Basic Sample Statistics and Parameters: Introduction to Estimation

Introduction to Estimation

First, let's discuss the basic concepts of sample statistics and population parameters, and the basic goal of estimation for point and interval estimates. Then we will talk about the degree of freedom, which is defined as the number of independent pieces of information on which a point estimate is based. Finally, we will discuss variance, which depends on the degrees of freedom.

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.

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%.

In an experiment on memory for chess positions, the mean recall for tournament players was 63.8 and the mean for non-players was 33.1. Therefore a point estimate of the difference between population means is 30.7. The 95% confidence interval on the difference between means extends from 19.05 to 42.35. You will see how to compute this kind of interval in another section.

Source: David M. Lane , https://onlinestatbook.com/2/estimation/intro.html
This work is in the Public Domain.

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