Sampling & Simulation Chapter 14

14.1 – Common Sampling Techniques  For researchers to make valid inferences about population characteristics, samples MUST be random  Random sample  Every member of population has an equal chance of being selected  Unbiased sample  Sample is chosen at random from population, and is representative of population  Biased sample  Sample is selected incorrectly by some type of systematic error

Why Use a Sample?  Samples are used to get information about populations for several reasons 1. It saves researcher time and money 2. It enables researcher to get information that he or she might not be able to obtain otherwise 3. It enables researcher to get more detailed information about a particular subject

Random Sampling  Basic requirement  For any sample size, all possible samples of this size have an equal chance of being selected from the population  Incorrect Methods 1. Ask “the person on the street” – many people will be at home or at work and did not have a chance of being selected 2. Ask question by radio or television – only those who feel strongly about issue may respond, others will ignore 3. Ask for mail ( ) responses – only whose who are concerned or have time will respond

Random Sampling, cont.  Preferred way of selected random samples is to use random numbers  Computers and calculators can generate random numbers  Random samples can be selected with or without replacement  Random sampling has one limitation  Using random numbers for extremely large populations is time consuming

Systematic Sampling  Systematic sample  Sample obtained by numbering each element in population and then selecting every third or fifth or tenth, etc., number from population to be included in sample  First number is selected at random  Example 14 – 2  Using population of 50 states, select a systematic sample of 10 states

Systematic Sampling cont.  Advantage of systematic sampling  Ease of selecting sample elements  In many cases, a numbered list of population units may already exist  Disadvantage of systematic sampling  Be careful of how items are arranged on numbered list  (such as male/female selecting every 2 nd item)

Stratified Sampling  Stratified sample  Sample obtained by dividing population into subgroups, called strata, according to various characteristics and then selecting members from each stratum for sample  Example 14 – 3 page 725

Stratified Sampling cont.  Advantage  Ensures representation of all population subgroups that are important to study  Disadvantages  Dividing a large population into representative subgroups requires a great deal of effort  If variables are complex or ambiguous (beliefs, attitudes, etc.) then it is difficult to separate individuals into subgroups according to these variables

Cluster Sampling  Cluster sample  Sample obtained by selecting a preexisting or natural group, called a cluster, and using members in cluster for sample  Advantages  Reduce costs  Simple fieldwork  Convenient  Disadvantage  Elements in cluster may not have same variations in characteristics selected individually from population

Other Types of Sampling Techniques  Sequence sampling  Used in quality control, successive units taken from production lines to ensure products meet certain standards set by company  Double sampling  Large population is given questionnaire to determine who meets qualifications  Sample is selected from those who meet qualifications of survey  Multistage sampling  Researcher uses a combination of sampling methods

Conducting a Sample Survey  Steps for conducting a sample survey 1. Decide what information is needed 2. Determine how data will be collected 3. Select information gathering instrument or design questionnaire if one is not available 4. Set up sampling list, if possible 5. Select best method for obtaining sample 6. Conduct survey and collect data 7. Tabulate data 8. Conduct statistical analysis 9. Report results

14.2 – Surveys & Questionnaire Design  Survey is conducted when a sample of individuals is asked to respond to questions about a particular subject  Two types of surveys 1. Interviewer-administered 2. Self-administered

Interviewer & Self Administered Surveys  Interviewer administered  Require a person to ask questions  Can be conducted face to face or via telephone  Self administered  Can be done by mail ( ) or in group setting such as a classroom

Common Questionnaire Mistakes 1. Asking biased questions 2. Using confusing words 3. Asking double-barreled questions 4. Using double negatives in questions 5. Ordering questions improperly

How bias occurs…  Many people will make responses on basis of what they think person asking questions wants to hear  People will respond differently depending on whether their identity is known  Time and place where a survey is conducted can affect results  Closed-ended vs. open-ended questions

Other survey tips  Use a pilot study to test design and usage of questionnaire  Helps researcher to pretest questionnaire to determine if it meets objectives of the study  Helps researcher to rewrite any questions that may be misleading, ambiguous, etc.  Surveys sent by mail ( )  Cover letter  Clear directions

14.3 – Simulation Techniques and the Monte Carlo Method  Simulation technique  Uses a probability experiment to mimic a real-life situation  Actual situations may be too costly, dangerous, or time-consuming  Simulations are created to be less expensive, less dangerous, and less time- consuming

Computers and Simulation  Mathematical simulation techniques use probability and random numbers to create real-life conditions  Computers’ role in simulation  Generate random numbers  Perform experiments  Tally outcomes  Compute probabilities

Monte Carlo Method  Monte Carlo method  Simulation technique using random number  Used in business and industry  Steps for simulating experiments using Monte Carlo method: 1. List all possible outcomes of experiment 2. Determine probability of each outcome 3. Set up correspondence between outcomes of experiment and random numbers 4. Select random numbers from table and conduct experiment 5. Repeat experiment and tally outcomes 6. Compute any statistics and state conclusions

Examples  Example 14 – 4  Using random numbers, simulate the gender of children born  Example 14 – 5  Using random numbers, simulate the outcomes of a tennis game between Bill and Mike, with the additional condition that Bill is twice as good as Mike.

Remember…  Simulation techniques do not give exact results  Number of times experiment is performed  Closer actual results get closer to theoretical results (law of large numbers)