1. Data Collection & Sampling Techniques
Algebra II Honors
Statistics Unit

2. Sampling… What is your population of interest?
To whom do you want to generalize your results?
All doctors
School children
Native Americans
Women aged years
Other
Can you sample the entire population?

3. Sampling… Factors that influence sampling
Sample size
Sampling procedure
Participation
When might you sample the entire population?
When your population is very small
When you have extensive resources
When you don’t expect a very high response

4. Terms
Population refers to the collection of people, animals, locations, items etc. with a characteristic the study wishes to understand.
A data sample is a set of data collected and/or selected from a statistical population. 

5. Objectives
Identify the six basic sample techniques

6. Data Collection
In research, statisticians use data in many different ways.
Data can be used to describe situations.
Data can be collected in a variety of ways, BUT if the sample data is not collected in an appropriate way, the data may be so completely useless that no amount of statistical torturing can salvage them.

7. Basic Methods of Sampling
Simple Random Sampling
Each individual in the population is chosen completely by chance and has an equal chance of being selected
Each individual subject (human or otherwise) has an equal chance of being selected
Examples:
Drawing names from a hat
Random Numbers
Lottery System

8. Basic Methods of Sampling
Simple Random Sampling
Applicable when population is small, homogeneous & readily available
Advantages – easy to calculate
Disadvantages – If sampling a large population, this method could be deemed impractical

9. Basic Methods of Sampling
Systematic Sampling
Members of the sample are chosen according to a rule, such as the nth individual in the population
Select a random starting point and then select every nth subject in the population
Advantage: sample is easy to select and & evenly spread out over the entire population

10. Basic Methods of Sampling
Convenience Sampling
Individuals are selected based on how accessible they are
Examples:
Using family members or students in a classroom
Mall shoppers

11. Basic Methods of Sampling
Convenience Sampling
The researcher using such a sample cannot scientifically make generalizations about the total population from this sample because it would not be representative enough.
For example, if the interviewer was to conduct a survey at a shopping center early in the morning on a given day, the people that he/she could interview would be limited to those given there at that given time, which would not represent the views of other members of society in such an area, if the survey was to be conducted at different times of day and several times per week.
This type of sampling is most useful for pilot testing

12. Basic Methods of Sampling
Stratified Sampling
Divide the population into at least two different groups with common characteristic(s), then draw SOME subjects from each group (group is called strata or stratum). Generally items from each group are selected through a simple random sample.

13. Basic Methods of Sampling
Cluster Sampling
Divide the population into groups (called clusters), randomly select some of the groups, and then collect data from ALL members of the selected groups
Population divided into clusters of homogeneous units, usually based on geographical contiguity.
Used extensively by government and private research organizations
Examples:
Exit Polls

14. Difference between Strata and Clusters
Although strata and clusters are both non-overlapping small groups of the population, they differ in several ways.
All strata are represented in the sample; but only small group of clusters are in the sample.
With stratified sampling, the best survey results occur when elements within strata are internally homogeneous. However, with cluster sampling, the best results occur when elements within clusters are internally heterogeneous.

15. Basic Methods of Sampling
Self Selected Sampling
Individuals volunteer to be part of the sample.
self-selection bias arises in any situation in which individuals select themselves into a group, causing a biased sample

16. Observational and Experimental Studies
Section 1-5

17. Objectives
Explain the difference between an observational and an experimental study

18. Types of Experiments Observational Studies
The researcher merely observes what is happening or what has happened in the past and tries to draw conclusions based on these observations
No interaction with subjects, usually
No modifications on subjects
Occur in natural settings, usually
Can be expensive and time consuming
Example:
Surveys---telephone, mailed questionnaire, personal interview

19. More on Surveys Telephone Mailed Questionnaire Personal Interviews
Less costly than personal interviews
Cover a wider geographic area than telephone or pi
Provides in-depth responses
Subjects are more candid than if face to face
Less expensive than telephone or pi
Interviewers must be trained
Challenge---some subjects do not have phone, will not answer when called, or hang up (refusal to participate)
Subjects remain anonymous
Most costly of three
Tone of voice of interviewer may influence subjects’ responses
Challenge –low number of subjects’ respond, inappropriate answers to questions, subjects have difficulty reading/understanding the questions
Interviewer may be biased in his/her selection of subjects

20. Types of Experiments Experimental Studies
The researcher manipulates one of the variables and tries to determine how the manipulation influences other variables
Interaction with subject occurs, usually
Modifications on subject occurs
May occur in unnatural settings (labs or classrooms)
Example:
Clinical trials of new medications ,treatments, etc.

21. Uses and Misuses of Statistics
Section 1-6

22. Objectives
Explain how statistics can be used and misused

23. Uses of Statistics Describe data Compare two or more data sets
Determine if a relationship exists between variables
Test hypothesis (educated guess)
Make estimates about population characteristics
Predict past or future behavior of data
Use of statistics can be impressive to employers.

24. Sources of Misuse There are two main sources of misuse of statistics:
Evil intent on part of a dishonest researcher
Unintentional errors (stupidity) on part of a researcher who does not know any better
Almost all fields of human endeavor benefit from the application of statistical method; however, the misuses of statistics are just as abundant, if not more so!

25. Misuses of Statistics Samples
Voluntary-response sample (or self-selected sample)
One in which the subjects themselves decide whether to be included---creates built-in bias
Telephone call-in polls (radio)
Mail-in polls
Internet polls
Small Samples
Too few subjects used
Convenience
Not representative since subjects can be easily accessed

26. Misuses of Statistics Graphs
Can be drawn inappropriately leading to false conclusions
Watch the “scales”
Omission of labels or units on the axes
Exaggeration of one-dimensional increase by using a two-dimensional graph

28. Misuses of Statistics Survey Questions
Loaded Questions---unintentional wording to elicit a desired response
Order of Questions
Nonresponse (Refusal)—subject refuses to answer questions
Self-Interest ---Sponsor of the survey could enjoy monetary gains from the results

29. Misuses of Statistics Missing Data (Partial Pictures) Precise Numbers
Detached Statistics ---no comparison is made
Percentages --
Precise Numbers
People believe this implies accuracy
Implied Connections
Correlation and Causality –when we find a statistical association between two variables, we cannot conclude that one of the variables is the cause of (or directly affects) the other variable