The Magic Number 30: Why a Sample Size of 30 Is Often Considered Sufficient for Statistical Significance (2024)

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The Magic Number 30: Why a Sample Size of 30 Is Often Considered Sufficient for Statistical Significance? ›

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.

Why is 30 the minimum sample size? The rule of thumb is based on the idea that 30 data points should provide enough information to make a statistically sound conclusion about a population. This is known as the Law of Large Numbers, which states that the results become more accurate as the sample size increases.

Sampling ratio (sample size to population size): Generally speaking, the smaller the population, the larger the sampling ratio needed. For populations under 1,000, a minimum ratio of 30 percent (300 individuals) is advisable to ensure representativeness of the sample.

If the sample size n is greater than 30 (n≥30) it is known as a large sample. For large samples, the sampling distributions of statistics are normal(Z test). A study of the sampling distribution of statistics for a large sample is known as the large sample theory.

The z-test is best used for greater-than-30 samples because, under the central limit theorem, as the number of samples gets larger, the samples are considered to be approximately normally distributed.

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.

For example, when we are comparing the means of two populations, if the sample size is less than 30, then we use the t-test. If the sample size is greater than 30, then we use the z-test.

If the sample size is 30, the studentized sampling distribution approximates the standard normal distribution and assumptions about the population distribution are meaningless since the sampling distribution is considered normal, according to the central limit theorem.

Most statisticians agree that the minimum sample size to get any kind of meaningful result is 100. If your population is less than 100 then you really need to survey all of them.

Based on studies that have been done in academia on this very issue, 30 seems to be an ideal sample size for the most comprehensive view, but studies can have as little as 10 total participants and still yield extremely fruitful, and applicable, results.

Why sample size 30 in social science? ›

A sample size of 30 percent of the target population is considered adequate for a study because it allows for generalization from the sample to the population and helps to avoid sampling errors or biases .

Central Limit Theorem: The central limit theorem states that if sample sizes are greater than or equal to 30, or if the population is normally distributed, then the sampling distribution of sample means is approximately normally distributed with mean equal to the population mean.

The parametric test called t-test is useful for testing those samples whose size is less than 30.

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. Therefore, the sampling distribution will only be normal if the population is normal.

The related law of large numbers holds that the central limit theorem is valid as random samples become large enough, usually defined as an n ≥ 30. In research-related hypothesis testing, the term "statistically significant" is used to describe when an observed difference or association has met a certain threshold.

A z-test is used if the population variance is known, or if the sample size is larger than 30, for an unknown population variance.

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.

Its principle is simply applied. With a sufficiently large sample size, the sample distribution will approximate a normal distribution, and the sample mean will approach the population mean. So if we have a sample size of at least 30, we can begin to analyze the data as if it fit a normal distribution.

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.