 researchers don’t assign choices, they observe them
 a study in which no manipulation of factors has been
 helpful for discovering trends and possible relationships
 although an observational study may identify important
variables related to an outcome. there is no guarantee that
we have found the right or most important related variable
Retrospective Study
 subjects are selected then
previous conditions or behaviors
are determined
 not based on random samples,
they focus on estimating
differences between groups or
associations between variables
 have a restricted view of the
world because they are usually
restricted to a small part of the
 because they are based on
historical data there could be
Prospective Study
 identifying subjects in advance
and collecting data as the events
 Observational studies that try to discover variables related
to rare outcomes are often retrospective
 Example: specific disease
 identify people with the disease
 look at their history and heritage
 something that could be related to their condition
 In 1981 a study was conducted at a high school in California.
Researchers compared the scholastic performance of music students
with that of non-music students.
 The music students had a higher GPA of 3.59 compared to 2.91 that
non-music students had
 16% of music students earned all A’s where only 5% of non-music
students earned all A’s
 Does this study tell us that music will improve students GPAs?
 students that study music might still differ from the others in some
important way that we failed to observe.
 Experiment:
 studies the relationships between two or more variables
 manipulates factor levels to create treatments, randomly assigns subjects to
these treatment levels, and then compares the responses of the subject
groups across treatment levels.
 Random assignment:
an experiment must assign experimental units to treatment groups at
random for the experiment to be valid.
 Factor: a variable whose levels are controlled by the experimenter.
Experiments attempt to discover the effects that differences in factor
levels may have on the responses of the experimental units
Response variable: a variable whose values are compared across
different treatments. In a randomized experiment, large response
differences can be attributed to the effect of differences in treatment
Subject/experimental unit: individuals on whom an experiment is
performed. (participants for humans too)
Level of the factor: the specific values that the experimenter chooses
for a factor
Treatment: the process, intervention, or other controlled circumstance
applied to randomly assigned experimental units. Treatments are the
different levels of a single factor or are made up of combinations of
levels of two or more factors
 Design an experiment to see whether the amount of sleep and exercise you
 Factor levels:
4 hours
 Factors: sleep and exercise
0 min
30 mins
6 hours
 Subjects: the people in the sleep study
0 min
30 min
8 hours
get affects your performance
0 min
30 min
 sleep: 4, 6, or 8 hours
 exercise: 0 min or 30 mins on a treadmill
 Treatment: 6 total
 Once all this is set up you need to
RANDOMLY assign each subject to a treatment
 only an experiment can justify a claim like “music lessons cause higher
 Music and GPA experiment
 take a group of 3rd graders (subjects)
 ½ study music and ½ never take music classes (factor and levels)
 collect data about their GPA (response variable)
4 Principles Of Experimental Design
 1) Control
 make conditions as similar as possible for all treatments groups.
 reduces the variability of the responses, making it easier to detect
differences among the treatment groups
 Risky!! we are testing laundry detergents. we control the water
temperature at 1800. this would reduce variation in our results due to water
temperature. BUT now we can’t say anything about the detergent in cold
 we control a factor by assigning subjects to different levels because we want
to see how the response will change at different levels
 we control other sources of variation to prevent them changing and
affecting the response variable
 2) Randomize
 allows us to equalize the effects of unknown or uncontrollable
sources of variation
 it does not eliminate the effects of these sources, it spreads them
out over all the treatments so we can see past them
 protects us from things we didn’t even know about
 “control what you can, and randomize the rest”
 3) Replicate
 we should repeat the experiment, applying the treatments to a
number of subjects
 only this can we estimate the variability of responses
 an experiment is only complete once you have assessed the
 the outcome of an experiment on a single subject is an anecdote,
not data
 when the subjects are not a representative sample of the population
of interest; repeat the experiment with people from different ages
and different time of year
 Replication of an entire experiment with controlled sources of variation
at different levels is an essential step in science
(Not Required)
 4) Block
 to reduce the effects of identifiable attributes of the subjects that cannot be
 example: 10 people – 2 math teachers and 8 math students
 we want to break them up into two groups for a math competition. if
we pick people randomly the math teachers could be on the same
team. (unfair) so we put 1 math teacher on each team then we
randomly assign 4 students to each team.
 we are “blocking” the occupation variable
 allowing us to remove the variability due to the differences among the
 an experiment is carried out over time with specific actions occurring in
a specified order
 a diagram of the procedure can help think about experiments
group #1
group # 2
Designing An Experiment:
 An ad for OptiGro plan fertilizer claims that with this product you will
grow “juicer, tastier” tomatoes.You would like to test this claim, and
wonder whether you might be able to get by with half the specified
 Basically we need to buy some tomato plants and use OptiGro on some
of them.
 We will set up a completely randomized experiment in one factor
 Plan: state what you want to know
 I want to now whether tomato plants grown with OptiGro yield juicer, tastier
tomatoes than plants raised in otherwise similar circumstances but without the
 Response variable
 I’ll evaluate the juiciness and taste of the tomatoes by asking a panel of judges to rate
them on a scale from 1 to 7 in juiciness and in taste.
 Treatments: specify the factor levels and the treatments
 The factor is fertilizer, specifically OptiGro. I’ll grow tomatoes at three different
factor levels; some with no fertilizer, some with half the specified amount, and some
with the full dose of OptiGro. These are the three treatments.
 Experimental Units:
 I’ll obtain 24 tomato plants of the same variety from a local garden store.
 Experimental Design: observe the principles of design
 Control: any source of variability you know of and can control
 Randomly assign: experimental units to treatments, to equalize the effects of unknown or
uncontrollable sources of variation
 Replicate: results by placing more than one plant in each treatment group
 I’ll locate the farm plots near each other so that the plants get similar amounts of
sun and rain and experience similar temperatures. I will weed the plots equally and
otherwise treat the plants alike. I’ll randomly divide the plants into three groups. I will
use random numbers from a table to determine the assignment. There will be 8
plants in each treatment group.
 Draw a picture
24 tomato plants
from a garden
Group 1
8 plants
Treatment 1
control (no
Group 2
8 plants
Treatment 2
½ dose
Group 3
8 plants
Treatment 3
full fertilizer
compare juiciness
and tastiness
 Specify any other experiment details.You must give enough details so
that another experimenter could exactly replicate your experiment. It’s
generally better to include details that might seem irrelevant than to
leave out matter that could turn out to make a difference. Specify how to
measure the response.
 I will grow the plants until the tomatoes are mature, as judged by reaching a standard
color. I will then harvest the tomatoes when ripe and store then for evaluation. I will
set up a numerical scale of juiciness and one for tastiness for the taste testers.
Several people will taste slices of tomato and rate them.
 Once you collect the data, you’ll need to display them and compare the
results for the three treatment groups.
 I will display the results with side-by-side box-plots to compare the three treatment
groups. I will compare the means of the groups.
 To answer the initial question, we ask whether the difference we
observe in the means of the three groups are meaningful.
Control Treatment
 another level of the factor in order to compare the treatment results to
a situation in which “nothing happens”
 example: the group of tomatoes that received no fertilized
 Different from “control” (one of the 4 principles of experiments).
 controlling extraneous sources of variations by keeping them constant
 example: buying the plants from the same nursery, weeding all the plots the same way
 To avoid bias, we disguise the levels of the factors
 There are two main classes of individuals who can affect the outcome of the
 those who could influence the results
 the subjects, treatment administrators, or technicians
 those who evaluate the results (judges, treating physicians, etc)
 Single Blind: when one of the groups is blinded
 Double Blind: when both of the groups are blinded
 Tomato Experiment: we don’t want our tasters to be bias so we will not tell
them plants received OptiGro
 a control treatment that mimics the real treatment
 the best way to blind subjects
 placebo effect: it is not unusual for 20% or more of subjects given a
placebo to report reduction or pain, improved movement, or greater
 highlights both the importance of effective blinding and the
importance of comparing treatments with a control
The best experiments are usually
 Tomato plants: we want 18 plants
 we get 12 from store A and 6 from store B
 The store the plants came from could effect our results
 So we break the 18 plants into two BLOCKS
 one for each store
 Then we randomly assign the plants in each block to one of the three
 This is called randomized block design
 blocking is the same idea for experiments as stratifying for samples
 we use blocks to reduce variability so we can see the effects of the factors,
we are nut usually interested in studying the effects of the blocks
Block A: 12 tomato
12 tomato plants
from store A and 6
plants from store B
Block B: 6 tomato
group 1
4 plants
treatment 1
group 2
4 plants
treatment 2
½ dose
group 3
4 plants
treatment 3
full dose
group 4
2 plants
treatment 1
group 5
2 plants
treatment 2
½ dose
group 6
2 plants
treatment 3
full dose
compare juiciness
and tastiness
compare juiciness
and tastiness
 Matching: when subjects are paired because they are similar in ways
NOT being studied in retrospective and prospective studies
 Music and grades: we might match each student who studies an instrument with
someone of the same sex and similar family income who doesn’t play an instrument
Example Problems
 Describe a strategy to randomly split the 24 tomato plants into the
three groups for the 3 treatments in the OptiGro experiment.
 A running shoe manufacturer wants to test the speed of its new
sprinting shoe on the 100-meter dash times. The company sponsors 5
athletes who are running the 100-meter dash in the 2004 Summer
Olympic games. To test the show, they have all 5 runners run the 100meter dash with a competitor's shoe and then again with their new
shoe. They use the difference in times as the response variable.
 Suggest some improvements to the design.
 Why might the shoe manufacturer not be able to generalize the results they find to
all runners?
 Athletes who had suffered hamstring injuries were randomly assigned to
one of two exercise programs. Those who engages in static stretching
returned to sports activity in a mean of 37.4 days (SD = 27.6 days).
Those assigned to a program of agility and trunk stabilization exercises
returned to sports in a mean of 22.2 days (SD = 8.3 days).
 Explain why it was important to assign the athletes to the two different treatments
 There was no control group of athletes who did not participate in a special exercise
program. Explain the advantage of including such a group in this experiment.
 How might blinding have been used in this experiment?
 Do you think the difference in times is statistically significant?
Adding More Factors
 OptiGro Experiment
 We want to add a factor about watering
 Levels: only natural watering (rain) and watering by hand daily
 Treatments: 6
No fertilizer
½ fertilizer
full fertilizer
No watering
Daily watering
 Completely randomized two-factor experiment
12 tomato
plants from a
garden store
Group 1
2 plants
Treatment 1
control/ no
Group 2
2 plants
Treatment 2
½ /no water
Group 3
2 plants
Treatment 3
full/no water
Group 4
2 plants
Treatment 4
Group 5
2 plants
Treatment 5
½ / water
Group 6
2 plants
Treatment 6
juiciness and
 When the levels of one factor are associated with the levels of another
factor, the factors are said to be confounding
 Example: A credit card bank wanted to test the sensitivity of the market
by two factors: the annual fee charged for a card and the annual
percentage rate charged. The bank selected 100,000 people at random
from a mailing list. It sent out 50,000 offers with a low rate and no fee
and 50,000 offers with a higher rate and a $50 annual fee.
 They found out people signed up (more than twice the rate) for the
card with low rate and no annual fee.
 Problem: The question that the bank was trying to answer was “how
much of the change is due to the rate and how much was due to the
 How could they have avoided this?