If your experiment needs statistics, you ought to have done a better experiment. Ernest Rutherford (1871-1937)

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If your experiment needs statistics, you ought to
have done a better experiment. Ernest
Rutherford (1871-1937)

• The Nature of Statistics Experimental Design

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Observation vs. Experimentation

• Observational Studies observe and reveal
  associations.
• Designed Experiments impose treatments and
  controls can help establish cause-effect
  relationships.

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Experimentation

• Deliberately imposes some treatment on the
  experimental units or subjects in order to
  observe a response.
• Intent of most experiments is to study the effect
  of changes in some variables by other variables.

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• Experiment
• A treatment is applied to part of a population
  and responses are observed.
• Example An experiment was performed in which
  diabetics took cinnamon extract daily while a
  control group took none. After 40 days, the
  diabetics who had the cinnamon reduced their risk
  of heart disease while the control group
  experienced no change. (Source Diabetes Care)

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Larson/Farber 4th ed.
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Terms used in Experimentation

• Experimental Units the individuals or items on
  which the experiment is performed (subjects).
• Block a group of subjects that are similar.
• Response Variable the variable of interest in
  the experiment. The variable that describes the
  outcome. That which will be measured. (Also
  called the dependent variable.)
• Factor(s) a variable or variables whose effect
  on the response variable is of interest in the
  experiment. (Also called the explanatory or
  independent variable.)

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Terminology (contd)

• Level(s) the different categories of the
  factor(s), or possible values of the factor(s).
• Treatments each experimental condition.
  Combinations of the factor(s).
• Treatment Group the group receiving the
  specified treatment.
• Control Group the group receiving the placebo,
  or no treatment.

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3 Key Elements (or Basic Principles) of
Experimental Design

• Control attempt to control factors not of
  interest to the study, but known to affect
  variation.
• Randomization allow each unit in the experiment
  an equal chance of receiving any particular
  treatment.
• Replication sufficient number of subjects to
  ensure that randomization creates groups that
  resemble each other and allow for repetition.

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Key Elements of Experimental Design Control

• Control for effects other than the one being
  measured.
• Confounding variables
• Occurs when an experimenter cannot tell the
  difference between the effects of different
  factors on a variable.
• Example A coffee shop owner remodels her shop at
  the same time a nearby mall has its grand
  opening. If business at the coffee shop
  increases, it cannot be determined whether it is
  because of the remodeling or the new mall.

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Larson/Farber 4th ed.
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Key Elements of Experimental Design Control

• Placebo effect
• A subject reacts favorably to a placebo when in
  fact he or she has been given no medical
  treatment at all.
• Blinding is a technique where the subject does
  not know whether he or she is receiving a
  treatment or a placebo.
• Double-blind experiment neither the subject nor
  the experimenter knows if the subject is
  receiving a treatment or a placebo.

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Larson/Farber 4th ed.
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Key Elements of Experimental Design Randomization

• Randomization is a process of randomly assigning
  subjects to different treatment groups.
• Completely randomized design
• Subjects are assigned to different treatment
  groups through random selection.
• Randomized block design
• Divide subjects with similar characteristics into
  blocks, and then within each block, randomly
  assign subjects to treatment groups.

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Larson/Farber 4th ed.
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Experimental Design Examples

• Completely Randomized Design all experimental
  units are assigned randomly among all treatments.
• Golf ball brands and driving distance Which
  brand of golf ball goes the furthest? A group of
  50 randomly selected golfers are randomly
  assigned to test five brands of golf balls.

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Completely Randomized Design for golf-ball
experiment
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• Randomized Block Design experimental units are
  assigned randomly among all treatments within
  blocks.
• If the experimenter wishes to control for gender
  of the golfer, here perhaps assuming that the
  distances a golf ball is hit is affected by
  gender, how might this difference be controlled
  for?

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Randomized Block Design for golf-ball experiment
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Key Elements of Experimental Design Randomization

• Randomized block design
• An experimenter testing the effects of a new
  weight loss drink may first divide the subjects
  into age categories. Then within each age group,
  randomly assign subjects to either the treatment
  group or control group.

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Larson/Farber 4th ed.
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Key Elements of Experimental Design Replication

• Replication is the repetition of an experiment
  using a large group of subjects.
• To test a vaccine against a strain of influenza,
  10,000 people are given the vaccine and another
  10,000 people are given a placebo. Because of the
  sample size, the effectiveness of the vaccine
  would most likely be observed.

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Larson/Farber 4th ed.
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Example Experimental Design

• A company wants to test the effectiveness of a
  new gum developed to help people quit smoking.
  Identify a potential problem with the given
  experimental design and suggest a way to improve
  it.
• The company identifies one thousand adults who
  are heavy smokers. The subjects are divided into
  blocks according to gender. After two months, the
  female group has a significant number of subjects
  who have quit smoking.

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Larson/Farber 4th ed.
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Solution Experimental Design

• Problem
• The groups are not similar. The new gum may have
  a greater effect on women than men, or vice
  versa.
• Correction
• The subjects can be divided into blocks according
  to gender, but then within each block, they must
  be randomly assigned to be in the treatment group
  or the control group.

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Larson/Farber 4th ed.
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Fabric Durability

• A fabric researcher is studying the durability
  of a fabric under repeated washings. Because the
  durability may depend on the water temperature
  and the type of cleansing agent used, the
  researcher decides to investigate the effect of
  these factors on durability. The water
  temperature used in the experiment will be hot
  (145 degrees F), warm (100 degrees F), and cold
  (50 degrees F). The cleansing agents used will
  be regular Tide, regular Cheer, and Ivory Liquid.
  Each piece of fabric used, will be washed 50
  times in a home automatic washer with a specific
  combination of water and cleansing agent. The
  strength of the fabric will then be tested by a
  machine which forces a steel ball through the
  fabric and records the fabrics resistance to
  breaking.

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Fabric DurabilityIdentify the components of the
experiment

• Identify what is being studied.
• What are the units?
• What is the Response Variable?
• What is/are the Factor(s)?
• How many levels per Factor?
• How many Treatments?
• Describe one Treatment Group.
• How have Control, Randomization and Replication
  been addressed? If not stated, how could they be
  addressed?

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Fabric Durability
Detergent type
Temperature
Ivory Liq.
Cheer
Tide
Trtmt. 1 Tide/145
Trtmt. 4 Cheer/145
Trtmt. 7 Ivory/145
145 deg.
Trtmt. 2 Tide/100
Trtmt. 5 Cheer/100
Trtmt. 8 Ivory/100
100 deg.
Trtmt. 3 Tide/50
Trtmt. 6 Cheer/50
Trtmt 9 Ivory/50
50 deg.
 
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The Experiment The Munchy Cookie Company is
famous for its Chewy Mango cookies. In order to
increase production the company wants to
determine if it can reduce cooking time and
increase temperature and still get the same
quality cookie (traditionally baked for eight
minutes at 350 degrees). The conditions under
consideration involve temperatures of 350 and
450 degrees and cooking times of six and eight
minutes. Chewy Mango cookies can be bent to a
300 degree outside angle before breaking. If
the change in cooking conditions replicates the
original conditions, the company will consider
this new cooking process.
Anatomy of an Experiment Terms and their
Relationships
EXPERIMENTAL UNITS Experimental Units are the
items (here cookies) or individuals (also called
Subjects) upon which the experiment is performed.
Experimental Units are assigned to Control and
Experimental Conditions at random.
Control Group One of the treatment
conditions may represent a Control Group to
which others are compared.
Factors applied to samples
FACTOR (aka INDEPENDENT VARIABLE or EXPLANATORY
VARIABLE) A FACTOR is a condition applied to the
Experimental Units, such as cooking time or
cooking temperature.
Control Group Here, the current baking process
(8 min 350o)
Random Sample of 250 dough balls to each
condition
350 Degrees 8 minutes
Take Measurements
350 Degrees 6 minutes
Compare Cooking Time/Temp. results and state
Conclusions
1000 Chewy Mango cookie dough balls
450 Degrees 8 minutes
TREATMENT A TREATMENT is comprised of Levels from
one or more Factors (Independent Variables). If
there is only one Factor, such as Temperature,
then the TREATMENTS are the Levels of the single
Factor, Temperature. If there is more than one
Factor, then the TREATMENTS represent the
combination of Levels from the Factors (here a
combination of Temperature and Time).
HELP! Were getting a bit crispy
450 Degrees 6 minutes
Six minutes represents a Level of the Time Factor
A Treatment representing one Level from each of
two Factors
LEVEL LEVELS represent the different values of a
Factor that are applied to the Experimental
Units, such as cooking at 350 and 450 degrees.
There is always a minimum of two Levels - one
which may represent the existing conditions and
thereby represent a Control Level (Control
Group) for a Factor and another which represents
an Experimental Level.
RESPONSE VARIABLE (aka DEPENDENT VARIABLE or
OUTCOME VARIABLE) A RESPONSE VARIABLE is the
characteristic of the experiment to be measured
or observed, such as the consistency of a cookie.
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