 # Relationship : CV, Margin of Error and Sample size

While browsing the journals related to Statistics , I found an article which shows the relationship between coefficient of variation, margin of error and sample size in a simple and self explanatory way. It also provides the algebraic equivalencies to the sample size formula supported by illustrations.
Determining the appropriate sample size is not an easy task.  The researcher must consider how precise the estimates must be and how much time and money are available to collect the required data.  There are three factors which play an important role in determining appropriate sample size, viz.,
i.                     The variability of the population characteristic under consideration;
ii.                   The level of confidence desired in the estimate and
iii.                  The degree of precision desired.

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There are four traditional approaches to determine the sample size.  They are

Judgmental/ arbitrarily
Analysis consideration
The budget
Applying standard error
Comparatively it is easy to find the margin of error for estimating  population proportion rather than for estimating population mean.  The article describes the relationship between the margin of errors, the coefficient of variations and resulting sample sizes to estimate the population mean.  The algebraic equivalent is given as
Sample size ( n) = Z2 * CV2/ (%)2
The observations are
a.       If two variables have the same CV and same percent is applied to determine the margin of errors, then the  sample sizes would be the same for both the variables.
b.      If two variables have different means and different standard deviations but identical CVs and identical percents are applied to determine the margin of errors, the sample size would be the same.
c.       If two variables have different CVs or different percents are applied to determine the margin of errors, the sample size will not necessarily be the same.

Written by

K Mohansundaram