Download 2.3 - 2.4

Collecting Samples
Chapter 2.3 – In Search of Good Data
Mathematics of Data Management (Nelson)
MDM 4U
Why Sampling?
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sampling is done because a census is too
expensive or time consuming
the challenge 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
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representative samples involve random sampling
random events are events that are considered to
occur by chance
random numbers are described as numbers that
occur without pattern
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
1) Simple Random Sampling
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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
2) Systematic Random Sampling
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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 ÷ 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 10th person
3) Stratified Random Sampling
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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 relative to the
size of the MSIP)
4) Cluster Random Sampling
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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 surveying all
students in those
5) Multistage Random Sampling
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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 a
school might randomly choose one period,
randomly choose MSIPs during that period
then randomly choose students from within
those MSIPs
6) Destructive Sampling
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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: taking a standardized test
(individuals may acquire learning during
sampling that would introduce bias if they
were tested again)
Example: do students at CPHS want a
longer lunch? (sample 200 of 800 students)
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Simple Random Sampling
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Create a numbered, alphabetic list of students,
have a computer generate 200 names and
interview those students
Systematic Random Sampling
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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
Example: do students at CPHS want a
longer lunch?
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Stratified Random Sampling
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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
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if there were 180 grade 10’s, 180 ÷ 800 = 0.225
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800 × 0.225 = 45 so we would need to interview 45
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grade 10s
Example: do students at CPHS want a
shorter lunch?
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Cluster Random Sampling
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randomly choose enough MSIPs to sample 200
students
say there are 25 per MSIP, we would need 8
MSIPs, since 8 x 25 = 200
interview every student in each of these rooms
Example: do UCDSB high school students
want a shorter lunch?
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Multi Stage Random Sampling
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Randomly select 4 high schools in the UCDSB
Randomly choose a period from 1-5
randomly choose 2 MSIP classes of 25
interview every student in those MSIPs
200 students total
Sample Size
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the size of the sample will have an effect on
the reliability of the results
the larger the better
factors:
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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
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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
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treatment group
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the part of the experimental group that receives
the treatment
control group
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the part of the experimental group that does not
receive the treatment
Vocabulary
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placebo
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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
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in this case, neither the subjects or the
researchers doing the testing know who has
received the treatment (why?)
Class Activity
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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?
MSIP / Homework
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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
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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
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Information
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ex: Circle your Age: 16 17 18+
Checklist
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ex: Courses currently being taken (check all
that apply):
□ Data Management
□ Advanced Functions
□ Calculus and Vectors
□ Other _________________
Types of Survey Questions
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Ranking Questions
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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
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Questions should…
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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
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Complete p. 105 #1, 2, 4, 5, 8, 9, 12
References
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Wikipedia (2004). Online Encyclopedia.
Retrieved September 1, 2004 from
http://en.wikipedia.org/wiki/Main_Page