Collecting Samples

1. Collecting Samples Chapter 2.3 – In Search of Good Data Mathematics of Data Management (Nelson) MDM 4U

2. Why Sampling? • A census can be expensive and time consuming • Must be confident that the sample represents the population • Convenience sampling: take data from the most convenient place • E.g. collecting data by walking around the hallways at school • Not representative

3. Random Sampling • Representative samples involve random sampling • Random events  occur by chance • Random numbers  no pattern • Random numbers can be generated using a calculator, computer or random number table • Random choice selects members of a population without introducing bias

4. 1) Simple Random Sampling • Requires that all selections be equally likely and that all combinations of selections be equally likely • Likely to be representative of the population • If it isn’t, this is due to chance (unintentional) • Example: put entire population’s names in a hat and draw them

5. 2) Systematic Random Sampling • Sample a fixed percent of the population using a random starting point and select every nth individual • Sampling interval n = (population size ÷ sample size) • Example: Sample 10% of 800 people. n = (800 ÷ 80) = 10, generate a random number between 1 and 10, start at this number and sample each 10th person

6. 3) Stratified Random Sampling • The population must be divided into groups called strata (e.g. grades) • A simple random sample is taken of each of these with the size of the sample proportional to the size of the strata • Example: sample CPHS students by grade, with samples randomly drawn from every grade (e.g. 10% of every grade)

7. 4) Cluster Random Sampling • The population is ordered in terms of groups • Groups are randomly chosen for sampling and then ALL members of the chosen groups are surveyed • Example: student attitudes could be measured by randomly choosing classes, and then surveying every student in the selected classes

8. 5) Multistage Random Sampling • Groups are randomly chosen from a population, subgroups from these groups are randomly chosen and then individuals in these subgroups are then randomly chosen to be surveyed • Example: to understand student attitudes the school board might randomly choose schools, randomly choose classes in those schools then randomly choose students in those classes

9. 6) Destructive Sampling • Sometimes the act of sampling will restrict the ability of a surveyor to return the element to the population • Examples: crash testing cars, standardized testing, life span of batteries and light bulbs

10. Example: Do students at CPHS want a longer lunch? (sample 200 of 800 students) • Simple Random Sampling • Create a numbered, alphabetic list of students, have a computer generate 200 random numbers and interview those students • Systematic Random Sampling • Sampling interval n = 800 ÷ 200 = 4 • Generate a random number between 1 and 4 • Start with that number on the list and interview each 4th person after that (4, 8, 12, 16, …)

11. Example: do students at CPHS want a longer lunch? • Stratified Random Sampling • Group students by grade and have a computer generate a random group of names from each grade to interview • The number of students interviewed from each grade is probably not equal, rather it is proportional to the size of the group • If there were 180 grade 10’s, 180 ÷ 800 = 0.225 • 800 × 0.225 = 45 so we would need to interview 45 grade 10s

12. Example: do students at CPHS want a longer lunch? • Cluster Random Sampling • Randomly choose 8 classes of 25 • Interview every student in each of these rooms

13. Example: do CPHS high school students want a longer lunch? • Multi Stage Random Sampling • Randomly select 1 of period (1, 3, 4, 5) • Randomly choose 20 classes of 25 in that period • Interview 10 students from each class

14. Sample Size • The size of the sample will have an effect on the reliability of the results • The larger the better • Factors: • Variability in the population (the more variation, the larger the sample required to capture that variation) • Degree of precision required for the survey • The sampling method chosen

15. Techniques for Experimental Studies • Experimental studies are different from studies where a population is sampled as it exists • In experimental studies some treatment is applied to some part of the population • The effect of the treatment can only be known in comparison to some part of the population that has not received the treatment

16. Vocabulary • Treatment group • the part of the experimental group that receives the treatment • Control group • the part of the experimental group that does not receive the treatment

17. Vocabulary • Placebo • a treatment that has no value given to the control group to reduce bias in the experiment (e.g. sugar pill) • no one knows whether they are receiving the treatment or not (why?) • Double-blind test • in this case, neither the subjects or the researchers doing the testing know who has received the treatment (why?)

18. MSIP / Homework • p. 99 #1, 5, 6, 10, 11 • For 6b, see Ex. 1 on p. 95

19. Warm Up - Class Activity • Describe how to take a 20% sample of the students in this class using the following methods: • a) Simple Random Sampling • b) Systematic Random Sampling? • c) Stratified Random Sampling? • d) Cluster Random Sampling? • 4 students will be randomly selected to conduct a sample

20. Creating Survey Questions Chapter 2.4 – In Search of Good Data Mathematics of Data Management (Nelson) MDM 4U

21. Surveys • A series of carefully designed questions • Commonly used in data collection • Types: interview, questionnaire, mail-in, telephone, WWW, focus group • Bad questions lead to bad data (why?) • Good questions may create good data (why?)

22. Question Styles Open Questions • respondents answer in their own words (written) • gives a wide variety of answers • may be difficult to interpret • offer the possibility of gaining data you did not know existed • sometimes used in preliminary collection of information, to gain a sense of what is going on • can clarify the categories of data you will end up studying

23. Question Styles Closed Questions • questions that require the respondent to select from pre-defined responses • responses can be easily analyzed • the options present may bias the result • options may not represent the population and the researcher may miss what is going on • sometimes used after an initial open ended survey as the researcher has already identified data categories

24. Types of Survey Questions • Information • ex: Circle your Age: 16 17 18+ • Checklist • ex: Math courses currently being taken (check all that apply): □ Data Management □ Advanced Functions □ Calculus and Vectors □ Other _________________

25. Types of Survey Questions • Ranking Questions • ex: rank the following in order of importance (1 = most important, 3 = least important) • __ Work __ Homework __ Sports • Rating Questions • ex: How would you rate your teacher? (choose 1) □ Great □ Fabulous □ Incredible □ Outstanding

26. Questions should… • Be simple, relevant, specific, readable • Be written without jargon/slang, abbreviations, acronyms, etc. • Not lead the respondents (ex: How do you feel… instead of Do you agree that…) • Allow for all possible responses on closed Qs • Be sensitive to the respondents

27. MSIP / Homework • Complete p. 105 #1, 2, 4, 5, 8, 9, 12

28. References • Wikipedia (2004). Online Encyclopedia. Retrieved September 1, 2004 from http://en.wikipedia.org/wiki/Main_Page