Collecting Samples

Chapter 2.3 – In Search of Good DataMathematics of Data Management (Nelson)MDM 4U

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

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 nth individual

Sampling intervaln = (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

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)

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, standardized testing, life span of batteries and light bulbs

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, …)

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

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

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

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

Control group the part of the experimental group that does not

receive the treatment

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 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

Creating Survey Questions

Chapter 2.4 – In Search of Good DataMathematics 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: 16 17 18+

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 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 (ex: How do you

feel… instead of Do you agree that…) Allow for all possible responses on closed Qs Be sensitive to the respondents

MSIP / Homework

Complete p. 105 #1, 2, 4, 5, 8, 9, 12

References

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