# SAMPLE SIZE CALCULATOR

### Knowing how many respondents you need for your online survey can be challenging so here is a sample size calculator and simple guide to make it easy.

## Easily calculate your sample size with this tool

Sample Size Calculator Guide

- The State of California (39.51 million)
- Pacifc Gas & Electic (PG&E) Customers (16 million)
- Active Members of the California Bar Association (190 thousand)

Enter your target population total.

*Increasing the confidence level will increase sample size.*

This is your estimated sample size based on the inputs provided. The calculator uses a p value of .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 use sample size estimates.

## How to Calculate the 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 a 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.

### 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. 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. 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.

### 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 the as a guide to get you started sampling. There are many straight forward sampling projects which the sample calculator will provide excellence 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 Nsize

A classic example will be calculating a representative sample for the U.S. population 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. 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 changes significantly up or down, this may impact your Nsize. The sample size calculator can be used at the cluster population level for example.

### 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 offer
- 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 to make a confident decision. Therefore obtaining a true random sample may not be required.

## Contact OvationMR

We are ready to get to work for you, by providing a project estimate/proposal, our latest Panel Book, ESOMAR28 response, or being your personal sample size calculator or audience advisor on your next online research project.

#### info@ovationmr.com

#### +1.212.653.8750

#### 39 Broadway, Suite 2010, New York, NY 10006 USA

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- Suite 2010
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