Warm up Which type of study is best for the following situations: cross-sectional or longitudinal? a) Determining what percent of high school students plan to attend university within 3 years? b) Determining the effect of a new pesticide on the growth of tomato plants? c) Testing the effectiveness of a new allergy medication? d) Predicting the results of next month’s election?

Collecting Samples Chapter 2.3 – In Search of Good Data Learning goal: outline methods to take random samples

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 through the hallways during MSIP Not representative

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

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

2) Systematic Random Sampling Sample a fixed percent of the population using a random starting point and select every n th individual Sampling interval n = (population size ÷ sample size) Generate a random # between 1 and n Sample this individual and then every nth person after

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 – NOT 20 students from every grade)

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

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

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; life span of batteries and light bulbs; standardized testing

Example: Do students at CPHS want a longer lunch? (sample 60 of 600 students) Simple Random Sampling  Create a numbered, alphabetic list of students, have a computer generate 60 random numbers and interview those students Systematic Random Sampling  Sampling interval n = 600 ÷ 60 = 10  Generate a random number between 1 and 10  Start with that number on the list and interview each 10 th person after that (e.g., 3, 13, 23, 33, …)

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 proportional to the size of the group  If there were 200 grade 12s, 200 ÷ 700 =  70 × = 20 so we would need to interview 20 grade 12s

Example: do students at CPHS want a longer lunch? Cluster Random Sampling  Randomly choose 3 classes of 25 students  Interview every student in each of these rooms Multi Stage Random Sampling  Randomly select 1 period  Randomly choose 6 classes in that period (assume all classes are the same size)  Randomly select 10 students from each class by drawing names from a hat

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

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

Vocabulary Treatment group  the part of the experimental group that receives the treatment (medication, drug) Control group  the part of the experimental group that does not receive the treatment (sugar pill, air inhaler, etc)

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?)

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

Warm Up - Class Activity Describe how to take an appropriately sized 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 NOTE: Point-form is ok

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) give 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: Math courses currently being taken (check all that apply): □ Data Management □ Advanced Functions □ Calculus and Vectors □ Other _________________

Types of Survey Questions Ranking Questions 1. Order a set of responses Ex: Rank the following in order of importance (1 = least important, 3 = most important) __ Work __ Homework __ Sports 2. Rank a set of responses individually Ex: Rank the following on a scale from 1 to 10 where 1 is not important and 10 is very important __ Work __ Homework __ Sports

Types of Survey Questions Rating Questions  ex: How would you rate your teacher? (choose 1) □ Good □ Great □ Incredible □ World-Class

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 (include Other as a catchall) Be sensitive to the respondents

MSIP / Homework (Unit 2) 2.1 p. 81 #4, 5, 6, 8, p. 89 # 1-6 and p. 99 #1, 5, 6, 10, 11 ** 2.4 p. 105 #1, 2, 4, 5, 8, 9, 12 ** 2.5 p. 113 # 1-7, p. 123 # 5, 7, 9

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