Collecting Data
Understanding
Random Sampling
Objectives:
 To develop the basic properties of
collecting an unbiased sample.
 To learn to recognize flaws in biased
sampling.
Intro…
Do you know what it
means when something
occurs randomly?
Randomly select a number
from the next slide. Ready…
1234
Question:
What would you except
to happen if when we
collected data on this
simple task?
How do we gather data?
 Surveys
 Opinion polls
 Interviews
 Studies
 Observational
 Retrospective
(past)
 Prospective (future)
 Experiments
Population
Population – the entire group
of individuals we want
information about.
Census – a complete count of
the entire population
Why would we not use a census all the
time?
1) Not accurate
2) Very expensive
3) Perhaps impossible
4) If using destructive sampling, you
would destroy population
• Breaking strength of soda bottles
• Lifetime of flashlight batteries
• Safety ratings for cars
Sample
A part of the population
that we examine in order
to gather information
Used to generalize
information about a
population
Sampling design
refers to the method used to
choose the sample from the
population
Sampling frame
a list of every individual in the
population
Simple Random Sample (SRS)
consist of n individuals from the
population chosen in such a
way that
every individual has an equal
chance of being selected
every set of n individuals has
an equal chance of being
selected
SRS
 Advantages
 Unbiased
 Easy
 Disadvantages
 Large
variance
 May not be
representative
 Must have
sampling frame
(list of population)
Systematic random sample
select sample by
following a systematic
approach
randomly select where
to begin
Systematic Random Sample
 Advantages
 Unbiased
 Ensure that the
sample is
distributed
across
population
 More efficient,
cheaper, etc.
 Disadvantages
 Large
variance
 Can be
confounded by
trend or cycle
 Formulas are
complicated
Identify the sampling design
A local restaurant manager wants to
survey customers about the service
they receive. Each night the manager
randomly chooses a number between 1
& 10. He then gives a survey to that
customer, and to every 10th customer
after them, to fill it out before they
leave.
Systematic random sampling
Bias
ERROR
favors certain
outcomes
 Note: We cannot ever draw
conclusions from bias data. Throw
it out and start over!
Voluntary response
People chose to respond
Usually only people with
very strong opinions
respond
Produces biased results
Convenience sampling
Ask people who are
easy to ask
Produces bias
results
Source of bias?
Suppose that you want to
estimate the total amount of
money spent by students on
textbooks each semester at Rice.
You collect register receipts for
students as they leave the
bookstore during lunch one day.
Convenience sampling – easy way to collect data
1970 Draft Lottery and the
Role of Randomization
In that first draft lottery (conducted on December 1, 1969), a
large, deep, cylindrical bowl was filled with 366 dates, one for
each day of the year (including February 29, of course). The
dates were placed inside small capsules (balls about the size
of a pecan), added to the bowl, and then mixed. After mixing,
the capsules were selected, one by one, and assigned a draft
priority. Draft registrants whose birthdays matched the first
100 or so dates selected were likely to be called for induction.
However, the bowl's small diameter and height (nearly arm's
length) made the mixing less than random because each
month's dates had been added sequentially in the yearly order
of months.
January's capsules were dumped in first, followed by
February's and so on until December.
Set of Data for 1970 Draft Lottery
1970 Draft Lottery
1970 Draft Number by Day of Year
Mean Draft Number by Month
How did the nonrandomness of the draft
effect the casualties (deaths) during the
Vietnam war?
This was recently studied by Paul Sommers
in "The Writing on the Wall",
Chance, Vol, 1, 2003, p35-38.
He examined the names of the casualties on
the Vietnam Memorial (available online at
thewall-usa.com) together with other sources
and found the number of casualties by birth
month:
Selecting a SRS
 For the AP exam: “Knowledgeable
users of statistics need to be able to
perform your sample exactly using the
described method.”
 Methods: we can “pick samples from a
hat”, use a random number generator,
or use a table of random digits to derive
our sample
SRS by picking out of a hat
 Say items in hat are “mixed thoroughly” and
state whether or not slips of paper are
replaced back in the hat (yes if stratified
sampling).
Random digit table
each entry is equally
likely to be any of the
10 digits
digits are independent
of each other
Suppose your population consisted of these 20 people:
1) Aidan
2) Bob
3) Chico
4) Doug
5) Edward
6) Fred
11) Kathy
16) Paul
will need
to use double17) Shawnie
7)We
Gloria
12) Lori
digit random
numbers, 18) Tracy
8) Hannah
13) Matthew
ignoring
9)
Israel any
14)number
Nancy greater
19) Uncle Sam
10) Jung
15) with
OpusRow 1 and
20) Vernon
than
20. Start
read across.
Ignore.
Ignore.
Use the following random
digits to select a sample of five from these
Ignore.Ignore.
people.
Row
Stop when five people are selected. So
1 4 5my sample
1 8 would
0 5 consist
1 3 of :7 1
2 0 1
5 5
8 0 1 5
7 0
3 Aidan,
8 9 Edward,
9 3 Matthew,
4 3 Opus,
5 0 and6 Tracy
3