# Sample Size

Sub Topics
Sample size is the act of determining the number of samples or replicates to include in the  statistical sample.

The important feature of this is to make inferences in the population of the sample.
It is based on the expenses of the data collection and plays a vital role to determine statical power.

## Sample Size Definition

The number of the individuals included in a finite sample is called the sample size.
Sample size is a number of observation used for calculating the estimates of the given population.Sample size should be enough large. Larger sample size increase the chance of significance .

## Sample Size Formula

n = $\left ( \frac{\sigma z}{E} \right )^{2}$Non-Statistical Sampling

Non-Statistical or Non-probability sampling is a sampling procedure, which does not have any probability involved in it.  All the items selected will be purposely selected for some reason.
Important Non-probability Sampling methods are:
(1)    Convenience Sampling
(2)    Quota Sampling
(3)    Judgment sampling
The non-statistical sampling methods are sometimes known as restricted sampling

Based on the method of sampling and some basic factors, we have to select the sample size.

Factors affecting the size of the sample

There are many factors affecting the size of the sample

1. The sample size depends on the budget of the survey.  For a big budget survey we can opt for a bigger sample size
2. It depends on the complexity of the design.  If the design is more complex, we will select a bigger sample
3. Sample size will depend upon the level of precision required
4. It depends upon the method of sampling used
5. It depends on the spread of the data in the population

## Determining Sample Size

A sample size is the plan of selecting the right number of items from the population to constitute the sample.

Sample size determination

It is the method of selecting the appropriate sample from the population.  It suggests how many items are to be included in the sample.

How to determine sample size

There are mainly two different methods of selecting a sample. They are : -
(1)    Simple Random sampling
(2)    Stratified Sampling
(3)    Systematic Sampling
The statistical sampling methods are sometimes known as unrestricted sampling.

## Sample Size Estimation

The determination of sample size for estimating a population mean or population proportion is an important problem to be considered. Selecting the sample size lower than the correct size may sometimes affect the reliability of the sample and selecting the sample size higher than the correct size may require more time and cost. So determination of the sample size is the most important factor for the purpose of the estimation of values of the population parameters.

## Sample Size Calculation

In order to determine the sample size for estimating the population mean, the following factors must be known.

a)    Confidence level (1- $\alpha$) %
b)    Margin of error E
c)    Standard deviation of the population $\sigma$

When we know the above values, the appropriate sample size n is given by
n = $\left ( \frac{\sigma z}{E} \right )^{2}$where z is obtained from the standard normal tables.

## Survey Sample Size

In order to determine the sample size for estimating the population mean, the following factors must be known.

d)    Confidence level (1- $\alpha$) %
e)    Margin of error E
f)    True proportion of success p

When we know the above values, the appropriate sample size n is given by
n = $\left ( \frac{z}{E} \right )^{2}$ p(1-p)where z is obtained from the standard normal tables.
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