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Chapter 7

Sampling

Book Version 1
By Boundless
Boundless Statistics
Statistics
by Boundless
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Section 1
Populations and Samples
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Populations

In statistics, a population includes all members of a defined group that we are studying for data driven decisions.

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Samples

A sample is a set of data collected and/or selected from a population by a defined procedure.

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Random Sampling

A random sample, also called a probability sample, is taken when each individual has an equal probability of being chosen for the sample.

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Random Assignment of Subjects

Random assignment helps eliminate the differences between the experimental group and the control group.

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Surveys or Experiments?

Surveys and experiments are both statistical techniques used to gather data, but they are used in different types of studies.

Section 2
Populations and Samples
Section 3
Sample Surveys
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The Literary Digest Poll

Incorrect polling techniques used during the 1936 presidential election led to the demise of the popular magazine, The Literary Digest.

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The Year the Polls Elected Dewey

In the 1948 presidential election, the use of quota sampling led the polls to inaccurately predict that Dewey would defeat Truman.

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Using Chance in Survey Work

When conducting a survey, a sample can be chosen by chance or by more methodical methods.

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How Well Do Probability Methods Work?

Even when using probability sampling methods, bias can still occur.

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The Gallup Poll

The Gallup Poll is a public opinion poll that conducts surveys in 140 countries around the world.

Telephone Surveys

Telephone surveys can reach a wide range of people very quickly and very inexpensively.

Chance Error and Bias

Chance error and bias are two different forms of error associated with sampling.

Section 4
Sampling Distributions
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What Is a Sampling Distribution?

The sampling distribution of a statistic is the distribution of the statistic for all possible samples from the same population of a given size.

Properties of Sampling Distributions

Knowledge of the sampling distribution can be very useful in making inferences about the overall population.

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Creating a Sampling Distribution

Learn to create a sampling distribution from a discrete set of data.

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Continuous Sampling Distributions

When we have a truly continuous distribution, it is not only impractical but actually impossible to enumerate all possible outcomes.

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Mean of All Sample Means (μ x)

The mean of the distribution of differences between sample means is equal to the difference between population means.

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Shapes of Sampling Distributions

The overall shape of a sampling distribution is expected to be symmetric and approximately normal.

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Sampling Distributions and the Central Limit Theorem

The central limit theorem for sample means states that as larger samples are drawn, the sample means form their own normal distribution.

Section 5
Errors in Sampling
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Expected Value and Standard Error

Expected value and standard error can provide useful information about the data recorded in an experiment.

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Using the Normal Curve

The normal curve is used to find the probability that a value falls within a certain standard deviation away from the mean.

The Correction Factor

The expected value is a weighted average of all possible values in a data set.

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A Closer Look at the Gallup Poll

The Gallup Poll is an opinion poll that uses probability samples to try to accurately represent the attitudes and beliefs of a population.

Section 6
Sampling Examples
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Measuring Unemployment

Labor force surveys are the most preferred method of measuring unemployment due to their comprehensive results and categories such as race and gender.

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Chance Models in Genetics

Gregor Mendel's work on genetics acted as a proof that application of statistics to inheritance could be highly useful.

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Measures of Variation
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Chapter 7
Sampling
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  • Sample Surveys
  • Sampling Distributions
  • Errors in Sampling
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Probability
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