Sample size calculator is an important tool used in statistics and research to determine the appropriate sample size required to ensure the accuracy and reliability of study results.

## What is the sample size?

The sample size is defined as the number of observations taken in the experiment for the estimation of the given population. It is not possible to take a survey of the whole population of survey data or large experimental data for statistical analysis.

For easiness, we choose a sample from the whole population and make the report of the survey or research experiment easily on the behavior of the selected sample. The process of selection of sample elements from the population is known as sampling. Roughly say that the number of elements of our selected sample from the population data is known as the sample size.

The sample is the subset of the population because it can be taken from the population to determine the characteristics of the large population data. The sample size is abbreviated as “SS” and mathematically denoted by the symbol “n” or “N”.

## Sample Size Formulas

The sample size cannot be figured out by counting the number of elements of the sample that are good for the experimental results of the population. For the exact number of the selection of the sample that gives better estimation results of the population, we need a level of confidence, margin of error, and percentage of the population.

There are two formulas according to the size of the population and required different components for the measure of sample size for finite population size and infinite population size.

### Sample Size Formula for Finite Population

For this formula, we need the size of the population and sample to find the exact sample size that is better for accurate results of survey/experiment data according to the population. The mathematical formula for the finite population is stated as:

**SS = Sample size = n/ [1+ {(n-1)/ P}]**

In this formula “n” and “P” represent as:

n = size of the sample

P = population size

**Example**

Find the sample size for a finite population when the sample’s elements are 500 and the population size is 45000.

Solution

Step 1: Note the data of the sample element and population size.

n = 500, P = 45000

Step 2: Put the above data in the sample size formula for a finite number and get the required sample size after simplification.

SS = Sample size = n/ [1+ {(n-1)/ P}]

= 500/ [1+ {(500 - 1)/45000}]

= 500/ [1+ {(499)/45000}]

= 500/ [1+ 0.01109]

= (500)/ (1.01109)

SS = 494.5158 ≈ 494

### Sample Size Formula for Infinite Population

If the population size of the data is not known then for the exact sample size we need the z-score value that can be calculated with the confidence level of the data and the use of a z-table, Also, know the value of the population percentage and margin of error of the given population data to find the sample size. The mathematical formula of the infinite population such as:

**SS = Sample size = [z2 × p × (1−p)]/ m2**

Where,

**Example**

Calculate the sample size for an infinite population when the percentage of the “4900” population is “7%” with a confidence level of “99” for this z-score value is “2.58” and the margin of error value is 0.02.

Solution

Step 1: Note the data from the above statement.

p =7% = 0.07, z = 2.58, m = 0.02

Step 2: Put the values in the infinite sample size formula and simplify to get the exact sample size for the experiment.

SS = Sample size = [z2 × p × (1−p)]/ (m2)

= [(2.58)2 × (0.07) × (1−0.07)]/ (0.02)2

= [(6.6564) × (0.07) × (0.93)]/ (0.0004)

= (0.43333)/ (0.0004)

SS = 1083.325 ≈ 1083

**Sample Size Formula for Surveys and polls:**

One commonly used formula for **calculating sample size** in surveys and polls is:

**n = {z**^{2} * p * (1 – p)} / E^{2}

Where:

**n** = sample size**z** = z-score corresponding to the desired level of confidence (e.g., **1.96 for 95% confidence**)**p** = proportion or percentage estimate of the population that is expected to have the characteristic of interest**E** = margin of error as a decimal (e.g., **0.03 for 3%**)

**How to calculate sample size for Surveys and polls?**

Here, provide the example to calculate the sample size of the surveys and polls by using its formula with detailed steps.

**Example**

If a researcher wants to conduct a survey with a **95%** confidence level and a margin of error of **3%**, and estimates that **50%** of the population will have the characteristic of interest, the sample size would be calculated as:

**Solution:**

Confidence level = 95%

Margin of error = 3%

Population = 50%

By putting values in the above formula

**n = (1.96)**^{2} * 0.5 * (1 - 0.5)) / (0.03)^{2}

**n = 1068.44 (rounded up to 1069)**

**Factors Affecting Sample Size:**

Several factors can affect the sample size required for a study. These factors include:

**Population size:** The size of the population from which the sample is drawn affects the sample size. A larger population size requires a larger sample size to achieve a representative sample.**Confidence level: **The level of confidence or the degree of certainty desired by the researcher also affects the sample size. A higher level of confidence requires a larger sample size to reduce the margin of error.**Margin of error: **The margin of error is the range within which the true value of a parameter is expected to fall. A smaller margin of error requires a larger sample size.**Variability:** The variability or the range of values within the population also affects the sample size. A larger variability requires a larger sample size to achieve a representative sample.**Effect size: **The effect size refers to the magnitude of the difference between the groups being studied. A larger effect size requires a smaller sample size to detect a significant difference.

**Importance of Sample Size in Research:**

The **sample size** is an important consideration in research because it affects the accuracy and reliability of the study results.

- A
**larger sample size** generally provides more reliable and accurate results, as it reduces the margin of error and increases the statistical power of the study. - A
**small sample size** may lead to biased or inconclusive results.

For example, a **researcher **wants to conduct a study to determine how common a certain disease is in a population. A small sample size in a disease prevalence study may not be representative of the actual rate in the population, while a larger sample size improves accuracy and representation.

## Frequently Asked Questions (Faq’s)

**What are the 4-ways to calculate the sample size?**

The four ways to calculate the sample size such as:

Power analysis

Convenience sampling

Random sampling

Stratified sampling

**How to calculate sample size?**

The sample size is the number of responses needed to get accurate results in a survey or experimental study. The minimum size needed for precise results is determined by collecting the data. To find its value use the appropriate formulas according to the size of the population for the finite size & infinite size of the population.

**Why is the sample size important?**

It is important to determine the accurate, precise, and favorable results of an experiment for the researchers. It helps the researcher to draw the real effects or relationships between variables.

**What is the Z-score for a 90% confidence interval?**

To find the Z-score value for the given confidence interval value use the z-table, the value of the z-score is different for different percentages of the confidence level. For 90% is equal to 1.64 and for 95% confidence level is equal to 1.96.

**What is the sample size for 250 population?**

To calculate the sample size first select the confidence level of your survey or experiment. If the confidence level is 95% and you require the 5% confidence in your result then the suitable size for the sample is 218 for the accurate results.