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.

**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.

**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)} / m^{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%**)

**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.

**How to calculate sample size?**

**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)**