# Sample Size Calculation Formula

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

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

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

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

These kinds of an example are everywhere in day-to-day life, like pathologists, taking a few drops of blood for a test, the quality controller taking one or two items and takes a decision, etc…

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

## What is meant by population in statistics?

a population is a group of items, units or subjects which is under the reference of study. The 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 is fixed then it’s called a finite population.

2) Infinite population

If the population consists of an infinite number of units then it’s called an 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 trials and is named a hypothetical population. For example 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 are limited like manpower, cost, time etc…

5) When the population area is big

## What is meant by random sample?

When the 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 the sample is drawn

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

3) Manpower, Equipment 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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