lab exam

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lab exam

• when Nov 27 - Dec 1
• length 1 hour
• each lab section divided in two
• register for the exam in your section so there is
  a computer reserved for you
• If you write in the 1st hour, you cant leave
  early! If you write in the second hour, you cant
  arrive late!

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lab exam

• format
• open book!
• similar to questions in lab manual
• last section in the lab manual has review
  questions
• show all your work hypotheses, tests of
  assumptions, test statistics, p-values and
  conclusions

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Experimental Design
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Experimental Design

• Experimental design is the part of statistics
  that happens before you carry out an experiment
• Proper planning can save many headaches
• You should design your experiments with a
  particular statistical test in mind

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Why do experiments?

• Contrast observational study vs. experiments
• Example
• Observational studies show a positive association
  between ice cream sales and levels of violent
  crime
• What does this mean?

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Why do experiments?

• Contrast observational study vs. experiments
• Example
• Observational studies show a positive association
  between ice cream sales and levels of violent
  crime
• What does this mean?

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Alternative explanation
Ice cream
Violent crime
Hot weather
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Alternative explanation
Ice cream
Correlation is not causation
Violent crime
Hot weather
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Why do experiments?

• Observational studies are prone to confounding
  variables Variables that mask or distort the
  association between measured variables in a study
• Example hot weather
• In an experiment, you can use random assignments
  of treatments to individuals to avoid confounding
  variables

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Goals of Experimental Design

• Avoid experimental artifacts
• Eliminate bias
• Use a simultaneous control group
• Randomization
• Blinding
• Reduce sampling error
• Replication
• Balance
• Blocking

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Goals of Experimental Design

• Avoid experimental artifacts
• Eliminate bias
• Use a simultaneous control group
• Randomization
• Blinding
• Reduce sampling error
• Replication
• Balance
• Blocking

12
Experimental Artifacts

• Experimental artifacts a bias in a measurement
  produced by unintended consequences of
  experimental procedures
• Conduct your experiments under as natural of
  conditions as possible to avoid artifacts

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Experimental Artifacts

• Example diving birds

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Goals of Experimental Design

• Avoid experimental artifacts
• Eliminate bias
• Use a simultaneous control group
• Randomization
• Blinding
• Reduce sampling error
• Replication
• Balance
• Blocking

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Control Group

• A control group is a group of subjects left
  untreated for the treatment of interest but
  otherwise experiencing the same conditions as the
  treated subjects
• Example one group of patients is given an inert
  placebo

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The Placebo Effect

• Patients treated with placebos, including sugar
  pills, often report improvement
• Example up to 40 of patients with chronic back
  pain report improvement when treated with a
  placebo
• Even sham surgeries can have a positive effect
• This is why you need a control group!

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Randomization

• Randomization is the random assignment of
  treatments to units in an experimental study
• Breaks the association between potential
  confounding variables and the explanatory
  variables

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Experimental units
Confounding variable
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Experimental units
Treatments
Confounding variable
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Experimental units
Treatments
Without randomization, the confounding variable
differs among treatments
Confounding variable
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Experimental units
Treatments
Confounding variable
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Experimental units
Treatments
With randomization, the confounding variable does
not differ among treatments
Confounding variable
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Blinding

• Blinding is the concealment of information from
  the participants and/or researchers about which
  subjects are receiving which treatments
• Single blind subjects are unaware of treatments
• Double blind subjects and researchers are
  unaware of treatments

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Blinding

• Example testing heart medication
• Two treatments drug and placebo
• Single blind the patients dont know which group
  they are in, but the doctors do
• Double blind neither the patients nor the
  doctors administering the drug know which group
  the patients are in

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Goals of Experimental Design

• Avoid experimental artifacts
• Eliminate bias
• Use a simultaneous control group
• Randomization
• Blinding
• Reduce sampling error
• Replication
• Balance
• Blocking

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Replication

• Experimental unit the individual unit to which
  treatments are assigned

Experiment 1
Experiment 2
Tank 1
Tank 2
Experiment 3
All separate tanks
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Replication

• Experimental unit the individual unit to which
  treatments are assigned

2 Experimental Units
Experiment 1
2 Experimental Units
Experiment 2
Tank 1
Tank 2
8 Experimental Units
Experiment 3
All separate tanks
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Replication

• Experimental unit the individual unit to which
  treatments are assigned

2 Experimental Units
Experiment 1
Pseudoreplication
2 Experimental Units
Experiment 2
Tank 1
Tank 2
8 Experimental Units
Experiment 3
All separate tanks
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Why is pseudoreplication bad?
Experiment 2
Tank 1
Tank 2

• problem with confounding and replication!
• Imagine that something strange happened, by
  chance, to tank 2 but not to tank 1
• Example light burns out
• All four lizards in tank 2 would be smaller
• You might then think that the difference was due
  to the treatment, but its actually just random
  chance

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Why is replication good?

• Consider the formula for standard error of the
  mean

Larger n
Smaller SE
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Balance

• In a balanced experimental design, all treatments
  have equal sample size

Better than
Balanced
Unbalanced
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Balance

• In a balanced experimental design, all treatments
  have equal sample size
• This maximizes power
• Also makes tests more robust to violating
  assumptions

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Blocking

• Blocking is the grouping of experimental units
  that have similar properties
• Within each block, treatments are randomly
  assigned to experimental treatments
• Randomized block design

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Randomized Block Design
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Randomized Block Design

• Example cattle tanks in a field

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(No Transcript)
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Very sunny
Not So Sunny
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Block 1
Block 2
Block 3
Block 4
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What good is blocking?

• Blocking allows you to remove extraneous
  variation from the data
• Like replicating the whole experiment multiple
  times, once in each block
• Paired design is an example of blocking

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Experiments with 2 Factors

• Factorial design investigates all treatment
  combinations of two or more variables
• Factorial design allows us to test for
  interactions between treatment variables

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Factorial Design
pH
5.5 6.5 7.5
25 n2 n2 n2
30 n2 n2 n2
35 n2 n2 n2
40 n2 n2 n2
Temperature
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Interaction Effects

• An interaction between two (or more) explanatory
  variables means that the effect of one variable
  depends upon the state of the other variable

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Interpretations of 2-way ANOVA Terms
Effect of pH and Temperature, No interaction
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Interpretations of 2-way ANOVA Terms
Effect of pH and Temperature, with interaction
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Goals of Experimental Design

• Avoid experimental artifacts
• Eliminate bias
• Use a simultaneous control group
• Randomization
• Blinding
• Reduce sampling error
• Replication
• Balance
• Blocking

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What if you cant do experiments?

• Sometimes you cant do experiments
• One strategy
• Matching
• Every individual in the treatment group is
  matched to a control individual having the same
  or closely similar values for known confounding
  variables

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What if you cant do experiments?

• Example Do species on islands change their body
  size compared to species in mainland habitats?
• For each island species, identify a closely
  related species living on a nearby mainland area

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Power Analysis

• Before carrying out an experiment you must choose
  a sample size
• Too small no chance to detect treatment effect
• Too large too expensive
• We can use power analysis to choose our sample
  size

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Power Analysis

• Example confidence interval
• For a two-sample t-test, the approximate width of
  a 95 confidence interval for the difference in
  means is
• (assuming that the data are a random sample from
  a normal distribution)

?2 ?n
precision 4 ?
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Power Analysis

• Example confidence interval
• The sample size needed for a particular level of
  precision is

2
? Precision
n 32
51
Power Analysis

• Assume that the standard deviation of exam scores
  for a class is 10. I want to compare scores
  between two lab sections. A. How many exams do I
  need to mark to obtain a confidence limit for the
  difference in mean exam scores between two
  classes that has a width (precision) of 5?

2
? Precision
n 32
2
10 5
n 32
128
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Power Analysis

• Example power
• Remember, power 1 - ?
• ? PrType II error
• Typical goal is power 0.80
• For a two-sample t-test, the sample size needed
  for a power of 80 to detect a difference of D is

? D
2
n 16
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Power Analysis

• Assume that the standard deviation of exam scores
  for a class is 10. I want to compare scores
  between two lab sections. B. How many exams do I
  need to mark to have sufficient power (80) to
  detect a mean difference of 10 points between the
  sections?

? D
2
n 16
2
10 10
16
n 16