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Collecting Samples

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

Why Sampling?

sampling is done because a census is too expensive or time consuming

the difficulty is being confident that the sample represents the population accurately

convenience sampling occurs when you simply take data from the most convenient place (for example collecting data by walking around the hallways at school)

convenience sampling is not representative

Random Sampling

representative sampling almost always uses random samples

random numbers are described as numbers that occur without pattern

random events are events that are considered to occur by chance

random numbers can be generated using a calculator, computer or random number table

random choice is used as a method of selecting members of a population without introducing bias

Simple Random Sampling

this sample requires that all selections be equally likely and that all combinations of selections be equally likely

the sample is likely to be representative of the population

but if it isn’t, this is due to chance example: put entire population’s names in a

hat and draw them

Systematic Random Sampling you decide to sample a fixed percent of the

population using some random starting point and you select every nth individual

n in this case is determined by calculating the sampling interval (population size divided by sample size)

example: you decide to sample 10% of 800 people. Generate a random number between 1 and 10, start at this number and sample each 10th person (n = 800 / 80 = 10)

Stratified Random Sampling

the population is divided into groups called strata (which could be MSIPs or grades)

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 CPHS students by MSIP, with samples randomly drawn from each MSIP (the number drawn is determined by the size of the MSIP)

Cluster Random Sampling

the population is ordered in terms of groups (like MSIPs or schools)

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 all students in these schools are surveyed

Multistage Random Sampling

groups are randomly chosen from a population and then individuals in these groups are then randomly chosen to be surveyed

example: to understand student attitudes a school might randomly choose MSIPs, and then randomly choose students from within these MSIPs

Destructive Sampling

sometimes the act of sampling will restrict the ability of a surveyor to return the element to the population

example: cars used in crash tests cannot be used again for the same purpose

example: individuals may acquire learning during sampling that would introduce bias if they were used again (like taking a test twice)

Example: do students at CPHS want a longer lunch? Simple Random Sampling

have a computer generate 200 names and interview each

Systematic Random Sampling sampling interval = 800 / 200 = 4 generate a random number from 1-4 start with that number on the list and interview

each 4th person after that

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 not equal, rather it is proportional to the size of the group

if there were 200 grade 10’s we would need to interview 50 of these

20050

800 200

xx

Example: do students at CPHS want a shorter lunch? Cluster Random Sampling

randomly choose enough MSIPs to sample 200 students

say there are 25 per MSIP, we would need 8 MSIPs (8 x 25 = 200)

interview each student in each of these rooms

Example: do students at CPHS want a shorter lunch? Multi Stage Random Sampling

group students by MSIP randomly choose 20 MSIPs randomly choose 10 students from each MSIP interview each of these students

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

however, 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 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?)

Exercises

try page 99 #1,5,6,10,11 for 6b, see example 1 on page 95

Creating Questions

Chapter 2.4 – In Search of Good DataMathematics of Data Management (Nelson)MDM 4U

Surveys

these are commonly used in data collection can be conducted by interview, mail-in,

telephone, internet they are a series of carefully designed

questions bad questions lead to bad data good questions may create good data

Question Styles

Open Questions respondents answer in own words 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 and possibly define the categories of data you will end up studying

Question Styles

Closed Questions questions that require the respondent to select from

pre-defined categories of responses options may be easily analyzed options present may bias the result options may not represent the population and

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 the correct response Gender M F

Checklist ex: Subjects currently being taken (check all that

apply):□ Math

□ Computer Science

□ Music

Types of Survey Questions

Ranking Questions ex: rank the following in order of importance (1 =

most important, 3 = least important) __ Health Care __ Security __ Tax Relief

Rating Questions ex: How would you rate your teacher?

□ 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 Not be open to interpretation Be as brief as possible

Exercises

try page 105 #1, 2 abc, 4, 5, 8, 9, 12

References

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