Estimation From Samples
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Estimation is the process of determining a likely value for a population parameter (eg, the true population mean or proportion) based on a random sample. In practice, a sample is drawn from the target population, and sample statistics (eg, the sample mean or sample proportion) are used to generate estimates of the unknown parameter. The sample should be representative of the population, ideally with participants selected at random from the population. Because different samples can produce different results, it is necessary to quantify the sampling error or variation that exists among estimates from different samples.
Appropriate classification of the key study variable, also referred to as the outcome or end point, as continuous or discrete is critically important in estimation and in other statistical applications. Once a variable or outcome is correctly classified, other issues such as the number of comparison groups and whether those groups are independent or dependent (ie, matched or paired) affect the determination of the appropriate estimation technique.
Two types of estimates can be produced for any population parameter: point estimates and confidence interval (CI) estimates. A point estimate for a population parameter is a single-valued estimate of that parameter. A CI estimate is a range of values for a population parameter with a level of confidence attached (eg, 95% confidence that the interval contains the unknown parameter). The CI starts with the point estimate and builds in a margin of error that incorporates the confidence level and the sampling variability or standard error. CIs are presented below for different types of variables. Sample size determination and issues related to interpretation and precision follow.
A CI is a range of values that are likely to cover the true population parameter, and the general form is point estimate±margin of error. The point estimate is determined first. For …