# Sample Size Calculator & Formula to Design Experiments

## Sample Size Calculation from Population Data

Confidence Interval Calculator
 Result: Sample Size %

sample size calculator - step by step calculation, formula & solved example problems online to calculate the sample size to design statistics data research experiments to have the experiment more generalised & enough power from the input values of confidence level, confidence interval & population data. In the field of probability & statistics, this calculator can be used to determine sample size to perform t-test, anova test etc. The increased samples always yield better results.

## Sample Size & its Formulas

Sample size is one of the key aspects in statistical data analysis and denoted by a positive integer n. The main objective of it is to draw the assumption of a population by using the sample data. It determines how much sample data from the population is required to have the statistical experiments' results more meaningful. The sample size can be easily calculated from the Margin of Error formula. Margin of error is 1.96 times of Standard Error (√((p(1-p)/n) )). Therefore ME = 1.96 x √((p(1-p)/n) ). 1.96 is the z-score for 95% confidence (commonly used), 1.64 is the z-score for 90% confidence and 2.58 is the z-score for 99% confidence.

The sample size calculation comes into effect wherever the experiment is not getting the complete population data for data analysis. It's mainly used in sample standard deviation calculation to determine total number of samples required from the population to design the experiments like clinical, material & chemical compound data analysis. It varies depends on the confidence level & accuracy of experiments. For example, lower confidence level & accuracy requires lower sample size and vice versa.

The below mathematical formula is used in this calculator to determine the sample size of a population according to the values of margin of error, probability & confidence level.

### Solved Example

The below solved example may be useful to understand how the values are being used in the mathematical formulas to determine how much sample size of a population is required to design an experiment produces reliable estimation. z-score gets changed based on the confidence level, so please carefully select the z-score for the expected confidence level.

Example Problem :
The result of experiment shows that 50% of Singapore people under the age of 55 to 60 living their life hassle free. To design a similar survey in United States of America, what is the required sample size to have 95% confidence interval & margin error of 0.06

Solution :
Data given
probability p = 0.5
confidence level = 95%
so the z-score is 1.96 for 95% confidence interval
z = 1.96
Margin of Error (ME) = 0.06

Step by step calculation
formula to find sample size n = (p(1-p) x z2)/ME2)
substitute the values
n = 0.5 x 0.5 x 1.962/0.062
= 266.77
The nearest round number is 267
The required sample size to design the experiment to have 95% confidence interval is 267

Sample size estimation is one of the major aspects in statistics & probability to design the experiments to provide the better assumption. The above formulas, step by step calculation & solved example may be useful to understand how to determine the sample size but for fast computation, when it comes to online this sample size calculator may be useful to perform & verify your such calculations online.

Related Calculators
 Standard Deviation Calculator Population Standard Deviation Calculator Coefficient of Variance Calculator Z Score Calculator Correlation Coefficient Calculator Frequency Standard Deviation Calculator
Related Calculators
 Factorial Calculator Permutation & Combination Calculator Standard Error Calculator Geometric Mean Calculator Linear Regression Calculator Mean Value Calculator