3.
Some notes before we begin
• We are entering the second part of the
statistics course “Experimental Design”
• In most real life applications, experimental
design begins the process of statistics
• Provided experiments (and surveys) are
carefully designed, we can use the
techniques of statistics to analyze the
results with increased “significance”
• Much of this material is covered in social
science courses (i.e. psychology)
4.
Population and Sample
Population-
• The entire group of individuals for which
information is produced
Sample-
• A subset of the population that is
examined in greater detail
• Results of the sample are generalized to
the population.
5.
Sample vs. Census
Census
• Information gathered from the entire
population (no exceptions!)
• Produces the most accurate description
of the population
• Usually expensive or impossible
6.
Samples
• By their nature, the success or failure of a
study or experiment depends on good
technique in sampling
• We want our sample to “look like” our
population
– We would like to minimize the effect of outlier
observations
– We would like to decrease ‘variability’ in our
sample
– We would like to decrease ‘bias’
7.
Some ‘bad’ sampling techniques
Voluntary Response Sampling
• Most often seen as a ‘call-in’ poll or an
‘internet poll’
• People with strong, often negative
opinions are most likely to respond
• Polls are easily “fixed”
• This sampling technique and its’ results
are not to be trusted!
8.
Some ‘bad’ sampling techniques
Convenience Sampling
• Individuals in the sample consist of those who are
easiest to reach
• Mall interviews
– The sample is only valid for people who visit the
mall (this is not everyone!)
– The sample tends to consist of the “easiest targets”
• Some telephone studies
• This is not to say that samples must be difficult
to construct, they just cannot consist of only the
easiest individuals to sample
9.
Bias
• In statistics, bias refers to the systematic
favoring of one outcome over another
• Try not to confuse this definition with a
non-statistical definition
• Bias is enemy #1 for sampling technique
10.
Some notation
• The lowercase script ‘n’ always denotes the
number of individuals in a sample
• The capital ‘N’ denotes the size of the
population
• ‘Table B’ (inside back cover) is the table of
random digits
• A random integer can be produced from a TI
with the command “RandInt(a, b, n)”
– a = smallest number, b = largest number,
n = number of digits to produce (optional)
11.
Simple Random Samples
• This is THE sampling technique for this
statistics course
– Other sampling techniques exist, but our
course is focused on the results of an SRS
• Every possible sample of size n has an
equal chance of being selected
• This is analogous to placing “names in a
hat” or “drawing straws”
12.
Choosing an SRS
1. Label Individuals
Assign each individual in the population a
unique “ID”
Each ID should have the same # of digits
2. Select Individuals
Use table B or your calculator to select
individuals
3. Stopping rule
Indicate when you will stop sampling
4. Identify Sample
Indicate which individuals/ID#’s are included
your sample
13.
Probability Samples
• Samples are chosen by chance
• All possible samples are known
• The probability of choosing each sample
is known
• SRS is one example of a probability
sample
14.
Stratified Random Sample
• Population is divided into strata
– These strata are segments of the population that are
similar in an important way
• Each stratum undergoes an SRS
• The samples from each stratum are combined to
form the full sample
• A stratified sample ensures that all groups are
represented at the appropriate proportion
– Would a sample that consists of 50% boys and 50%
girls make sense for a population of IT consultants?
15.
Stratified Random Sample
Suppose the population contains 100
juniors and 50 seniors
• We would like our samples to reflect this
proportion between juniors and seniors
1. Choose an SRS n=10 from the juniors
2. Choose and SRS n=5 from the seniors
3. The 15 individuals chosen will be the
sample for our Stratified Random Sample
16.
Cluster Sampling
1. The population is divided into clusters or
groups
Each cluster must be representative of
the population (no bias!)
2. One cluster is randomly chosen
Random ID selection (table B, names in a
hat, calculator)
3. The entire cluster that is chosen
becomes the sample
17.
Multistage sampling
• Used when the population is very large
• Take samples from the samples
repeatedly until the sample size is
“manageable”
• Refer to pg 341
18.
Cautions about Sample Surveys
Undercoverage
• Sample does not include all segments of the
population, or systematically favors one
segment of the population
• Many telephone samples will contain an
undercoverage bias simply because many
people do not have telephones
– (yes, it’s true)
• This is most serious when the
“undercovered” individuals differ
significantly from the rest of the population.
19.
Cautions about Sample Surveys
Nonresponse
• Many people contacted for a survey choose not to
participate
• Extremely significant if the non-responders differ
from the responders
• Simply “sampling more people” will not eliminate
bias, esp. if the bias is systematically linked to
the nonresponse
– We are likely to get more nonresponse!
• We should either:
(1) redesign the survey, or
(2) follow up on the nonresponders
20.
Cautions about Sample Surveys
Response Bias
• Respondents answer in a way that is
different from the actual opinion
• Can be caused by the interviewer
– Appearance and gender sensitive questions
can be influenced by the appearance and
gender of interviewer
21.
Cautions about Sample Surveys
Wording of Questions
• Questions that are “confusing”
– Complicated wording affects responses
• Questions that are “leading”
– Present a scenario that can influence a
response before prompting for a response
– Use words that color the respondent's
opinions
22.
Sample Survey Wisdom
• Insist of knowing the following before
trusting results:
1. The exact questions asked
2. Rate of nonresponse
3. Date and method of survey
• Larger samples produce more accurate
results than smaller samples
25.
Definitions
An experiment is conducted to reveal the
response of one variable (response
variable) to changes in other variables
(explanatory variable/s)
26.
Definitions
Experimental Units
• The individuals upon whom the
experiment is conducted
• Human experimental units are called
“subjects”
Treatment
• The specific experimental condition
applied to the experimental units
27.
Definitions
Factors
• Another term for explanatory variables in
an experiment
• An experiment can examine the effects
of multiple factors
Levels
• Factors can be applied to experimental
units in different amounts or levels
28.
Principles of Design
• Control
– Minimize effect confounding variables
– Obtain and apply treatments to exp. units
• Replication
– Minimize effects of outlier observations
– Use multiple exp units
• Randomization
– Minimize effects of variability from individual
responses
29.
Control
• Try to detect and separate effects from the
treatment from effects from other variables
• Control Group
– Represents the population with no treatment
– Often applied a placebo treatment
– Provides a “baseline” for comparison
• Don’t confuse “Control” (the principle)
with “Control Group” (the treatment group)
30.
Replication
• We would like exp. units within each
treatment group to respond similarly to the
treatment, and differently from exp. units
in other treatment groups
• BUT variability (and outliers) exists
throughout each treatment group
• If the experiment is replicated many times
(many exp. units), the effects of variability
(and outliers) will “average out”
31.
Replication
• Use enough experimental units to
eliminate “chance variation”
• Replication (in terms of experimental
design) does not mean “repeat the entire
experiment”
• Remember: larger samples produce more
accurate results than smaller samples
32.
Randomization
• Assign experimental units to treatments
using a randomized design (SRS)
• Minimize bias due to individual’s response
level to different treatments
33.
Statistical Significance
• After experimentation, we hope to see a
difference in response level that is
large/measurable
• A difference that is too large to have
happened “by chance” is called statistically
significant
• We try to produce statistically significant
results!
• We will discuss how large the difference
must be in future chapters.
35.
Randomized Comparative
Experiments
• Completely Randomized Design
– Most basic
• Block Design
– Used when we believe there is a difference
in response levels of different groups
• Matched Pairs Design
– Compares only two treatments
– Measures effect of treatment on two very
similar exp units
36.
Completely Randomized Design
• Can be used for many treatments
• Exp units assigned to treatment group
randomly
• Response in each treatment group is
averaged
• Average of each treatment group is
compared
38.
Block Design
• This is an instance of control
• Exp Units are known to have similar
response level groups (i.e. gender
differences)
• Exp units are “blocked” according to
these groups
• Each block undergoes an SRS into
treatment groups
39.
Block Design
• Each treatment group is averaged an
compared within the block
• Each block may (or may not) have a
control group
• Form blocks based on the most
important unavoidable sources of
variability among exp units
• “Control what you can, block what you
can’t control, randomize the rest”
41.
Matched Pairs Design
• Exp units are matched into pairs that are
similar in terms of the experiment
• Each of two experimental units will
receive a different treatment
• Many times, the subjects in the pair are
the same person
• The effect of the response from the
matched pair is measured with a simple
subtraction
42.
Matched Pairs Design
• Randomization-
– Randomized which member of the pair
receives which treatment
– Randomize the order the treatments are
applied
– Often randomization can be done with a coin
flip!
– Sometimes, it is important to have a length
of time between treatment applications
43.
Matched Pair Design
(example diagram – single subject)
Subject #1
treatment
control
compare
Subject #2
control
treatment
compare
Subject #3
treatment
control
compare
Subject #n
control
treatment
compare
Randomize
order
compare
44.
Matched Pair Design
(example diagram – paired subjects)
Subject #1 treatment
control compareSubject #2
Subject #3 treatment
control
compare
Subject #n
treatment
control
compare
Randomize
treatment
Subject #4
Subject #n-1
Match Pairs
45.
Cautions about Experimentation
Double Blind Experiment
• Sometimes bias is produced unconsciously
• Sometimes a subject will produce bias if he
knows he as receiving placebo treatment
• Effects can be controlled if neither the
experimenter nor the subject know which
treatment was administered
• Typically, the treatment is given an ID number
and only the researcher will know which
treatment corresponds to which ID.
• Controls the placebo effect
46.
Cautions about Experimentation
Lack of realism
• Experimental results are produced under
conditions that cannot be realistically
duplicated
• Subjects who know they are exp units
may behave differently than the
population
• The laboratory setting itself may be a
variable of the experiment!
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