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
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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
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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