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Chapter 6

This

**preview**shows half of the first page. to view the full**3 pages of the document.**Chapter 6: Estimation Procedures

6.2 Bias and Efficiency

Estimators can be selected according to two criteria: Bias and efficiency

Bias

o An estimator is unbiased if and only if, the mean of its sampling distribution is equal to the

population value of interest

o Sample proportions are also unbiased

o Knowing that sample means and proportions are unbiased allows us to determine the

probability that they lie within a given distance of the population values we are trying to

estimate

o If an estimator is unbiased, it is probably an accurate estimate of the population parameter

o In less than 15 of the cases, a sample mean will be more than +/- 3 Z's away from the mean

of the sampling distribution by random chance

Efficiency

o The extent to which the sampling distribution is clustered about its mean

o Efficiency is essentially a matter of dispersion

o The smaller the standard deviation of a sampling distribution, the greater the clustering/

higher the efficiency

o The standard deviation of the sampling distribution of sample means (standard error of the

mean) is equal to the population standard deviation divided by the square root of n

o We can improve the efficiency for any estimator by increasing the sample size

o Basically says: much more confidence can be placed in large samples than in small

6.3: Estimation Procedures: Introduction

Interval estimates are much safer than point estimates due to the range of values

1. The first step is to find the probability of error, called alpha

Sociologists mostly use 0.5 alpha which states that we have a 95% confidence interval

Over the long run, the researcher is willing to be wrong 5% of the time

2. Second step is to divide the probability of error equally in the upper and lower tails of the

distribution

For example, if we had a 95% confidence interval we would put 2.5% on the lower tail

and 2.5% on the higher tail

3. Find the Z-Score of alpha 0.5 which is always +/- 1.96 with a confidence interval of 95%

95% of all possible sample outcomes fall within +/- 1.96 z-score units of the

population value

6.4: Interval Estimation Procedures for Sample Means (Large Samples)

Formula 6.1: constructing a confidence interval based on sample means is located on page 169

Formula 6.2: constructing a confidence interval based on sample means where the population

standard deviation is unknown is located on page 170

Examples using this formula on Page 171

6.5: Graphing a Confidence Interval of a Sample Mean

A confidence interval of a sample mean can be depicted using a graph called the error bar

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