Sample Size Calculator
When conducting research, it is important to have a large enough sample size to make accurate statistical inferences. A sample size that is too small can lead to inaccurate conclusions, while a sample size that is too large can be a waste of resources.
Confidence Level (α): | |
Margin of Error (e): | % |
Population Proportion (p): | % |
Population Size (N) (optional) |
Your recommended sample size is: 51 |
Formula
The formula for determining the minimum sample size needed for a study is:
where:
- n = minimum sample size
- Zα/2 = critical value of the standard normal distribution at a given level of significance (such as 1.96 for a 95% confidence level)
- E = margin of error
- p = estimated proportion of the population with the desired characteristic
Example
Suppose a researcher wants to estimate the proportion of people in a certain town who are vegetarian. They want to have a 95% confidence level with a margin of error of 5%.
The researcher can use the sample size calculator to determine the minimum sample size needed for the study:
- Zα/2 = 1.96 (for a 95% confidence level)
- E = 0.05 (for a margin of error of 5%)
- p = unknown
The researcher may estimate the proportion of vegetarians to be 50%, which would yield the maximum sample size required:
Therefore, the researcher needs at least 385 people to participate in the study in order to obtain results with a 95% confidence level and a margin of error of 5%.
Importance of Sample Size
The sample size is a crucial component of research design. It affects the accuracy and reliability of statistical inferences made from the sample to the population. A small sample size may lead to imprecise and unreliable estimates, while a large sample size may result in unnecessary expenses and time.
Thus, the appropriate sample size should be determined based on the research question, the variability of the population, the level of confidence desired, and the margin of error acceptable.
Popular Math Calculators
Here are some of the most popular Math calculators used on iCalculator™ over the past 24 hours.
- Golden Ratio Calculator
- Ratio Division Calculator
- Angle Between Two Lines In A Plane Calculator
- Equivalent Fractions Calculator
- 3x3 Matrix Division Calculator
- Metric Converter
- Decimal Hexadecimal Number Calculator
- Imperial Converter
- Equal Share Verse Ratio Share Calculator
- Ratio Calculator
- Cosecant Of An Angle Calculator
- Acceleration Conversion