Download 2.3 - 2.4

How do Carleton Place High School
students use the Learning Commons?
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Suppose you want to survey at least 10% of
the 500 students at Carleton Place High
School
How could you select students…
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At an all-school assembly?
From a numbered list?
During period 4?
During a day when there are grade assemblies?
Collecting Samples
Chapter 2.3 – In Search of Good Data
Learning goal: Outline methods to take random samples
Questions? 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
A representative sample will give reliable
results
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You must be confident that the sample represents
the population
Convenience Sampling
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Collect data in a convenient manner
No random selection
e.g., hand out surveys at the front doors from
7:30-7:45
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Not likely to give a representative sample
Why?
Random Sampling
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Representative samples must be randomly chosen
Random numbers can be generated using a
calculator, computer or object of chance
Random choice selects members of a population
without bias (no intentional or unintentional influence
on the data)
 Every member of the population must have the
same chance of being selected!
1) Simple Random Sampling
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Select n members from the entire population
i) Put all names in a hat and draw n of them
ii) Number the entire population and generate n
unique random numbers
Survey those individuals
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All selections are equally likely
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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 the
sample is NOT biased
2) Systematic Random Sampling
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Sample a fixed percent of the population
1. Number every member of the population
2. Calculate the Sampling interval
n = (population size) ÷ (sample size)
3. Generate a random # between 1 and n
4. Sample that individual and then every nth person
after
3) Stratified Random Sampling
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Divide the population into groups or strata
Take a proportional simple random sample of
each stratum (group)
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Sample the same % from each group (NOT
necessarily the same # from each group)
Ideal for a small number of large groups
4) Cluster Random Sampling
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The population is split into groups
Groups are randomly chosen for sampling
and then ALL members of the chosen groups
are surveyed
Ideal for a large number of small groups
5) Multistage Random Sampling
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Randomly select groups from a population
Then, take a simple random sample from the
selected groups
This is a combination of Stratified and Simple
Random Sampling
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
Ex: crash testing cars; life span of batteries
and light bulbs; standardized testing
Can be combined with other methods
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e.g., Destructive Stratified Sampling
Sampling at Carleton Place High School
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Outline how you would sample 60 out of 600
students at CPHS using:
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Simple Random Sampling
Systematic Random Sampling
Stratified Random Sampling
Cluster Random Sampling
Multi-Stage Random Sampling
Sampling at Carleton Place High School
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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
Roll a 10-sided die
Start with that person (e.g., 3) and interview every
10th person after that (3, 13, 23, 33, …)
Sampling at Carleton Place High School
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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
60 × 0.333 = 20
So we would need to interview 20 grade 12s
Sampling at Carleton Place High School
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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 classes of
20)
Draw names from a hat to randomly select 6
students from each class
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
Confidence Interval
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For a population of 600 students, what
sample size is required for a margin of error
of:
20%? ________
10%? ________
5%?
________
Determine Sample Size
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Confidence Level
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Confidence Interval
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The % of the time the data will be within the
confidence interval
The higher, the better
The range ±n that the actual value will be in
The lower, the better
See calculators on web site
Techniques for Experimental Studies
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Experimental studies are different from data
collection studies
In experimental studies a treatment is
applied to some part of the population (e.g.,
testing a new medication)
The effect of the treatment can only be
known in comparison to the 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 medicinal value
given to the control group to reduce bias in the
experiment (e.g., sugar pill that looks like the
actual drug, air inhaler)
The test group doesn’t know whether they are
receiving the treatment or not (why?)
Double-blind test
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An experiment where neither the subjects nor 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
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Describe how to take an appropriately sized
sample of the students in this class using two
of 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 survey questions
Questions? p. 99 #1, 5, 6, 10, 11
MSIP / Home Learning: p. 105 #1-2, 4-5, 8-9, 12
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
tonight (1 = lowest, 3 = highest)
__ Work __ Homework __ Sports
Types of Survey Questions
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Rating Questions
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Rate a set of responses individually
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Ex: Rate each of the following on a scale of 1 to 5 (1 is
lowest): __ Work __ Homework __ Sports
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Ex: How would you rate your teacher? (check one)
□ Good □ Great □ Incredible □ World-Class
MSIP / Home Learning Recap
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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
* = on test