# Sample Size Calculation Formula

Sampling is part of our day to day life which we use knowingly or unknowingly.

The simple example of a sampling is housewife takes one or two grains of rice from cooking pan and decides whether the rice is cooked or not.

Here one or two grains of rice considered as a sample, entire rice from cooking pan considered as population.

The procedure is known as the sampling procedure and the decision considered as an outcome based on sample observations.

These kinds of an example everywhere in day to day life, like pathologist, take a few drops of blood for a test, the quality controller takes oner or two items and takes a decision, etc…

Most of the cases complete enumeration is not possible because of time and cost.

## What is mean by population in statistics?

population is a group of items, units or subjects which is under reference of study. Population may consist finite or infinite number of units.

### What are different types of populations?

Populations can be classified into four

1) Finite population

If the number of units fixed then it’s called as finite population.

2) Infinite population

If the population consists of infinite number of units then it’s called as infinite population.

3) Real population

If the items are physically present then it’s called as real population

4) Hypothetical population

The population consists of the results of repeated trails is named as hypothetical population. Example like the repeated measure of a coin toss or die etc…

Nonparametric Methods

## When sampling is required?

1) When population is infinite

2) When results required in short time.

3) When the unit is destroyed under investigation

4) When resources limited like, man power, cost, time etc…

5) When population area is big

## What is mean by random sample?

When equal probability of selection is attached to each sampling unit at each draw and the results obtained from random samples have highly desirable properties.

Chi Square Distribution Examples

## How to fix the sample size for an experiment?

The size of a sample depends upon following factors.

1) The purpose for which sample is drawn

2) The heterogeneity of the sampling units in the population.

3) Man power, Equipment’s availability, Time and Money

4) Precision of estimates required is an important factor. Higher precision required large sample size.

#### Which is important Standard Error Or Standard Deviation?

Standard Error is not much influenced by the extreme values present in the population.

What is NULL Hypothesis?

## Sample Size Calculation Formula

The mathematical formula is given below.

n= (Reliability level*Standard Deviation)/Difference to be Detected

Reliability level: -Reliability level usually at 95%,that is 1.96.

Standard Deviation: -Need to calculate based on previous study or trails

Difference to be Detected: – The extent of difference which is desired to be detected.

In another way to calculate, keep degrees of freedom always greater than 12 for a consistent result.

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