**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.

*Where:*

SS= Sample Size for Infinite Population

Ss=Sample size for finite population

Pop=Finite Population (Known target population) (e.g 4,500 as in the example)

Example:

Note:

Note that in order to determine sample size for finite population, Sample Size (SS) for infinite population MUST first be computed.

Anthony M. Wanjohi

Read more about Krejcie and Morgan Table of Determining Sample Size …

**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