Topics for Today
Sampling Methods
Sample vs Population
Law – of – Large Numbers
Stat203
Fall 2011 – Week 5 Lecture 1
Page 1 of 23
Importance of Sampling Method
When we have a data set, it is critical to know
how the ___________ comprising the data
were ________.
Can we measure entire population?
- every _______ on earth
- every ______ with a ____________
If not, we’re forced to take a sample.
Did every member of the population have the
same chance of being included?
Were individuals excluded?
Why do we care?
Stat203
Fall 2011 – Week 5 Lecture 1
Page 2 of 23
Sampling and Population
The results from analyzing our ______ can
only ______ conclusions on the __________
they came from.
Can we analyze the results of a _______of
people in this class then make ___________
about “______”?
Stat203
Fall 2011 – Week 5 Lecture 1
Page 3 of 23
Sampling Methods
The ________ method used in any particular
problem is determined by the researcher in the
initial _____________stage.
There are several types of sampling methods
(note that this is different from the data
collection methods of earlier)
They are broadly classified as
- __________
- ______
Stat203
Fall 2011 – Week 5 Lecture 1
Page 4 of 23
Non-Random Sampling Methods:
Accidental or Convenience Sampling
A particular sample or subset of a population
is used because it is convenient for the
researcher.
Example:
I may wish to obtain ___________ about
young adults living in the greater _________
area and I choose __________ as my sample
(because this is very __________ for me).
What are some of the reasons why this class
is a ____ sample?
Stat203
Fall 2011 – Week 5 Lecture 1
Page 5 of 23
- Some people in this class may
__________ to the population (young).
- The _____ of men to women in this class
may be quite _________ than in the
general population.
- People in this class are
_______________ than in the general
population. etc.
Stat203
Fall 2011 – Week 5 Lecture 1
Page 6 of 23
Non-Random Sampling Methods:
Volunteer Sampling
People _________ for your sample – most
commonly this is now ______, but also streetcorner and _____ interviews.
Example:
A TV news broadcast or program asks it’s
viewers to _____ in or go to their _______ and
register a (Yes/No) opinion on a certain
question.
- Are the viewers of this news broadcast
______________ of the adult public in the
area?
- Even if they were, are those who ‘phone
in’ or ‘e-mail in’
____________________________?
Stat203
Fall 2011 – Week 5 Lecture 1
Page 7 of 23
Non-Random = Non-Representative
Non-random samples are generally ______ in
some way.
Whether known or unknown, an individual with
particular ______________ is ___________ to
be ________.
When some individuals are more likely to be
included, or some are specifically excluded,
the sample is automatically not
______________ of the population at large.
Does this mean non-random samples are
useless?
Stat203
Fall 2011 – Week 5 Lecture 1
Page 8 of 23
Random Sampling
Each member of the population has an
_____________of being selected for the
sample.
(Note: In each of the non-random methods
discussed above, this characteristic of a good
sample is missing.)
Stat203
Fall 2011 – Week 5 Lecture 1
Page 9 of 23
Random Sampling Methods:
Simple Random Sampling
How can we produce a SRS?
Suppose in a large class with 427 students we
wish to select a simple random sample of 5
students. How do we do this?
i) Give the each student a different
______ starting at 1 and going to 427.
ii) Use Table B (page 517) to choose the 5
people in the following way.
- Choose a _________________ in
the random digit table.
- Disregard _________ selections.
- _________ numbers selected
_______ the range of 1 to 427.
Stat203
Fall 2011 – Week 5 Lecture 1
Page 10 of 23
Random Sampling Methods:
Systematic sampling
This method produces a random sample from
an ________ list.
Example:
A sample of size 10 is required from a list of
size ____.
i) Divide the _______________ by the
___________ to get 10 groups of size 155
with
7 left over. (1557/10 = 155 +7 remainder)
ii) Randomly choose one number
between 1 & ___ (say 17 … or a number
from a random number table).
iii) Keep adding ___ to the number
chosen in (ii) until one number is chosen from
____ of the large groups.
Stat203
Fall 2011 – Week 5 Lecture 1
Page 11 of 23
The sample chosen consists of those items
on the list in positions
__, 172, ___, 482, … , 1412.
Let’s try this in class – it’s very easy.
Systematic sampling is often used in
__________ __________ where the every k-th
item is taken out of the _______________.
Stat203
Fall 2011 – Week 5 Lecture 1
Page 12 of 23
Random Sampling Methods:
Stratified sampling
Partition the population into ___________
groups (______) and take a SRS from each
one of them. The members of each strata are
similar in some way.
Example
__________ = all SFU students.
Each strata could consist of one of the SFU
_________ (Arts, Science, Health, Business
etc.)
Take a ____________________ from each
_______.
Stat203
Fall 2011 – Week 5 Lecture 1
Page 13 of 23
Random Sampling Methods:
Cluster sampling
Cluster is also called __________ Sampling.
Partition the population into _____________
groups (clusters) and take a SRS of clusters.
From each selected cluster chose a ___.
Example:
A city is subdivided into districts, each of which
is similar in _______________ to the whole
city. A ___ of these districts is chosen and a
___ is chosen from each of these districts.
Stat203
Fall 2011 – Week 5 Lecture 1
Page 14 of 23
Let’s let someone else do the explaining as
well and see which explanation works better
for you:
http://youtu.be/xh4zxC1OpiA
and
http://youtu.be/wUwH7Slfg9E
Stat203
Fall 2011 – Week 5 Lecture 1
Page 15 of 23
Samples and Populations
We’ve discussed a number of different things
that we _______ … _____, standard
deviations, range, ___, median … etc
Whether measured on an entire __________
or just a ______, these measures all have the
same ______________.
But …
We often use different symbols to denote
whether they are measured on a sample or the
entire population.
Stat203
Fall 2011 – Week 5 Lecture 1
Page 16 of 23
Parameters vs Statistics
A _________ is something measured on a
__________.
A _________ is the same thing, but measured
on the ______.
Stat203
Fall 2011 – Week 5 Lecture 1
Page 17 of 23
Parameters and statistics have exactly the
same _______, ______________ and are
__________ the same way.
Consider the following ___________ and the
parameter which could be calculated for each:




Median Age of _________________ in
Vancouver
Average wage of _______ of the
International Machinists Union
The standard deviation of the weight of
widgets _____________________ by the
Acme Widget Company
Maximum temperature in July for major
_______________
Stat203
Fall 2011 – Week 5 Lecture 1
Page 18 of 23
… but for larger populations, we could take
only a ______.



Median Age of all _____________ in
Vancouver
Average wage of ______________
The standard deviation of the weight of
_____________________by the Acme
Widget Company
Clearly these cannot be measured directly, so
we take a ______ and use the sample to
‘guess’ at the true parameter.
This is _____________________ … and we
all perform inference every day.
_____________________?
Stat203
Fall 2011 – Week 5 Lecture 1
Page 19 of 23
Question:
For a school project, a friend of yours
randomly samples ____________________
and asks them if they’ve ever _____________.
2 people had been arrested and s/he
calculates that __________ of people
approximately her age have been arrested.
The next day you read a newspaper article
about a nation-wide study of
______________________university students
your age concluding that _____ of people
approximately your age have been arrested.
Which do you think is closer to the ____
percentage for the population? Why?
Stat203
Fall 2011 – Week 5 Lecture 1
Page 20 of 23
The Law of Large Numbers
You already know this law.
This says that as the size of a sample
_________, the __________________ gets
closer to the true mean of the population.
http://www.stat.tamu.edu/~west/ph/sampledist.html
Stat203
Fall 2011 – Week 5 Lecture 1
Page 21 of 23
Today’s Topics
Sampling Methods
- Non-Random (convenience, volunteer)
- Random
o SRS
o Stratified
o Cluster
o Systematic
Sample vs Population
- Usually have one or the other
- Statistic vs Parameter
o Calculated the same
o Mean the sam
Law-of-Large-Numbers
- As sample size increases, the sample mean
approaches the population mean
Stat203
Fall 2011 – Week 5 Lecture 1
Page 22 of 23
Reading for next lecture
Chapter 6
Stat203
Fall 2011 – Week 5 Lecture 1
Page 23 of 23