Sampling > Sampling Variability
What is sampling variability?
Sampling variability is how much an estimate varies between samples. “Variability” is another name for range; Variability between samples indicates the range of values differs between samples.
Sampling variability is often written in terms of a statistic. The variance (σ2) and standard deviation (σ) are common measures of variability. You might also see reference to the variability of the sample mean (x&772;), which is just another way of saying the sample mean differs from sample to sample. Sampling variability only refers to a statistic (i.e. a number generated from a sample) — never a population.
Variability and Sampling Error
A closely related term (almost a synonym) is sampling error. An error in sampling isn’t a mistake — it’s a measure of how much a value differs from the “true” value. Let’s say the true weight of a population is 150 lbs. You take a sample and find the mean weight for the sample is 151 lbs. The 1 lb difference is an “error.” If you sample again, you might get different mean weights of 148 lbs, or 150.5 lbs, or 153 lbs. The different errors — 1/2 lb, 1 lb, 2 lbs, 3 lbs — are a reflection of the variability between your samples, or sampling variability.
Variability and Sample Sizes
Increasing or decreasing sample sizes leads to changes in the variability of samples. For example, a sample size of 10 people taken from the same population of 1,000 will very likely give you a very different result than a sample size of 100.
There is no “perfect” sample size that will give you accurate estimates for the sample mean, variance and other statistics. Instead, you take your best “guess” — using standardized statistical procedures (see: Finding the sample size). In general, estimates will change from sample to sample and will probably never exactly match the population parameter.
Next: Sampling Distributions.
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