Transcript 1.2
Chapter 1
Section 2
Observational Studies, Experiments,
and Simple Random Sampling
Sullivan – Fundamentals of Statistics – 2nd Edition – Chapter 1 Section 2 – Slide 1 of 22
Chapter 1 – Section 2
● Learning objectives
1
Distinguish between an observational study and an
experiment
2 Obtain a simple random sample
Sullivan – Fundamentals of Statistics – 2nd Edition – Chapter 1 Section 2 – Slide 2 of 22
Chapter 1 – Section 2
● Learning objectives
1
Distinguish between an observational study and an
experiment
2 Obtain a simple random sample
Sullivan – Fundamentals of Statistics – 2nd Edition – Chapter 1 Section 2 – Slide 3 of 22
Chapter 1 – Section 2
● There are different ways to collect data
Census
Existing sources
Survey sampling
Designed experiments
● These are good methods of data collection, if
done correctly
Sullivan – Fundamentals of Statistics – 2nd Edition – Chapter 1 Section 2 – Slide 4 of 22
Chapter 1 – Section 2
● A census is a list
Of all the individuals in a population
That records the characteristics of the individuals
An example is the US Census held every 10 years
(this is only an example though)
● Advantages
Answers have 100% certainty
● Disadvantages
May be difficult or impossible to obtain
Costs may be prohibitive
Sullivan – Fundamentals of Statistics – 2nd Edition – Chapter 1 Section 2 – Slide 5 of 22
Chapter 1 – Section 2
● An existing source is
An appropriate data set has already been collected
That can be used for this study
● Advantages
Saves time and money
● Disadvantages
There may not be an applicable data set
Sullivan – Fundamentals of Statistics – 2nd Edition – Chapter 1 Section 2 – Slide 6 of 22
Chapter 1 – Section 2
● A survey sample is
A study when only a subset of the population is
considered
A study where there is no attempt to influence the
value of the variable of interest
● Advantages
Saves time and money
● Disadvantages
Choosing an appropriate sample could be difficult
Sullivan – Fundamentals of Statistics – 2nd Edition – Chapter 1 Section 2 – Slide 7 of 22
Chapter 1 – Section 2
● A survey sample is an example of an
observational study
An observational study is one where there is no
attempt to influence the value of the variable
An observational study is also called an ex post facto
(after the fact) study
● Advantages
It can detect associations between variables
● Disadvantages
It cannot isolate causes to determine causation
Sullivan – Fundamentals of Statistics – 2nd Edition – Chapter 1 Section 2 – Slide 8 of 22
Chapter 1 – Section 2
● A designed experiment is an experiment
That applies a treatment to individuals
Often compares the treated group to a control
(untreated) group
Where the variables can be controlled
● Advantages
Can analyze individual factors
● Disadvantages
Cannot be done when the variables cannot be
controlled
Cannot apply in cases for moral / ethical reasons
Sullivan – Fundamentals of Statistics – 2nd Edition – Chapter 1 Section 2 – Slide 9 of 22
Chapter 1 – Section 2
● Observational studies and designed
experiments have some fundamental differences
Observational studies do not control the variable
under analysis while designed experiments do
Because variables are uncontrolled in an
observational study, the results can only be
associations
Because variables are controlled in a designed
experiment, the results can be conclusions of
causation
Sullivan – Fundamentals of Statistics – 2nd Edition – Chapter 1 Section 2 – Slide 10 of 22
Chapter 1 – Section 2
● A danger in observational studies are lurking
variables
● In an observational study, two variables can be
determined to be associated
● Associated does not mean that one causes the
other
● A simple observational study may find that
smoking and cancer are associated
Cannot conclude that smoking causes cancer
Cannot conclude that cancer causes people to smoke
Sullivan – Fundamentals of Statistics – 2nd Edition – Chapter 1 Section 2 – Slide 11 of 22
Chapter 1 – Section 2
● Usually only a part of the population can be
analyzed
● How do you choose your sample?
● The process is called sampling
● We will discuss
Simple random sampling
Stratified sampling
Systematic sampling
Cluster sampling
Convenience sampling
Sullivan – Fundamentals of Statistics – 2nd Edition – Chapter 1 Section 2 – Slide 12 of 22
Chapter 1 – Section 2
● Learning objectives
1
Distinguish between an observational study and an
experiment
2 Obtain a simple random sample
Sullivan – Fundamentals of Statistics – 2nd Edition – Chapter 1 Section 2 – Slide 13 of 22
Chapter 1 – Section 2
● A simple random sample is when every possible
sample of size n out of a population of N has an
equally likely chance of occurring
● Examples
For a simple random sample of size n = 1 from a
population size of N = 5, each of the 5 possible
samples has an equally likely chance of occurring
For a simple random sample of size n = 2 from a
population size of N = 4, each of the 6 possible
samples has an equally likely chance of occurring
Sullivan – Fundamentals of Statistics – 2nd Edition – Chapter 1 Section 2 – Slide 14 of 22
Chapter 1 – Section 2
● Simple random sampling requires that we have
a list of all the individuals within a population
● This list is called a frame
● If we do not have a frame, then a different
sampling method must be used
Sullivan – Fundamentals of Statistics – 2nd Edition – Chapter 1 Section 2 – Slide 15 of 22
Chapter 1 – Section 2
● A simple (but not foolproof) method
Write each individual’s name on a separate piece of
paper
Put all the papers into a hat
Draw a random paper from the hat
● Physical methods have some issues
Are the papers sufficiently mixed?
Are some of the papers folded?
Sullivan – Fundamentals of Statistics – 2nd Edition – Chapter 1 Section 2 – Slide 16 of 22
Chapter 1 – Section 2
● A method using a table of random numbers
List and number the individuals
Decide on a way to pick the random numbers (how to
choose the starting point and what rule to use to
select which digits to choose after that)
Select the random numbers
Match the numbers to the individuals
● With the technology available today, this method
is outdated
Sullivan – Fundamentals of Statistics – 2nd Edition – Chapter 1 Section 2 – Slide 17 of 22
Chapter 1 – Section 2
● A method using technology
List and number the individuals
Use software (a calculator, software such as MINITAB
or Excel) to generate random numbers
Match the random numbers to the individuals
● The method must be decided in advance … it is
not statistically correct to choose a series of
samples until a “good” one comes up
Sullivan – Fundamentals of Statistics – 2nd Edition – Chapter 1 Section 2 – Slide 18 of 22
Chapter 1 – Section 2
● Simple random sampling example
● We wish to select a random sample of 3 out of a
group of 30 students
● We generate a two digit random number to
choose the first student
● Examples
If the number is “63”, we disregard this random
number and choose another one
If the number is “17”, we pick student number 17
Sullivan – Fundamentals of Statistics – 2nd Edition – Chapter 1 Section 2 – Slide 19 of 22
Chapter 1 – Section 2
● We generate another two digit random number
to choose the second student
Assume that the first student was number 17
● Examples
If the second number is “17”, we disregard this
random number and choose another one (we want 2
different people)
If the number is “65”, we disregard this random
number and choose another one
If the number is “8”, we choose student 8 as our
second student
Sullivan – Fundamentals of Statistics – 2nd Edition – Chapter 1 Section 2 – Slide 20 of 22
Chapter 1 – Section 2
● We generate another two digit random number
to choose the third student
Assume that the first student was number 17 and the
second was number 8
● Examples
If the third number is “17”, or “8”, or anything “31” and
higher, we disregard this random number and choose
another one (we want 3 different people)
If the number is “2”, we choose student 2 as our third
and final student
● Our sample is {student 17, student 8, student 2}
Sullivan – Fundamentals of Statistics – 2nd Edition – Chapter 1 Section 2 – Slide 21 of 22
Summary: Chapter 1 – Section 2
● There are different ways of collecting data
A census uses the entire population
An existing source use an existing data set
An observational study measures the characteristics
of a sample without influencing the variable of interest
A designed experiment applies a treatment to a
sample to isolate the effects of a variable
● The method of simple random sampling can be
used to select the sample
Sullivan – Fundamentals of Statistics – 2nd Edition – Chapter 1 Section 2 – Slide 22 of 22