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

Why Sampling? We use sampling because a census is too expensive or time consuming  the challenge is being confident that the sample represents the population accurately If you simply take data from the most convenient place, it will not representative of the population

Random Sampling Representative samples should involve random sampling Random numbers can be generated using a calculator or computer

1) Simple Random Sampling All selections are equally likely, and all combinations of selections are equally likely  It is likely to be representative  If it isn’t representative, it is due to chance Example: put entire population’s names in a hat and draw them

Example: do students at OHA want a longer lunch? (sample 30 of 150 students) Simple Random Sampling  Create a numbered, alphabetic list of students, have a computer generate 30 names and interview those students

2) Systematic Random Sampling you decide to sample a fixed percent of the population using a random starting point and you select every n th individual n in this case is determined by calculating the sampling interval (population size ÷ sample size)  example: you decide to sample 10% of 800 people. n = 800 ÷ 80 = 10, so generate a random number between 1 and 10, start at this number and sample each 10 th person

Example: do students at OHA want a longer lunch? (sample 30 of 150 students) Systematic Random Sampling  sampling interval n = 150/30 = 5  generate a random number between 1 and 5  start with that number on the list and interview each 5 th person after that

3) Stratified Random Sampling the population is divided into groups called strata a simple random sample is taken of each of these with the size of the sample determined by the size of the strata  example: sample OHA students by grade, with samples randomly drawn from each grade (the number drawn is relative to the size of the grade)

Example: do students at OHA 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 30 grade 10’s, 30 ÷ 150 = 0.2  30 × 0.2 = 6 so we would need to interview 6 grade 10s

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 schools from across Ontario, and then surveying all students in those schools

Example: do students at OHA want a longer lunch? Cluster Random Sampling  randomly choose enough study hall periods to sample 30 students  say there are 10 per study hall, we would need 3 study halls, since 3 x 10 = 30  interview every student in each of these study halls

5) Multistage Random Sampling 1. groups are randomly chosen from a population 2. subgroups from these groups are randomly chosen 3. individuals in these subgroups are then randomly chosen to be surveyed  example: to understand student attitudes a school might randomly choose one period, randomly choose grades during that period then randomly choose students from within those grades

Example: do Ontario high school students want a longer lunch? Multi Stage Random Sampling  Randomly select 4 high schools in Ontario  Randomly choose a period from 1-6  randomly choose 2 classes of 25  interview every student in those classes  200 students total

6) Destructive Sampling Sometimes the act of sampling will make those sampled unable to be sampled again  Example: cars used in crash tests cannot be used again for the same purpose  Example: taking a standardized test

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

Class Activity How would we take a sample of the students in this class using the following methods: a) 40% Simple Random Sampling b) 20% Systematic Random Sampling? c) 40% Stratified Random Sampling? d) 50% Cluster Random Sampling?

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

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

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?)

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

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

Types of Survey Questions Information  ex: Circle your Age: Checklist  ex: Courses currently being taken (check all that apply): □ Data Management □ Advanced Functions □ Calculus and Vectors □ Other _________________

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

Questions should… Be simple, relevant, specific, readable Be written without jargon/slang, abbreviations, acronyms, etc. Not lead the respondents Allow for all possible responses on closed Qs Be sensitive to the respondents

MSIP / Homework Classwork:  For each of your research questions, design: An open question An information question A checklist question A ranking question A rating question  Show me your questions before end of class for a project progress check Complete p. 105 #1, 2, 4, 5, 8, 9, 12

References Wikipedia (2004). Online Encyclopedia. Retrieved September 1, 2004 from