Smaller random samples give more accurate results than larger ones.

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BlackTom AI · Accepted Answer

The claim presented asserts that smaller random samples yield more accurate results than larger ones. This is generally not true in statistics.

Consider what we mean by accuracy in this context: accuracy often relates to how well a sample statistic estimates a population parameter, which is affected by sampling error. Sampling error tends to decrease as sample size increases, because larger samples tend to average out random fluctuations, leading to estimates that more closely reflect the true population value. This principle is formalized in the law of large numbers and is a foundational idea behind confidence intervals and hypothesis testing.

A smaller sample is typically more prone to sampling error because it captures less of the population’s variability and may be more influenced by outliers or unusual observations. Consequently, the estimate from a small sample is often less reliable and less precise than that from a larger sample.

There are scenarios where a smaller sample might be used for practical reasons (cost, time, feasibility), but stating that it gives more accurate results is misleading. In those cases, one might compensate with techniques like stratified sampling, pooling data, or increasing measurement precision, but these do not make small samples inherently more accurate.

In summary, the accuracy of sample estimates generally improves with larger sample sizes, reducing sampling error and increasing representativeness of the population.

STAT 1450.02 SP2025 (28132) Checkpoint 8.4 & 8.5

Smaller random samples give more accurate results than larger ones.

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