Sampling

Neuman and Robson Ch. 7

Qualitative and Quantitative Sampling

Introduction Qualitative vs. Quantitative Sampling

Non-Random Sampling Non-probability Not representative of population

Random sampling Probability Representative of population

The sampling distribution Used in probability sample to allow us to generalize from

sample to population

Non-Probability Samples

Haphazard, convenience or accidental Choose any convenient cases Highly distorted

Quota Establish categories of cases Choose fixed number in each category

Purposive (judgmental) Use expert judgment to pick cases Used for exploratory or field research

Non-Probability (cont.)

Snowball Network or chain referral Use of sociograms to represent

Other types Deviant case

Choose cases for difference from dominant pattern Sequential

Select cases until all possible information obtained

Probability Sampling

Used for quantitative research

Representative of population

Can generalize from sample to population through use of sampling distribution

Logic Behind Probability Sampling

Problem: The populations we wish to study are almost always so large that we are unable to gather information from every case.

Logic (cont.)

Solution: We choose a sample -- a carefully chosen subset of the population – and use information gathered from the cases in the sample to generalize to the population.

Terminology

Statistics are mathematical characteristics of samples.

Parameters are mathematical characteristics of populations.

Statistics are used to estimate parameters.

PARAMETER

STATISTIC

Probability Samples: Must be representative of the population.

Representative: The sample has the same characteristics as the population.

How can we ensure samples are representative? Samples drawn according to the rule of

EPSEM (every case in the population has the same chance of being selected for the sample) are likely to be representative.

The Sampling Distribution

We can use the sampling distribution to calculate our population parameter based on our sample statistic.

The single most important concept in inferential statistics.

Definition: The distribution of a statistic for all possible samples of a given size (N).

The sampling distribution is a theoretical concept.

The Sampling Distribution

Every application of inferential statistics involves 3 different distributions.

Information from the sample is linked to the population via the sampling distribution.

Population

Sampling Distribution

Sample

The Sampling Distribution: Properties

1. Normal in shape.

2. Has a mean equal to the population mean.

μx=μ

3. Has a standard deviation (standard error) equal to the population standard deviation divided by the square root of N.

σx= σ/√N

First Theorem

Tells us the shape of the sampling distribution and defines its mean and standard deviation. If we begin with a trait that is normally distributed

across a population (IQ, height) and take an infinite number of equally sized random samples from that population, the sampling distribution of sample means will be normal.

Central Limit Theorem

For any trait or variable, even those that are not normally distributed in the population, as sample size grows larger, the sampling distribution of sample means will become normal in shape.

Note: The Census is a sample of the entire population

Simple Random Sampling (SRS)

Sampling frame and elements

Selection techniques Table of random numbers

Other types of samples are variants of the simple random sample

Other Probability Samples

Systematic Random Sampling

Stratified Random Sampling

Cluster Sampling

Random Route Sampling

Other Strategies and Issues Related to Random Sampling

Random Digit Dialing (RDD)

Hidden Populations

Sampling Error and Bias

Sample Size