Sampling & Simulation

1. Sampling & Simulation Chapter 14

2. 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

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

4. 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 • Ask “the person on the street” – many people will be at home or at work and did not have a chance of being selected • Ask question by radio or television – only those who feel strongly about issue may respond, others will ignore • Ask for mail (e-mail) responses – only whose who are concerned or have time will respond

5. 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

6. 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

7. 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 2nd item)

8. 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 – 3page 725

9. 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

10. 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

11. 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

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

13. 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 • Interviewer-administered • Self-administered

14. 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 (e-mail) or in group setting such as a classroom

15. Common Questionnaire Mistakes • Asking biased questions • Using confusing words • Asking double-barreled questions • Using double negatives in questions • Ordering questions improperly

16. 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

17. 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 (e-mail) • Cover letter • Clear directions

18. 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

19. 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

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

21. 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.

22. 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)