# SAMPLE SIZE CALCULATOR

How many people do you need for your survey? Check out this sample size calculator and a simple guide to make it easy.

## Easily Calculate Sample Size with this Tool

Sample Size Calculator Guide

**Provide the population size for the target population that your survey results will be representing**

This is not your sample size but the entire population size you want to represent. Examples would be:

- The state of California (39.51 million)
- Pacific Gas & Electic (PG&E) Customers (16 million)
- Active members of the California Bar Association (190 thousand)

*Enter your target population size.*

**The margin of error represents how precise your results will be**

The margin of error represents the ** difference of proportion from the true proportion** that is acceptable to the researcher.

In the social sciences, 5 percent is an acceptable margin of error. You can change the margin of error depending on your precision needs. If you have no preference, choose a 5 percent default.

*Sample size increases as the margin of error decreases.*

**Select the reliability level**

In statistics, this a measure of the reliability of a result and should not be confused with the *confidence interval*.

A confidence level of 95 percent means there is a probability of at least 95 percent the result accurately represents the population.

*Increasing the confidence level will increase the sample size.*

**This is your estimated sample size based on the inputs provided**

The calculator uses a p-value of 0.50 which is the standard distribution or deviation recommend for most research where you don’t know the previous or actual deviation.

All other inputs are controllable with the calculator. However, 95% confidence levels and 5% margin of error are generally accepted settings for research.

Please refer to * best practices for sample size calculator* later in this article for how to calculate sample size and use sample size estimates.

## How to Calculate Sample Size for Your Survey

If you are searching for a sample size calculator you know the goal of a survey is to acquire conclusions from a representative sample of a target population. But one problem of designing a survey is figuring out just how many participants to include to have a sample that can truly represent the population. Statistics solves this problem, giving survey designers a clear-cut way of calculating the number of participants needed in a survey for the survey to be “valid” in science’s eyes. This method of calculating sample size for your survey is easy enough for even the first-time survey-creator to implement.

### Choose the alpha level and corresponding confidence level

The alpha level is the probability of rejecting the null hypothesis of the survey (usually that there is no difference between the groups you wish to investigate) assuming that the null hypothesis is actually true.

In most sciences, 0.05 is the standard alpha level. However, alpha levels 0.01 and 0.1 are not uncommon. If you do not know which alpha level to choose, set alpha = 0.05. The confidence level will be 100 minus the alpha value. If the alpha is 0.05 the confidence level is 0.95 or 95%.

### Choose the margin of error

The margin of error represents how precise your results will be. Technically, the margin of error represents the *difference of proportion from the true proportion* that is acceptable to the researcher. If you want the *difference of the absolute value* of the range, run a confidence interval test.

The margin of error is the range of a confidence interval. In the social sciences, 0.05 is an acceptable margin of error. You can change the margin of error depending on your precision needs. If you have no preference, choose e = 0.05 as the default.

### Estimate the standard deviation

If you have previous studies researching what you are currently researching than you can use the standard-deviation reported in that study. However, it is often the case that there is no prior research for your topic of interest. In this case, for the sake of being conservative, set the standard deviation, p = 0.5.

Please note if you are going to use a distribution value other than 0.5 you have the replace p^{2} with p(1-p) in the initial sample size calculator equation below.

### Find the z-score for the confidence level

You can find this value by using a t-table, which is available in most introductory statistics books. The bottom two rows include the most frequently used confidence levels, along with their z-scores.

Use the alpha value or the confidence level to look up the corresponding value while assuming the degrees of freedom value in the table is large (this way your estimate will still be conservative).

For example, you will find that for an alpha level of 0.05, the corresponding z-score in the table assuming a large degrees of freedom value is 1.96. So, z = 1.96.

#### Example expressions:

- Sample population = 1,000
- Margin of error = ± 5%
- 95% confidence interval = (𝜇 + 2𝜎)

- 𝜇 – Population parameter mean
- 𝜎 – Standard deviation

### Calculate the initial sample size estimate

Simply calculate N = ( z ^{ 2 }× p ^{ 2 } ) / e ^{ 2 }

### Calculate the final sample size estimate

Divide N by 1 + (N / population), where “population” is the size of the population

## Best Practices for Using the Sample Calculator

Tools are great and like all tools, there are different tools for different jobs. This sample size calculator is best to use them as a guide to get you started sampling. There are many straight forward sampling projects in which the sample calculator will provide excellent guidance to get you started in acquiring your sample or having a discussion with your sample provider.

Here are best practices to consider when using the tool…

### Giving priority to your sample subgroups when calculating for the sample size

A classic example will be calculating a representative sample from the U.S. population size of approximately 330 million people. Using the 95 percent confidence level and considering a 5 percent margin of error; the calculator will yield an appropriate N=278 estimated sample size. However, if you are looking to compare ethnic subgroups, then African Americans represent 15 percent of the U.S. population and would only yield N=42 respondents from a sample of N=278.

Therefore it is not uncommon for a U.S.population representative survey that will be published to have a sample base of N=1000 or even N=2000. These sample bases would allow for statistically valid subgroup sizes for African American, Hispanic, and Asian subgroups without having to weight the data.

### Re-calibrate sample calculation when using sample stratification and clustering

Remember when you are using stratification or clustering methods you are potentially changing the target population size. In many cases, you may be dealing with very large population sizes to start with and after clustering, it is still large. So the impact on your sample size will not be significant.

However if by clustering or stratifying your sample population, the population size changes significantly up or down, this may impact your sample size. In cases where you are clustering, you can calculate sample size at the individual population clusters.

### Do all research projects require a random sample?

In the final analysis, many surveys you conduct may not require the precision that a random sample would provide. You may be collecting any of the following types of data:

- Feedback from customers generated from a customer list or collected from a website offering
- Targeted people who you surveyed in the past during a tracking study where they indicated they had used a certain brand or product
- Members of your club or membership association.

These are all samples where it would be important to obtain as broad a representation of responses as possible certainly. In these circumstances it is the feedback which is a priority and the level of precision for making a decision either may not be present or you have the complete set of respondents (meaning a list of the entire population size) to make a confident decision. Therefore obtaining a truly random sample may not be required.

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- Suite 2010
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