Experimental Design
Dec 20, 2015
Experimental Design
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
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?
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?
Alternative explanation
Hot weather
Ice cream
Violentcrime
Alternative explanation
Hot weather
Ice cream
Violentcrime
Correlation is not causation
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
Goals of Experimental Design
• Avoid experimental artifacts• Eliminate bias
1. Use a simultaneous control group2. Randomization3. Blinding
• Reduce sampling error1. Replication2. Balance3. Blocking
Goals of Experimental Design
• Avoid experimental artifacts• Eliminate bias
1. Use a simultaneous control group2. Randomization3. Blinding
• Reduce sampling error1. Replication2. Balance3. Blocking
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
Goals of Experimental Design
• Avoid experimental artifacts• Eliminate bias
1. Use a simultaneous control group2. Randomization3. Blinding
• Reduce sampling error1. Replication2. Balance3. Blocking
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
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!
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
Experimental unitsC
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Experimental unitsC
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Treatments
Experimental unitsC
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Treatments
Without randomization, the confounding variable differs among treatments
Experimental unitsC
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Treatments
Experimental unitsC
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Treatments
With randomization, the confounding variable does not differ among treatments
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
Goals of Experimental Design
• Avoid experimental artifacts• Eliminate bias
1. Use a simultaneous control group2. Randomization3. Blinding
• Reduce sampling error1. Replication2. Balance3. Blocking
Replication
• Experimental unit: the individual unit to which treatments are assigned
Experiment 1
Experiment 2
Experiment 3
Tank 1 Tank 2
All separate tanks
Replication
• Experimental unit: the individual unit to which treatments are assigned
Experiment 1
Experiment 2
Experiment 3
Tank 1 Tank 2
All separate tanks
2 Experimental Units
2 Experimental Units
8 Experimental Units
Replication
• Experimental unit: the individual unit to which treatments are assigned
Experiment 1
Experiment 2
Experiment 3
Tank 1 Tank 2
All separate tanks
2 Experimental Units
2 Experimental Units
8 Experimental Units
Pseudoreplication
Why is pseudoreplication bad?
• 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 it’s actually just random chance
Experiment 2
Tank 1 Tank 2
Why is replication good?
• Consider the formula for standard error of the mean:
SEY
s
n
Larger n Smaller SE
Balance
• In a balanced experimental design, all treatments have equal sample size
Better than
Balanced Unbalanced
Balance
• In a balanced experimental design, all treatments have equal sample size
• This maximizes power
• Also makes tests more robust to violating assumptions
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
Randomized Block Design
Randomized Block Design
• Example: tanks in a field
Very sunny
Not So Sunny
Block 1
Block 4
Block 2
Block 3
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
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
Factorial Design
5.5 6.5 7.5
25 n=2 n=2 n=2
30 n=2 n=2 n=2
35 n=2 n=2 n=2
40 n=2 n=2 n=2
Tem
pera
ture
pH
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
Interpretations of 2-way ANOVA Terms
0
10
20
30
40
50
60
70
25 30 35 40
Temperature
Gro
wth
Rate
pH 5.5
pH 6.5
pH 7.5
Effect of pH and Temperature,No interaction
0
5
10
15
20
25
30
35
40
45
25 30 35 40
Temperature
Gro
wth
Rate
pH 5.5
pH 6.5
pH 7.5
Interpretations of 2-way ANOVA Terms
Effect of pH and Temperature,with interaction
Goals of Experimental Design
• Avoid experimental artifacts• Eliminate bias
1. Use a simultaneous control group2. Randomization3. Blinding
• Reduce sampling error1. Replication2. Balance3. Blocking
What if you can’t do experiments?
• Sometimes you can’t 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
What if you can’t 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
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