• A number that describes a population is a parameter. A number that describes a sample (is computed from the sample data) is a statistic. The purpose of sampling or experimentation is usually inference: use sample statistics to make statements about unknown population parameters.
• A statistic from a probability sample or a randomized experiment has a sampling distribution that describes how the statistic varies in repeated data productions. The sampling distribution answers the question “What would happen if we repeated the sample or experiment many times?” Formal statistical inference is based on the sampling distributions of statistics.
• A statistic as an estimator of a parameter may suffer from bias or from high variability. Bias means that the center of the sampling distribution is not equal to the true value of the parameter. The variability of the statistic is described by the spread of its sampling distribution. Variability is usually reported by giving a margin of error for conclusions based on sample results.
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• Properly chosen statistics from randomized data production designs have no bias resulting from the way the sample is selected or the way the experimental units are assigned to treatments. We can reduce the variability of the statistic by increasing the size of the sample or the size of the experimental groups.