Sampling

Chapter 5
Sampling

Modified: 2007-02-22

I. Sampling terminology
- A. Sample: A subset of the population.
- B. Population: An entire set of scores.
- C. Target population: exactly who is being studied, the research sample will be drawn from here
- D. Sampling frame: a list of the population, or some way of defining the population
- E. Unit of analysis: the defined unit used in the research (fire stations, fires, arsonists)
- F. Parameter: numbers/measurements related to the entire population
- G. Statistic: numbers/measurements related to the sample studied
- H. Sampling error: an estimate of how well the sample matches the population
- I. Standard error: Standard deviation of the sampling distribution of the mean.
- J. Sample bias: systematic misrepresentation of the population in the sample

K. Sampling fraction: proportion of the
L. Sample designs
- 1. Probability sample designs
- 2. Nonprobability sample designs

II. Sampling designs: every member of population has an equal chance of being in the sample
- A. Probability sample designs: A sample from a population obtained by applying a random sample technique.
  - 1. Simple random sampling
    - a. Defined
    - b. Simple random sampling with replacement
    - c. Simple random sampling without replacement
  - 2. Systematic sampling
    - a. Defined
    - b. Skip interval: to determine sample size
    - c. Periodicity: check for variations in time (e.g., weekends, Fridays, Wednesdays)
  - 3. Stratified random sampling
    - a. Defined
    - b. Proportionate stratified sampling: equal size samples from equal size populations
    - c. Disproportionate stratified sampling: larger samples from smaller populations
  - 4. Cluster and multistage sampling
    - a. Defined: county->township->neighborhood keep taking random samples from each
    - b. Uses: reduces work but still gives a good sample
- Random Samples or Probability Sample:
  - A sample from a population obtained by applying the random sampling technique
    - Represent mathematically-based subsets of a population and are typically used in quantitative research.
  - Simple Random Sampling
    - A procedure is established to create a random sample from a population. For example, pulling 100 names (the sample) from a container of 1000 names (the population).
  - Systematic Random Sampling
    - A random sample is created by choosing the nth person from a large ordered record of a population. The start point of the selection process must be randomly selected. For example, making a sample from a telephone book by selecting every 64th person starting at a random page and location and then running through the entire phone book. Typically, the interval is selected by dividing the size of the population by the size of the sample desired.
  - Stratified Random Sampling
    - When equal or nearly equal numbers of participants are desired along certain categories or dimensions, a stratified random sample is used. The groups, or strata, are selected ahead of time, and then random samples are created by one of the techniques above. For example, if two random samples, one for males and one for females are desired, then two collections of names are created. One collection contains the names of all of the males in the population the other contains the names of all the females in the population. Random samples are then created from each sub-population.
- B. Nonprobability sampling designs: A sample that was not obtained randomly from the population.
Convenience Samples
- A sample that was not obtained randomly from the population.
- Non-Probability Samples
  - Represent samples that do not rely or conform to mathematically-based subsets of a population. Instead, they are created quasi-randomly, conveniently, or in an ad hoc manner. External validity is usually lower when non-probability samples are used. These types of samples are used in both quantitative and qualitative research.
- Convenience, Accidental, or Availability Sampling
  - These multiple terms are used to describe samples created easily. Much social science research comes from these kinds of samples. For example, using participants from college classes is a very common form of this kind of sampling. However, researchers should realize that external validity may not be very high with this kind of sample.
- Community Snowball Sampling
  - Like the fist size snowball that when rolled becomes the large lower body of the snowman, this sample grows. In this technique, a small initial sample is recruited, and then those participants, in turn, recruit additional participants similar to themselves. For example, an initial small group of drug users could be asked to find other drug users like themselves.
- Judgmental or Purposive Sampling
  - In this sampling technique, researchers select participants based on preselected criteria. Typically, judgmental or purposive sampling is used to study groups not well represented in the population. For example, parents who home school their children might be used as a sample.
- Quota Sampling
  - In quota sampling, a sample is created that approximates previously known characteristics of a population. However, the matching procedure is not mathematical nor based on sampling theory. Instead, rough approximations are made of the population's characteristics and then a sample is created to match those them. For example, a researcher might create a sample that roughly matches the age distribution of the population it is drawn from.
III. Sample size
- A. Sampling and nonsampling errors

B. Formula for determining sample size
C. Confidence level and confidence interval: Range of scores that is expected with a specified degree of confidence to capture a parameter.
D. Accuracy and standard error
E. Population size

IV. Sample size for different types of studies
- A. Sampling for experiments
- B. Sample size and statistical power
V. Nonsampling errors
- A. Defined
- B. Causes of nonsampling error
VI. Assessing sample quality

Web Pages

Populations and Samples
Web pages

Populations
Page displays definitions of the word population.
http://www.answers.com/topic/population

Random samples
Page discusses random samples and randomization procedures.
http://www.tufts.edu/~gdallal/rand.htm

Research randomizer
Page creates sets of random numbers based on user specifications.
http://www.randomizer.org/

Convenience samples
Page defines and illustrates convenience samples.
http://www.ryerson.ca/~mjoppe/ResearchProcess/ConvenienceSample.htm

Internal and External Validity
Web page

Internal and external validity
Page explains internal and external validity.
http://www.une.edu.au/WebStat/unit_materials/c2_research_design/validity_internal_external.htm

Design and Statistics
Web page

How do you select an experimental design?
Comprehensive page helps researchers select the appropriate experimental design.
http://www.itl.nist.gov/div898/handbook/pri/section3/pri33.htm

Statistical Methods
Web pages

Descriptive statistics
Page defines and illustrates descriptive statistics.
http://www.socialresearchmethods.net/kb/statdesc.htm

Inferential statistics
Page defines and illustrates inferential statistics.
http://www.socialresearchmethods.net/kb/statinf.htm

Line graphs and scatterplots Page shows how to make simple line graphs and scatterplots.
http://www.ncsu.edu/labwrite/res/gh/gh-linegraph.html

Rice Virtual Lab in Statistics
Site explains and demonstrates descriptive and inferential statistics.
http://onlinestatbook.com/rvls.html

Exploring and Describing Scaled Variables

Web pages

Statistical Primer for Psychology Students
Introduction to statistics covers descriptive, correlational, and inferential statistics.
http://www.mhhe.com/socscience/intro/cafe/common/stat/

Exploratory Data Analysis
Site from National Institute of Standards explains exploratory data analysis in detail.
http://www.itl.nist.gov/div898/handbook/eda/eda.htm

Wikipedia on Outliers
Wikipedia’s page discusses outliers and their computation.
http://en.wikipedia.org/wiki/Outlier

Central Tendency
Presents the mean, median, and mode and suggests when to use each properly.
http://www.quickmba.com/stats/centralten/

Dispersion
Presents the range, average deviation, and standard deviation and suggest when to use each properly.
http://www.quickmba.com/stats/dispersion/

Wikipedia on Standard Deviation
Wikipedia’s page on standard deviation explains concept and gives examples.
http://en.wikipedia.org/wiki/Standard_deviation

Interquartile Range
Short page defines the interquartile range and links to methods of graphing distributions.
http://mathworld.wolfram.com/InterquartileRange.html

Standard Error of the Mean
Gives the formula for calculating the standard error of the mean.
http://davidmlane.com/hyperstat/A103735.html

Confidence Intervals
Interactive Java applet displays 95% and 99% confidence intervals from a population with a mean of 50 and a standard deviation of 10 for 100 samples with sample sizes of 10, 15, or 20.
http://www.ruf.rice.edu/~lane/stat_sim/conf_interval/

Frequency Polygons
Introduces frequency polygons and shows creation and use.
http://cnx.org/content/m10214/latest/

Histogram
Interactive page displays histograms for several user-selectable distributions.
www.shodor.org/interactivate/activities/histogram/

Skewness
Detailed page on skewness defines the concept and displays formulas for calculating skew in a set of distributions.
http://mathworld.wolfram.com/Skewness.html

Boxplots
Explains the creation and interpretation of boxplots.
http://www.netmba.com/statistics/plot/box/

The Link Between Error Bars and Statistical Significance
Brief tutorial explains how to estimate statistical significance graphically when error bars for the standard error of the mean are added to graphs.
http://www.graphpad.com/articles/errorbars.htm

Create A Graph
Site for kids from the National Center for Education Statistics allows users to create bar, line, area, pie, and XY graphs.
http://nces.ed.gov/nceskids/createagraph/

Line Graphs and Scatterplots
Short tutorial covers scatterplots, line graphs, and provides hints on creating them using Excel.
http://www.ncsu.edu/labwrite/res/gh/gh-linegraph.html

Wikipedia on the Normal Curve
Wikipedia’s page on the normal curve details the history, properties, and uses of the normal curve.
http://en.wikipedia.org/wiki/Normal_distribution

Sampling Distribution of the Mean
Tutorial module covers the sampling distribution of the mean and graphically shows how the distribution of a sample means approaches a normal distribution.
http://cnx.org/content/m11131/latest/

Effect Statistics
Tutorial covers effect statistics or ways of measuring differences between means.
http://www.sportsci.org/resource/stats/index.html

Effect Size Calculators
Page calculates Cohen’s d and the effect size correlation using means and standard deviations or for the independent groups t test.
http://web.uccs.edu/lbecker/Psy590/escalc3.htm

Correlation Coefficient Calculation
Page provides example of how to graph and calculate a correlation coefficient.
http://helios.bto.ed.ac.uk/bto/statistics/tress11.html

Web pages

Wikipedia on Confidence Intervals
Wikepedia’s page explains confidence intervals in detail.
http://en.wikipedia.org/wiki/Confidence_interval

A Student’s Guide to Analyzing Data

Web pages

Exploratory Data Analysis
Site summarizes techniques and assumptions of exploratory data analysis.
http://www.itl.nist.gov/div898/handbook/eda/eda.htm

Wikepedia on Exploratory Data Analysis
Wikipedia’s page on exploratory data analysis covers history and software used.
http://en.wikipedia.org/wiki/Exploratory_data_analysis

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Chapter 5 Sampling

Chapter 5
Sampling