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  1. Introduction
  2. Graphing Distributions
  3. Summarizing Distributions
  4. Describing Bivariate Data
  5. Probability
  6. Research Design
  7. Normal Distribution
  8. Advanced Graphs
  9. Sampling Distributions

  10. Estimation
    1. Contents
      Standard  
    2. Introduction
      Standard         Video
    3. Degrees of Freedom
      Standard         Video
    4. Characteristics of Estimators
      Standard         Video
    5. Bias and Variability Simulation
      Standard
    6. Confidence Intervals
      Standard         Video
    7. Confidence Intervals Intro
      Standard         Video
    8. Confidence Interval for Mean
      Standard         Video
    9. t distribution
      Standard         Video
    10. Confidence Interval Simulation
      Standard
    11. Difference between Means
      Standard         Video
    12. Correlation
      Standard         Video
    13. Proportion
      Standard         Video
    14. Statistical Literacy
      Standard
    15. Exercises
      Standard

  11. Logic of Hypothesis Testing
  12. Tests of Means
  13. Power
  14. Regression
  15. Analysis of Variance
  16. Transformations
  17. Chi Square
  18. Distribution Free Tests
  19. Effect Size
  20. Case Studies
  21. Calculators
  22. Glossary
 

Estimation

Author(s)

David M. Lane

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. Statistical Literacy
  7. Exercises

PDF (A good way to print the chapter.)

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. Section C, "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 intervals show how to compute confidence intervals for a variety of parameters.