Thesis: How do Carleton Place High
School students use the Learning
Commons?
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Suppose you want to survey 10% of the 600
students at Carleton Place High School
Describe 3 different ways you could select 60
students
NOTE: You can group / arrange students
however you like.
Collecting Samples
Chapter 2.3 – In Search of Good Data
Learning goal: outline methods to take random samples
Due now
Read Ex.1 to 3 on pp. 86 - 89
Complete p. 89 # 1-6 and 10
MSIP / Home Learning: p. 99 #1, 5, 6, 10, 11
For 6b, see Ex. 1 on p. 95
Why Sampling?
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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
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E.g. collecting data by walking through the
hallways during MSIP
Not representative
Random Sampling
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Representative samples must be randomly chosen
Random numbers can be generated using a
calculator, computer or random number table
Random choice selects members of a population
without bias
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Every member of the pop’n must have the same chance of
being selected
1) Simple Random Sampling
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To sample n members of the population
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All selections are equally likely
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Put all names in a hat and draw n of them
Number the entire population and generate n
random numbers
All combinations of selections are equally likely
Likely to be representative of the population
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If not, it is due to chance (unintentional) so no bias
2) Systematic Random Sampling
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Sample a fixed percent of the population
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Number every member of the population
Calculate 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
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Divide the population into groups called strata
(e.g. grades)
Take a simple random sample of each stratum
The sample sizes must be proportional to the
group size
Example: Sample 10% of the students in each
grade
Do NOT: Sample 15 students from each grade
4) Cluster Random Sampling
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The population is split into groups e.g.
classes
Groups are randomly chosen for sampling
and then ALL members of the chosen groups
are surveyed
Example
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Select 3 classes randomly (avg 20 per class)
Survey EVERYONE in those classes
5) Multistage Random Sampling
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Groups are randomly chosen from a
population
Subgroups from these groups are randomly
chosen
Individuals in these subgroups are then
randomly chosen to be surveyed
Example: randomly choose 10 high schools
in the board, randomly choose 5 classes in
those schools then randomly choose 10
students in those classes
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
Examples: crash testing cars; life span of
batteries and light bulbs; standardized testing
E.g. Destructive Stratified Sampling
Example: Do students at CPHS want a
longer lunch? (sample 60 of 600 students)
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Simple Random Sampling
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Create a numbered, alphabetic list of students
Have a computer generate 60 random numbers
Interview those students
Systematic Random Sampling
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Calculate the sampling interval n = 600 ÷ 60 = 10
Generate a random number between 1 and 10
Start with that number on the list and interview
each 10th person after that (e.g., 3, 13, 23, 33, …)
Example: do students at CPHS want a
longer lunch?
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Stratified Random Sampling
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Group students by grade
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:
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200 ÷ 600 = 0.33
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60 × 0.333 = 20
So we would need to interview 20 grade 12s
Example: do students at CPHS want a
longer lunch?
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Cluster Random Sampling
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Randomly choose 3 classes of 20 students
Interview every student in each of these classes
Multi Stage Random Sampling
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Randomly select 10 classes (assume all classes
of 20)
Randomly choose 2 rows in each class
Randomly select 3 students from each row
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
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 (medication, drug)
Control group
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the part of the experimental group that does not
receive the treatment (sugar pill, air inhaler, etc)
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 (e.g. sugar
pill)
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?)
MSIP / Home Learning
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p. 99 #1, 5, 6, 10, 11
For 6b, see Ex. 1 on p. 95
Warm Up - Class Activity
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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
Learning goal: Write good questions of various types
Due now: p. 99 #1, 5, 6, 10, 11
MSIP / Home Learning: p. 99 #1, 5, 6, 10, 11
Surveys
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A series of carefully designed questions
Commonly used in data collection
Types: interview, questionnaire, mail-in,
telephone, online, focus group
Bad questions lead to bad data (why?)
Good questions may create good data
(why?)
Questions should…
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not lead the respondents
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Bad: Do you agree that…
Good: How do you feel about…
not use loaded language to sway the respondent
be written without jargon/slang, abbreviations,
acronyms, etc.
allow for all possible responses on closed Qs
(include Other as a catchall)
be sensitive to the respondents
be simple, relevant, specific, readable
Question Styles
Open Questions
 respondents answer in their own words
 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
 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: 14 15 16 17 18+
Checklist
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ex: Math courses being taken this year
(check all that apply)
□ Data Management
□ Calculus and Vectors
□ Advanced Functions
□ Other _________________
Types of Survey Questions
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Ranking Questions
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Order a set of responses
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Ex: Rank the following in order of priority
(1 = lowest priority, 3 = highest priority)
__ Work __ Homework __ Sports
Types of Survey Questions
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Rating Questions
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Rate a set of responses individually
Ex: Rate the following on a scale of 1 to 5
where 1 is low priority and 5 is high
__ Work __ Homework __ Sports
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Ex: How would you rate your teacher?
(choose 1)
□ Good □ Great □ Incredible □ World-Class
MSIP / Homework (Unit 2)
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2.1 p. 81 #4, 5, 6, 8, 13
2.2 p. 89 # 1-6 and 10
2.3 p. 99 #1, 5, 6, 10, 11
** 2.4 p. 105 #1, 2, 4, 5, 8, 9, 12 **
2.5 p. 113 # 1-7, 11
2.6 p. 123 # 5, 7, 9
References
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Wikipedia (2004). Online Encyclopedia.
Retrieved September 1, 2004 from
http://en.wikipedia.org/wiki/Main_Page