# SAMPLE SIZE CALCULATOR

Sample size calculator that’s simple and precise to estimate how many respondents you need to state your survey results with certainty.

### Sample Size Calculator

## 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 (also known as the confidence interval) represents how precise your results will be + or – the population statistic. **

The margin of error represents the ** difference of proportion from the true proportion** that is acceptable to the researcher for a given population statistic.

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.*

Trying to figure out how sample size affects the margin of error? Use our margin of error calculator

**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 minimum sample needed for the survey to be “valid” in science’s eyes.

This method of calculating the required sample size for your survey is easy enough for even the first-time survey-creator or an experienced research expert to estimate probability sampling needs.

### 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 (confidence interval)

The margin of error represents how precise your results will be + or – a given population statistic. Technically, the margin of error represents the *difference in proportion from the true proportion* acceptable to the researcher for the population statistic. If you want the *difference of the absolute value* of the range, run a confidence interval test.

The margin of error also referred to as the confidence interval, is often expressed as a range ± the population parameter σ. 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.

Use our margin of error calculator to check to see if the sample size relative to the population size is within an acceptable parameter. Anything above five percent, you may want to increase your sample size.

### Estimate the standard deviation

It’s best to use standard-deviation data from previous or similar studies for your current. Often it is the case there is no prior research for your topic of interest. In these circumstances, for the sake of being conservative, set the standard deviation, p = 0.5.

Please note, if you are planning 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 value = 1.96.

### T-Table with Z Scores

### 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 total population you are targeting.

## 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 as a guide to get you started sampling. There are many projects where the sample calculator will provide excellent guidance to get you started in scoping your sample needs or having a discussion with a market research panel provider.

Here are some best practices to consider when using this tool…

### Sample size calculation considerations with population subgroups and quotas

A classic example will be calculating a representative sample from the whole population of the United States at a 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.

When you are looking to compare ethnic subgroups:

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 common for a U.S.population representative survey that is intended to be published to have a larger sample size of N=1000 or even N=2000.

An appropriate sample size base of greater than N=1000 would allow for statistically valid subgroup sizes for the African American, Hispanic, and Asian subgroups without weighting the data.

### Re-calibrating sample size calculation when using stratification sampling and cluster sampling

Remember, you are potentially changing the target population size when you are using stratification sampling or cluster sampling methods. 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 the sample size at the individual population clusters.

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

Many surveys you conduct may not require the precision that a random sample will provide, or it is not possible or practical to obtain a random sample.

In such cases, you have the option of using quota sampling methodology, which gives you the ability to approximate the representation of all groups that might otherwise be underrepresented when relying on strictly convenience sampling methods.

Using the sample size calculator in combination with quota sampling is a useful practice if you are collecting any of the following types of data:

- Feedback generated from a customer list or collected from a website offering
- Targeted people surveyed during a past tracking study which indicated usage of a specific brand or product
- Members of your club or membership association.

For any of the above sample frames, it would be important, based on feasibility, to obtain as broad a representation of responses as possible. In these circumstances, the feedback 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 target population) to make a confident decision. Therefore you can either sample the entire population, or obtaining a truly random sample may not be required.

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