What are 3 factors that determine sample size

Sample size is a frequently-used term in statistics and market research, and one that inevitably comes up whenever you’re surveying a large population of respondents. It relates to the way research is conducted on large populations.

Discover how to improve your overall market research tenfold. 

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

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

The size of the sample is very important for getting accurate, statistically significant results and running your study successfully.

• If your sample is too small, you may include a disproportionate number of individuals which are outliers and anomalies. These skew the results and you don’t get a fair picture of the whole population.
• If the sample is too big, the whole study becomes complex, expensive and time-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 can get to the right sample size quickly with the online sample size calculator below:

Confidence Level:
90%95%99%

Margin of Error:
1%2%3%4%5%6%7%8%9%10%

If you want to start from scratch in determining the right sample size for your market research, let us walk you through the steps.

Free eBook: The ultimate guide to conducting market research

Learn how to determine sample size

To choose the correct sample size, you need to consider a few different factors that affect your research, and gain a basic understanding of the statistics involved. You’ll 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. data that is counted numerically. It doesn’t apply to categorical data – i.e. put into categories like green, blue, male, female etc.

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

Stage 1: Consider your sample size variables

Before you can calculate a sample size, you need to determine a few things about the target population and the level of accuracy you need:

1. Population size

How many people are you talking about in total? To find this out, you 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 one dog. (You may include or exclude those who owned a dog in the past, depending on your research goals.) Don’t worry if you’re unable to calculate the exact number. It’s common to have an unknown number or an estimated range.

2. Margin of error (confidence interval)

Errors are inevitable – the question is how much error you’ll allow. The margin of error, AKA confidence interval, is expressed in terms of mean numbers. You can set how much difference you’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’ve seen a confidence interval and how it’s expressed. It will look something like this: “68% of voters said yes to Proposition Z, with a margin of error of +/- 5%.”

3. Confidence level

This is a separate step to the similarly-named confidence interval in step 2. It deals with how confident you want to be that the actual mean falls within your margin of error. The most common confidence intervals are 90% confident, 95% confident, and 99% confident.

4. Standard deviation

This step asks you to estimate how much the responses you receive will vary from each other and from the mean number. A low standard deviation means that all the values will be clustered around the mean number, whereas a high standard deviation means they are spread out across a much wider range with very small and very large outlying figures. Since you haven’t yet run your survey, a safe choice is a standard deviation of .5 which will help make sure your sample size is large enough.

Stage 2: Calculate sample size

Now that you’ve got answers for steps 1 – 4, you’re ready to calculate the sample size you need. This can be done using the online sample size calculator above or with paper and pencil.

5. Find your Z-score

Next, you need to turn your confidence level into a Z-score. Here are the Z-scores for the most common confidence levels:

• 90% – Z Score = 1.645
• 95% – Z Score = 1.96
• 99% – Z Score = 2.576

If you chose a different confidence level, use our Z-score table to find your score.

6. Use the sample size formula

Plug in your Z-score, standard of deviation, and confidence interval into the sample size calculator or use this sample size formula to work it out yourself:

This equation is for an unknown population size or a very large population size. If your population is smaller and known, just use the sample size calculator above, or find it here.

What does that look like in practice?

Here’s a worked example, assuming you chose a 95% confidence level, .5 standard deviation, and a margin of error (confidence interval) of +/- 5%.

((1.96)2 x .5(.5)) / (.05)2

(3.8416 x .25) / .0025

.9604 / .0025

384.16

385 respondents are needed

Voila! You’ve just determined your sample size.

Free eBook: The ultimate guide to conducting market research

Troubleshooting your sample size results

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

• decreasing your confidence level
• increasing your margin of error

This will increase the chance for error in your sampling, but it can greatly decrease the number of responses you need.

This chapter answers parts from Section A(d) of the Primary Syllabus, "Describe bias, types of error, confounding factors and sample size calculations, and the factors that influence them )".  This topic was examined in Question 2 (p.2) from the first paper of 2009.  It is expanded upon in the Required Reading chapter for the Part II exam ("Study power, population and sample size").

In summary, calculation of sample size involves the following factors:

• Alpha value: the level of significance (normally 0.05); i.e. the level of probability you accept as "real", i.e. not due to chance.
• Beta-value: the power (normally 0.2), i.e. the percentage chance of detecting a treatment effect if there actually is one. 
• The statistical test you plan to use
• The variance of the population (the greater the variance, the larger the sample size)
• The effect size (the smaller the effect size, the larger the required sample)
• The control group outcome rate: How many of the control group are expected to develop the treatment effect.
• Study design, i.e. is it an RCT? In randomised controlled trials, there is an additional benefit to randomisation which develops above a certain sample size (N=200).

How many patients does my trial need?

That depends on several factors.

The magnitude of the treatment effect: The larger the effect, the smaller the required sample size. For a truly tiny treatment effect, one would require truly massive numbers.

The control group outcome rate: How many of the control group are expected to develop the treatment effect.

The agreed-upon significance level (alpha): The level of probability you accept as "real", i.e. not due to chance. The greater your demands for significance, the larger the number of patients needs to be enrolled.

The power (beta): the percentage chance of detecting a treatment effect if there actually is one. This is something you decide upon before commencing the trial; the higher the power value, the more patients you will need. Typically, beta is 0.8, so there is a 20% chance (1-beta) of commiting a Type 2 error , or a "false negative".

Obviously, if your trial has too few patients, you are more likely to commit a Type 2 error. The negative results of this trial will force you to discard a treatment which does actually have a beneficial effect, an effect which you and your tiny useless trial have failed to reveal.

The concept of statistical efficiency demands that the randomised controlled trial achieve its goal (discriminating the treatment effect) with the smallest possible number of patients. However, there is probably a minimum.

In randomised controlled trials, there is an additional benefit to randomisation which develops above a certain sample size (N=200). This is the benefit of randomization, which ensures an approximately equal distribution of unknown confounding factors (such as weird genetic variations and other such unpredictable things). In trials smaller than N=200, this effect of randomisation can no longer be relied upon- one simply cannot guarantee that one group is sufficiently similar to the other group in its incidence of unpredictable features.