What is a good number for a sample size?
A good maximum sample size is usually around 10% of the population, as long as this does not exceed 1000. For example, in a population of 5000, 10% would be 500. In a population of 200,000, 10% would be 20,000.
For populations under 1,000, a minimum ratio of 30 percent (300 individuals) is advisable to ensure representativeness of the sample. For larger populations, such as a population of 10,000, a comparatively small minimum ratio of 10 percent (1,000) of individuals is required to ensure representativeness of the sample.
As a very rough rule of thumb, 200 responses will provide fairly good survey accuracy under most assumptions and parameters of a survey project. 100 responses are probably needed even for marginally acceptable accuracy.
A sample size of 30 is fairly common across statistics. A sample size of 30 often increases the confidence interval of your population data set enough to warrant assertions against your findings.4 The higher your sample size, the more likely the sample will be representative of your population set.
When the sample size increases to 25 [Figure 1d], the distribution is beginning to conform to the normal curve and becomes normally distributed when sample size is 30 [Figure 1e].
A good sample should be a representative subset of the population we are interested in studying, therefore, with each participant having equal chance of being randomly selected into the study.
Many statisticians concur that a sample size of 100 is the minimum you need for meaningful results. If your population is smaller than that, you should aim to survey all of the members. The same source states that the maximum number of respondents should be 10% of your population, but it should not exceed 1000.
In general, the precision of an estimate is related to the square root of the sample size—in other words, to double the precision, the sample size must be quadrupled. As a general rule, sample sizes of 200 to 300 respondents provide an acceptable margin of error and fall before the point of diminishing returns.
If the research has a relational survey design, the sample size should not be less than 30. Causal-comparative and experimental studies require more than 50 samples. In survey research, 100 samples should be identified for each major sub-group in the population and between 20 to 50 samples for each minor sub-group.
Rule of Thumb #1: A larger sample increases the statistical power of the evaluation. Rule of Thumb #2: If the effect size of a program is small, the evaluation needs a larger sample to achieve a given level of power. Rule of Thumb #3: An evaluation of a program with low take-up needs a larger sample.
What is a small sample size?
the size of the sample is small when compared to the size of the population. When the target population is less than approximately 5000, or if the sample size is a significant proportion of the population size, such as 20% or more, then the standard sampling and statistical analysis techniques need to be changed.
(This goes back to excellence in recruiting.) Our general recommendation for in-depth interviews is a sample size of 30, if we're building a study that includes similar segments within the population. A minimum size can be 10 – but again, this assumes the population integrity in recruiting.
In general, a larger sample size will lead to a higher power. With a sample size of 30, we can achieve a reasonable level of power for most statistical tests.
It's that you need at least 30 before you can reasonably expect an analysis based upon the normal distribution (i.e. z test) to be valid. That is it represents a threshold above which the sample size is no longer considered "small".
By convention, we consider a sample size of 30 to be “sufficiently large.” When n < 30, the central limit theorem doesn't apply. The sampling distribution will follow a similar distribution to the population.
The main results should have 95% confidence intervals (CI), and the width of these depend directly on the sample size: large studies produce narrow intervals and, therefore, more precise results. A study of 20 subjects, for example, is likely to be too small for most investigations.
A larger sample size should hypothetically lead to more accurate or representative results, but when it comes to surveying large populations, bigger isn't always better. In fact, trying to collect results from a larger sample size can add costs – without significantly improving your results.
The 10-times rule method
Among the variations of this method, the most commonly seen is based on the rule that the sample size should be greater than 10 times the maximum number of inner or outer model links pointing at any latent variable in the model (Goodhue et al., 2012).
Population Size | Sample Size per Margin of Error | Sample Size per Margin of Error |
---|---|---|
500 | 345 | 80 |
1,000 | 525 | 90 |
3,000 | 810 | 100 |
5,000 | 910 | 100 |
A good sample is representative and random. Representative means that the sample includes only members of the population being studied. Random means that every member of the population being studied has an equal chance to be selected for the sample.
How do you find a good sample?
2. Get a field recorder (or your phone!) Great samples haven't all been locked away in digital files or vinyl records – The great outdoors is teeming with them! Whether you're on a trip into nature, bustling through the city or lazing on the beach, there are cool sounds happening around us all the time.
The logic behind the rule of 30 is based on the Central Limit Theorem (CLT). The CLT assumes that the distribution of sample means approaches (or tends to approach) a normal distribution as the sample size increases.
Too small a sample may prevent the findings from being extrapolated, whereas too large a sample may amplify the detection of differences, emphasizing statistical differences that are not clinically relevant.
Professional researchers typically set a sample size level of about 500 to optimally estimate a single population parameter (e.g., the proportion of likely voters who will vote for a particular candidate). This will construct a 95% confidence interval with a Margin of Error of about ±4.4% (for large populations).
For most surveys with a general population or broad consumer-base audience, 400 responses puts your margin of error at just under 5%. See chart below: A 400 person sample size (n=400) gets your margin of error just under 5%, which is a common target in market research studies.
References
- https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4296634/
- https://www.betterevaluation.org/tools-resources/six-rules-thumb-for-determining-sample-size-statistical-power
- https://www.greenbook.org/marketing-research/What-is-the-ideal-Sample-Size-in-Qualitative-Research-1022244
- https://s4be.cochrane.org/blog/2020/11/18/what-are-sampling-methods-and-how-do-you-choose-the-best-one/
- https://erj.ersjournals.com/content/erj/32/5/1141.full.pdf
- https://wp.stolaf.edu/iea/sample-size/
- https://uregina.ca/~morrisev/Sociology/Sampling%20from%20small%20populations.htm
- https://www.research-advisors.com/tools/SampleSize.htm
- https://people.fish/how-many-people-should-you-survey/
- https://www.linkedin.com/pulse/magic-number-30-why-sample-size-often-considered-sufficient
- https://onlinelibrary.wiley.com/doi/pdf/10.1111/isj.12131
- https://survicate.com/blog/survey-sample-size/
- https://www.alchemer.com/resources/blog/representative-sample/
- https://www.khanacademy.org/test-prep/praxis-math/praxis-math-lessons/gtp--praxis-math--lessons--statistics-and-probability/a/gtp--praxis-math--article--random-sampling--lesson
- https://help.surveymonkey.com/en/surveymonkey/solutions/calculating-respondents/
- https://www.investopedia.com/terms/c/central_limit_theorem.asp
- https://jasemjournal.com/wp-content/uploads/2020/08/Memon-et-al_JASEM_-Editorial_V4_Iss2_June2020.pdf
- https://files.eric.ed.gov/fulltext/EJ919871.pdf
- https://www.researchgate.net/post/What_is_the_rationale_behind_the_magic_number_30_in_statistics
- https://mixedinkey.com/captain-plugins/wiki/sample-sourcing-101-10-top-tips-for-better-digging/
- https://www.troneresearch.com/blog/sample-size-requirements-reliable-study
- https://www.scribbr.com/statistics/central-limit-theorem/
- https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3915399/
- https://greatbrook.com/survey-statistical-confidence-how-many-is-enough/