Size

A sample is a smaller (but hopefully representative) collection of units from a population used to determine truths about that population (Field, 2005). Sample size determination involves establishing the number of observations to include in a statistical sample while ensuring representativeness.

Determination of sample size differs depending on the research design. For instance, survey research design requires huge sample size for the purpose of representativeness; in census, everyone in the target population is selected to participate in the study, hence the sample size is equal to the size of the target population; in experimental research design, with treatment and control groups, sample size may differ in each group.

There are different ways of determining a sample size. For the purpose of this article, sample size determination formula for infinite population (‘unknown’) and finite population are briefly discussed.

Sample Size Formula for Infinite Population

The following sample size formula for infinite population is used to arrive at a representative number of respondents (Godden, 2004):

Where:

SS= Sample Size for infinite population (more than 50,000)

Z = Z value (e.g. 1.96 for 95% confidence level)
P = population proportion (expressed as decimal) (assumed to be 0.5 (50%) since this would provide the maximum sample size).

M = Margin of Error at 5% (0.05)

Example:

In a study on the major causes of malnutrition among children in Kibera Slums, the percentage for the prevalence of malnutrition among children in the slum is estimated at 30% (0.3) (this is population proportion). Use of the listed standard values in the formula translates to the following calculation.

Sample Size Formula for Finite Population

If the target population is finite (‘known’), the following formula is used to determine the sample size.

Sample Size Formula for Finite Population

If the target population is finite, the following formula (Krejcie & Morgan, 1970) may be used to determine the sample size.

Where:

S          =   Sample size

X          =   Z value (e.g. 1.96 for 95% confidence level)

N         =   Population Size

P          =   Population proportion (expressed as decimal)                      (assumed to be 0.5 (50%) – this provides the maximum sample size).

d          =   Degree of accuracy (5%), expressed as a proportion  (.05);                                  It is margin of error

Note

To simplify the process of determining the sample size for a finite population, Krejcie & Morgan (1970), came up with a table. Thus, there is no need of using the formula. Instead use Krejcie and Morgan Table of Determining Sample Size for Finite Population.

Anthony M. Wanjohi

References

Field, A. P. (2005). Discovering statistics Using SPSS. London: Sage.