# Sample Size Calculator for Survey Researchers

### Sample Size Calculator

### Calculator Guide

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? Learn more about the margin of error here.

**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 how many participants to include in the sample to have a group of people representing the population. Statistics solves this problem, giving survey designers a clear-cut way of calculating the minimum number of subjects 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 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 if the sample size relative to the population size is within an acceptable parameter. For example, you may want to increase the number of people in your sample size for anything above five percent.

### Estimate the standard deviation

It’s best to use standard-deviations data from previous or similar studies for your current. However, 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 deviations, p = 0.5.

Please note that if you plan to use a distribution value other than 0.5, you have to 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 any t-table, which will be 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, at the 95 confidence level (expressed as a percentage), you will find for an alpha level of 0.05, the corresponding z-score in the table assuming a large degree of freedom value is 1.96. So, z value = 1.96.

We have included a simplified z-score lookup table with the most common survey research confidence intervals used below:

### 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

This sample size calculator is best to use as a guide to get you started sampling. The tool will provide excellent guidance to get you started in scoping your sample needs or discussing with a market research panel provider.

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

### Sample size calculation with population subgroups and quotas

There will be times when you need to compare subgroups in your target population. However, due to the natural fallout size of the subgroups, they may be too small to yield a statistically reliable base size.

In these cases, you may end up with segments of your sample population that will be either under or over-represented. When this occurs, you have the option to use data weighting measures, or you will need to override the sample size calculator estimate and oversample.

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 and would not yield statistically significant findings.

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

An appropriate sample size greater than N=1000 would allow for subgroup sizes that could yield statistically significant findings for the African American, Hispanic, and Asian subgroups without weighting the data.

### Estimating sample size when using stratification and cluster sampling

Remember, you are potentially changing the target population size when 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 significant. So the impact on your sample size will not be substantial.

However, if by clustering or stratifying your sample population, the population size changes significantly up or down, this may impact your sample size.

In such cases, you can calculate the sample size at the individual population clusters or strata cells using the calculator tool.

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

There are many types of surveys you conduct which may not require the precision a random sample provides. It is also true that it may not be 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 good 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 and, when asked about a specific brand or product usage, picked that answer affirmatively.
- Members of your club or membership association.

For any of the above sample frames, it would be necessary, based on feasibility, to obtain as broad a representation of responses as possible. In these circumstances…

- The feedback is a priority
- The level of precision for making a decision may not be present
- 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 perhaps obtaining a truly random sample may not be required.

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