Sample Size Calculator

Describe the Research

The first step in using this calculator is to describe the research you are conducting.

• Sampling method: This calculator can work with three sampling methods: simple random sampling, stratified sampling, and cluster sampling. With stratified sampling, you have the option to choose proportional stratification. And with cluster sampling, you can choose between one-stage sampling and two-stage sampling.

  Simple random sampling Stratified sampling Cluster sampling
  Proportional stratification

  One-stage cluster sampling
  Two-stage cluster sampling

• Purpose of research: Most surveys are designed to estimate a population parameter. Some surveys also test a hypothesis about that parameter. In the dropdown box below, indicate whether your survey is focused only on estimation or whether it also includes a hypothesis test.

  Estimation only Estimation and hypothesis test

• Sample statistic: Most surveys use a sample statistic to estimate a population parameter. This calculator can work with two types of statistics: a mean score and a proportion. From the dropdown box below, select the sample statistic that you will use.

  Mean score Proportion

• Population parameter: Most surveys use a sample statistic to estimate a population parameter. From the dropbox below, identify the population parameter that you want to estimate.

  Population mean or proportion Population total

Define the Output

In this section, specify the output that you desire from the Sample Size Calculator - your main goal plus any optional analyses.

Main goal

Optional analyses (select all that apply)

Define Statistical Constraints

Please provide the following additional information:

• Significance level: The significance level is the probability of rejecting the null hypothesis when it is, in fact, true. Researchers often use significance levels of 0.01 or 0.05.

Significance level

0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.05 0.055 0.06 0.065 0.07 0.075 0.08 0.085 0.09 0.095 0.10 0.105 0.11 0.115 0.02 0.125 0.13 0.135 0.14 0.145 0.15 0.155 0.60 0.165 0.17 0.175 0.18 0.185 0.19 0.195 0.20 0.205 0.21 0.215 0.22 0.225 0.23 0.235 0.24 0.245 0.25 0.255 0.26 0.265 0.27 0.275 0.28 0.285 0.29 0.295 0.30

• Confidence level: A confidence level refers to the percentage of all possible samples that can be expected to include the true population parameter. For example, suppose all possible samples were selected from the same population, and a confidence interval were computed for each sample. A 95% confidence level implies that 95% of the confidence intervals would include the true population parameter.

Confidence level

99.5% 99% 98.5% 98% 97.5% 97% 96.5% 96% 95.5% 95% 94.5% 94% 93.5% 93% 92.5% 92% 91.5% 91% 90.5% 90% 89.5% 89% 88.5% 88% 87.5% 87% 86.5% 86% 85.5% 85% 84.5% 84% 83.5% 83% 82.5% 82% 81.5% 81% 80.5% 80%

• Margin of error: The margin of error is a measure of sampling error in a survey result. The bigger the margin of error, the less confidence a researcher can place in the survey result. To be meaningful, a confidence level should be reported along with the margin of error. For example, a margin of error of 3 percent based on a 95% confidence level is more impressive than a margin of error of 3 percent based on a 90% confidence level.

  Margin of error

• Null hypothesis: The null hypothesis is the hypothesis that sample observations result purely from chance. For example, if a coin were fair and balanced, we would expect that half the flips would result in Heads and half, in Tails. Thus, the null hypothesis would state that the proportion of coin flips resulting in heads would equal 0.5.

  Null hypothesis The population mean is equal to:

• Alternative hypothesis: The alternative hypothesis, denoted by H_a, describes the region of rejection for a null hypothesis. Typically, an alternative hypothesis states that the true value of a population parameter (μ) is not equal to the value in the null hypothesis, less than the value in the null hypothesis, or greater than the value in the null hypothesis. Which option describes the alternative hypothesis for your study?

  H_a: μ ≠ null value
  H_a: μ < null value
  H_a: μ > null value

• True value: The power of the hypothesis test measures the probability of rejecting the null hypothesis when the true value does not equal the hypothesized value. This calculator will compute power based on the true value that you provide.

  True value
  The true population mean is:

Describe the Population and Sample

Specify population and sample properties. If you don't know the exact values for these inputs, estimate. Base your estimate on the best information that you have - personal experience with similar studies, previous research by others, or even subjective judgment.

In the table below, enter the following information for each for each stratum: population size, sample size, sample mean, sample standard deviation, and sample proportion.

Write Report

To analyze data you've entered and write a report summarizing key findings, click the Calculate button.