l7a sampling

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Chapter 7

Sampling and

Sampling Distributions

David Chow

Oct 2014


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Learning Objectives

In the first part of this chapter, you will learn:

Different sampling methods

How to evaluate survey worthiness


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An Example of Sampling


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Why Sample?

Instead of selecting every item inthe population (ie, doing a census),

A sample is

less costly to select, and

more practical to analyze


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Types of Samples

In a nonprobability sample, items included are chosen

without regard to their probability of occurrence Eg: conveniencesampling

Eg:judgmentsample, you get the opinions of pre-selected

experts in the subject matter

Types of

Samples

Nonprobability

Samples

Probability

Samples


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Types of Samples

In aprobability sample, items in the sample are chosen

on the basis of known probabilities.

Probability Samples

Simple Random SystematicStratified

Cluster

each possible sample of size n

has the same probability of

being selected


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Simple Random Sampling

Every individual or item from the frame has an equalchance of being selected

Selection may be with or without replacement Samples obtained from table of random numbers or

computer random number generators.

Excel command:

=RAND(), OR=RANDBETWEEN(lower l imi t, upper limit)


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Systematic Sampling

Decide on sample size: n

Divide all N individuals into groups of k

individuals: k = N/n

Randomly select one individual from the 1stgroup

Select every kthindividual thereafter

Eg: Suppose you were sampling n = 5 from a population of N = 50

Step 1: Divide the population into n groups, each with k = 50/5 = 10 individuals

Step 2: Randomly select a member from group 1, say individual 3

Step 3: Select every kthindividual thereafter. The sample is {3, 13, 23, 33, 43}


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Stratified Sampling

Divide population into two or more subgroups (calledstrata)

By some common characteristic like age, gender, industry, etc

A simple random sample isselected from each stratum

Samples from subgroups arecombined into one

Eg: Sampling CU students bystratifying across ____

Arome Bakerys mango mousse cakeFigure


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Cluster Sampling

Population is divided into several clusters, each

representative of the population

A cluster is a small-scale version of the population

A simple random sample of clusters is selected

Eg: Election exit polls, where certain election districts are

selected and sampled

Eg: How to divide CU students into cluster?


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Comparing Sampling Methods

1. Simple random sample and systematic sample

Simple to use

May not be a good representation of the population

2. Stratified sample

Ensures representation of individuals across the entire

population

3. Cluster sample

More cost effective, but less efficient (i.e., a ____ sample

needed for the same level of precision).


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Evaluating Survey Worthiness

Any bias

Sometimes, we want to know who conducts the survey

Sample size? Four common errors

1. Coverage error, or selection bias

2. Non-response error

3. Measurement error

4. Sampling error


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Types of Survey Errors1. Coverage error or selection bias

Exists if some groups are excluded from the frame and have no chanceof being selected.

2. Non-response error

People who do not respond may be different from those who do respond.

3. Measurement error

Due to weaknesses in question design, respondent error, andinterviewers impact on the respondent.

4.Sampling error Variation from sample to sample, cannot be fully eliminated.

Which of these errors are (a) inevitable, (b) fatal?

Remember the saying:Garbage in, ____ !


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Eg: A Poll on Occupy CentralBy the largest political party, the pro-Beijing Democratic

Alliance for the Betterment and Progress of Hong Kong

Potential Problems

Sampling: 70% of the 1,097

respondents are aged 50+

Loaded Question: Are you worried

that Central will be paralyzed & HK

will suffer severe economic loss?

The poll did catch considerable attention from the media, though:

70pc frown on Occupy Central: DAB poll (SCMP, 2013-04-10)

Most HK residents oppose 'Occupy Central (China Daily Asia, 2013-04-08)

DAB says majority against Occupy Central plan (Standard, 2013-04-09)

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