**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.

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**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.

Godden, W. (2004). *Sample Size Formulas.* Retrieved from http://williamgodden.com/samplesizeformula.pdf

International Fund for Agricultural Development (IFAD). *Gender and Household Food Security*. Retrieved from http://www.ifad.org/gender/tools/hfs/ anthropometry/ant_3.htm