How To Find Sample Size Without Standard Deviation

What is sample size?

Sample size is a frequently-used term in statistics and market research, and one that inevitably comes upward whenever you're surveying a large population of respondents. Information technology relates to the fashion inquiry is conducted on large populations.

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So what is sampling, and why does sample size thing?

When you survey a big population of respondents, yous're interested in the entire group, but it'south not realistically possible to get answers or results from absolutely everyone. So y'all take a random sample of individuals which represents the population as a whole.

The size of the sample is very of import for getting authentic, statistically meaning results and running your study successfully.

If your sample is too pocket-sized, y'all may include a disproportionate number of individuals which are outliers and anomalies. These skew the results and you don't go a off-white picture of the whole population.
If the sample is likewise large, the whole written report becomes complex, expensive and fourth dimension-consuming to run, and although the results are more accurate, the benefits don't outweigh the costs.

If you've already worked out your variables you tin get to the right sample size quickly with the online sample size calculator below:

Confidence Level:

Population Size:

Margin of Error:

Ideal Sample Size:

If you desire to kickoff from scratch in determining the right sample size for your market inquiry, let us walk you through the steps.

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Acquire how to determine sample size

To choose the right sample size, you demand to consider a few unlike factors that impact your inquiry, and gain a bones understanding of the statistics involved. You'll and then be able to use a sample size formula to bring everything together and sample confidently, knowing that there is a high probability that your survey is statistically accurate.

The steps that follow are suitable for finding a sample size for continuous data – i.e. information that is counted numerically. It doesn't apply to categorical information – i.due east. put into categories like green, blueish, male, female etc.

Download your sample size guide at present, including Z-score table.

Stage one: Consider your sample size variables

Earlier y'all can calculate a sample size, you need to decide a few things well-nigh the target population and the level of accuracy you need:

one. Population size

How many people are you talking nigh in full? To find this out, yous need to be clear about who does and doesn't fit into your group. For example, if you want to know about dog owners, you'll include everyone who has at some point owned at least ane dog. (Y'all may include or exclude those who owned a canis familiaris in the past, depending on your research goals.) Don't worry if you're unable to calculate the verbal number. It's common to take an unknown number or an estimated range.

two. Margin of mistake (confidence interval)

Errors are inevitable – the question is how much mistake y'all'll allow. The margin of error, AKA confidence interval, is expressed in terms of mean numbers. Y'all can ready how much deviation y'all'll allow between the mean number of your sample and the mean number of your population. If you've ever seen a political poll on the news, you lot've seen a confidence interval and how it's expressed. Information technology volition look something like this: "68% of voters said yes to Proposition Z, with a margin of mistake of +/- five%."

3. Conviction level

This is a carve up step to the similarly-named confidence interval in step ii. It deals with how confident you desire to be that the bodily mean falls within your margin of error. The most common confidence intervals are ninety% confident, 95% confident, and 99% confident.

4. Standard departure

This step asks you lot to estimate how much the responses you receive will vary from each other and from the mean number. A low standard difference means that all the values volition exist amassed around the mean number, whereas a high standard departure means they are spread out across a much wider range with very modest and very large outlying figures. Since you oasis't yet run your survey, a rubber option is a standard deviation of .5 which will help make sure your sample size is large enough.

Phase 2: Summate sample size

Now that yous've got answers for steps ane – 4, yous're ready to calculate the sample size you demand. This tin can exist done using the online sample size calculator higher up or with paper and pencil.

five. Find your Z-score

Next, y'all demand to turn your confidence level into a Z-score. Here are the Z-scores for the most mutual conviction levels:

ninety% – Z Score = 1.645
95% – Z Score = 1.96
99% – Z Score = 2.576

If y'all chose a different conviction level, utilise our Z-score table to observe your score.

six. Use the sample size formula

Plug in your Z-score, standard of deviation, and conviction interval into the sample size figurer or use this sample size formula to piece of work information technology out yourself:

Sample size formula graphic

This equation is for an unknown population size or a very big population size. If your population is smaller and known, just use the sample size computer above, or discover it hither.

What does that expect like in practice?

Here's a worked instance, assuming you lot chose a 95% confidence level, .5 standard deviation, and a margin of fault (confidence interval) of +/- five%.

((ane.96)ii x .five(.v)) / (.05)2

(iii.8416 x .25) / .0025

.9604 / .0025

384.16

385 respondents are needed

Voila! You've but determined your sample size.

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Troubleshooting your sample size results

If the sample size is too big to manage, you lot tin can adjust the results by either

decreasing your confidence level
increasing your margin of mistake

This will increment the run a risk for mistake in your sampling, but it can greatly decrease the number of responses you need.