**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. On the other hand,
- 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.

**Calculations:**

Sample size calculations involve using statistical formulas to determine the minimum number of participants or observations required to achieve a certain level of statistical power and accuracy in a study or experiment.

**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.

**Examples:**

**Example 1:**

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)