Sample size calculator calculates the sample size in order to design statistics data research experiments. It's an online statistics and probability tool requires confidence level, confidence interval, and the population proportion to determine sample size to perform t-test, anova test, etc. The increased samples always yield better results.
It is necessary to follow the next steps:
Sample size, denoted by a positive integer `n`, is one of the key aspects in statistical data analysis. The main objective of the sample size 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 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 a total number of samples required from the population to design the experiments like clinical, material and chemical compound data analysis. It depends on the confidence level and accuracy of experiments.
Margin of error also known as the confidence interval provides a range of values which is likely to contain the population parameter of interest.
An interval estimate of a parameter is an interval within which the value of a parameter of a population has a stated probability of occurring. This estimate may or may not contain the value of the parameter being estimated.
A confidence level of interval estimate of a parameter is the probability that the interval estimate contains the parameter. A confidence interval is the specific interval estimate of the parameter determined by using data obtained from a sample and by using the specific confidence level of the estimate. A $c\%$ confidence interval depends on the sample. A confidence interval may or may not contain the population mean.
A $c\%$ confidence interval contains the population mean for $c\%$ of samples whose elements are chosen randomly and independently. The most common used confidence intervals are: $90\%$, $95\%$, and $99\%$.
The Central Limit Theorem states that when the sample size is large, approximately $95\%$ of the sample, means have $\pm 1.96$ standard errors of the population mean, i.e., $\mu\pm1.96\Big(\frac{\sigma}{\sqrt{n}}\Big).$ If a specific sample mean is selected, there is a $95\%$ probability that it falls within the range of $\mu\pm1.96\Big(\frac{\sigma}{\sqrt{n}}\Big).$
This means that there is a $95\%$ probability that $\mu$ belongs to the interval
Confidence level ($c\%$) | `z`-value |
---|---|
80% | 1.28 |
85% | 1.44 |
90% | 1.65 |
95% | 1.96 |
99% | 2.58 |
To calculate a sample size, $n$, we use the following formula
Sample size gives us the number of participants or observations included in an experiment. The sample size has two important statistical properties:
Practice Problem 1:
Find the minimum sample size required in order to estimate three percentage points, the proportion of voters who intend to vote for a presidential candidate with $95\%$ confidence.
Practice Problem 2:
Find the minimum sample size required to estimate the proportion of adults who have consulted a fortune teller. The confidence is $99\%$ and the margin error is $0.06$. Earlier studies give an estimate of $0.17$ for the population proportion.
The sample size is important in the field of statistical data analysis to increase the precision of estimates. The manual calculations can be done by using the above formulas. However, when it comes to online to verify the results or to perform such calculations, this sample size calculator makes calculations as simple as possible. The sample size formulas solved example problem along with step by step calculation would be very useful for grade school students (K-12 education) to understand how the population proportion, margin of error and confidence level values are being used in such calculations.