Estimation

Prerequisites
See individual sections

  1. Introduction
  2. Degrees of Freedom
  3. Characteristics of Estimators
  4. Bias and Variability Simulation
  5. Confidence Intervals
    1. Introduction
    2. Confidence Interval for the Mean
    3. t distribution
    4. Confidence Interval Simulation
    5. Confidence Interval for the Difference Between Means
    6. Confidence Interval for Pearson's Correlation
    7. Confidence Interval for a Proportion
  6. Exercises

One of the major applications of statistics is estimating population parameters from sample statistics . For example, a poll may seek to estimate the proportion of adult residents of a city that support a proposition to build a new sports stadium. Out of a random sample of 200 people, 106 say they support the proposition. Thus in the sample, 0.53 of the people supported the proposition. This value of 0.53 is called a point estimate of the population proportion. It is called a point estimate because the estimate consists of a single value or point.

The concept of degrees of freedom and its relationship to estimation is discussed in Section B. "Characteristics of Estimators" discusses two important concepts: bias and precision.

Point estimates are usually supplemented by interval estimates called confidence intervals . Confidence intervals are intervals constructed using a method that contains the population parameter a specified proportion of the time. For example, if the pollster used a method that contains the parameter 95% of the time it is used, he or she would arrive at the following 95% confidence interval: 0.46 < π < 0.60. The pollster would then conclude that somewhere between 0.46 and 0.60 of the population supports the proposal. The media usually reports this type of result by saying that 53% favor the proposition with a margin of error of 7%. The sections on confidence interval show how to compute confidence intervals for a variety of parameters.

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