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August 14, 2019 As providers of sample, we are often asked what sample size is needed for a study.  The answer to this question is complicated – not only because the statistical formula to calculate sample size is complicated, but also because there are other factors that determine base size – primarily quotas and the level of risk of the study.

(Keep in mind that this is a rough guideline.)

For the true statistical method of calculating sample, you will need to know the following variables:

#### Population Size:

How big is the true population of the group you’re surveying?  Generally in market research, we deal with rather large population sizes and use a constant for this input. When using statistical probability, the same sample size can be used to represent the opinions of 100,000 people or many million.  That’s why you generally see political polls as small as 500 try to predict a presidential election in the United States, which has a population well over 300 million.

#### Confidence Level:

How certain do you want to be that the results are accurate?  Typically, the following confidence levels are utilized, although you can really pick any number:

• 99% = High Risk.  For example, if you are making a billion-dollar investment decision you may want to be extremely confident in the data.
• 95% = Medium-to-High Risk. When you want high confidence, but at a smaller base size.
• 90% = Medium-to-Low Risk. This is rather typical in most consumer research.
• 80% = Low Risk. If you only need to be reasonably confident in the research and your business decision is low risk, this is ideally the lowest confidence level you would ever choose.

For the formula, the confidence level corresponds to a z-score. Here are the z-scores for the above confidence levels:

• 99% = 2.326
• 95% = 1.96
• 90% = 1.645
• 80% = 1.282

The z-score is the number of standard deviations a given proportion is away from the mean.

#### Margin of Error:

A percentage that tells you how much you can expect your survey results to reflect the views of the overall population. The smaller the margin of error, the closer you are to having the exact answer at a given confidence level. The margin of error is often mentioned when discussing presidential polling as the poll is +/- 3%.

Typical margins of error are:

• 2% = High Risk
• 5% = Normal or Low Risk

#### Standard Deviation:

Measures how much variance you expect in the data. We typically use .5 as a constant.

There are a couple of things to watch for when calculating sample size:

• If you want a smaller margin of error, you must have a larger sample size given the same population.
• The higher the sampling confidence level you want to have, the larger your sample size will need to be.

Does having a statistically significant sample size matter?  Generally, the rule of thumb is that the larger the sample size, the more statistically significant it is—meaning there’s less of a chance that your results happened by coincidence.

Necessary Sample Size = (Z-score)² * StdDev*(1-StdDev) / (margin of error)²

#### Here is a quick cheat sheet for sample size (based on some basic assumptions):

Low Risk

• Margin of error:  5%
• Confidence level: 80%
• Recommended sample = 165

Low-to-Mid Risk

• Margin of error:  5%
• Confidence level: 90%
• Recommended sample = 271

Mid-to-High Risk

• Margin of error:  4%
• Confidence level: 95%
• Recommended sample = 600

High Risk

• Margin of error:  2%
• Confidence level: 99%
• Recommended sample = 4,130

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