Sample Size Determination Using Krejcie and Morgan Table

The ever increasing need for a representative statistical sample in empirical research has created the demand for an effective method of determining sample size. Determination of sample size differs depending on the research design. For instance, survey research design requires huge sample size for the purpose of representation; 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, the sample size may differ in each group.

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

Sample Size Formula for Infinite Population

The following sample size formula for infinite population (more than 50,000) is used to arrive at a representative number of respondents when population estimate is known (Godden, 2004):

sample-size-formular

Where:

n          =   Sample Size for infinite population

Z          =   Z value (e.g. 1.96 for 95% confidence level)
P          =   population proportion (expressed as decimal) (assumed to be 0.5 (50%)
M         =   Margin of Error at 5% (0.05)

Example

The following worked out example uses a population proportion (P) of 30% (0.3) to determine a sample size (n) of an infinite population.

Note

You can use a particular population proportion based on established statistics of the population you are targeting. For instance, you may target 30% (0.3) of a population in particular location of your study (as in the worked out example). You may also opt to use the standard population proportion of 50% (0.5) which is the maximum sample size one can select from a population.

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.

formular-finite-sample-size-kenpro-2014

Where:

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

Table for determining sample size for finite population

To simplify the process of determining the sample size for a finite population, Krejcie & Morgan (1970), came up with a table using sample size formula for finite population.

krejcie-morgan-sample-size-table

Note:

There is no need of using sample size determination formula for ‘known’ population since the table has all the provisions one requires to arrive at the required sample size.  For a population which is equal to or greater than 1,000,000, the required sample size is 384.

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