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Published Sep 14, 2023

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The number 30 is often used as a rule of thumb for a minimum sample size in statistics because it is the point at which the central limit theorem begins to apply. The central limit theorem states that the distribution of sample means will be approximately normal, regardless of the distribution of the population from which the samples are drawn, as long as the sample size is large enough.

This is important because many statistical tests, such as t-tests and ANOVA, rely on the assumption that the sample means are normally distributed. If the sample size is too small, the distribution of sample means may not be normal, and the results of these tests may be unreliable.

While 30 is a good starting point for sample size, it is important to note that the optimal sample size will vary depending on the specific statistical test being used, the desired level of confidence, and the amount of variability in the population. In general, a larger sample size will provide more accurate results, but it may also be more expensive and time-consuming to collect.

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Here are some specific reasons why a sample size of 30 may be considered sufficient for statistical significance:

- The central limit theorem provides a good approximation of the sampling distribution of the mean for sample sizes of 30 or more. This means that we can use the normal distribution to calculate confidence intervals and p-values for our results.
- For most statistical tests, the probability of rejecting the null hypothesis when it is true (Type I error) is controlled at a level of 0.05 or 5%. This means that we are willing to accept a 5% chance of making a Type I error, which means rejecting the null hypothesis when it is actually true. With a sample size of 30, we can achieve this level of control for most statistical tests.
- The power of a statistical test is the probability of rejecting the null hypothesis when it is false (Type II error). Power is affected by a number of factors, including the sample size. 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 is important to note that the 30-sample size rule of thumb is just a general guideline. In some cases, a larger sample size may be needed to achieve the desired level of confidence and power. For example, if the population is highly variable or the statistical test is very sensitive, a larger sample size may be required.

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2 Comments

Michael Bugden

Secondary teacher | Curriculum innovator | Leader of student success by designing and creating engaging learning experiences | Environmental Scientist | Designer | Interested in introducing students to the circle economy

1mo

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Statistically, you need 30 to get a good fit the normal curve; 15 for a rough fit to the normal curve; 6 to be able to show enough difference for a non-parametric Wilcoxon paired t-test, or a Spearman's Rank Correlation; and 2 or more samples, because the mean of two samples is closer the true mean than one is.

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ashwin .D

Senior Consultant at Self Employed

4mo

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In climatology we use 30 year data as a minimum sample.

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