problem with the neyman-pearson formulationstachenz/group 3... · problem with the neyman-pearson...
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Problem with the Neyman-Pearson Formulation
Anabella Fong, Goh Jie Sheng, Bok Wen Xuan
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Richard Peto
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Fishers Experimental design
● Randomized selection of patients for treatment
● Results were compared between treatment and non-treatment groups
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Randomized selection
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Problem with Fisher’s experimental design
Randomized Treatment Patients
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Problem with Fisher’s experimental design
HUMANS!!!!
EXPERIMENTS
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Peto’s ‘intent to treat’
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Peto’s ‘intent to treat’● Patients were randomly selected to receive specific treatment ● Each patient is treated as if they are on their assigned
treatment; all changes in treatment are ignored
A A A
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Problem with Peto’s solution
Differences
Equivalent
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Problem: Rigidity of Neyman-Pearson Formulation
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Neyman-Pearson Formulation
Hypothesis testing is the probability that the test correctly rejects null hypothesis as much as possible, when the alternate is true.
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Neyman-Pearson Formulation
P-value < α Reject Null Hypothesis
P-value > α Do not reject Null Hypothesis
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Fishers problem with the formulation
● No rigorous requirements should be subjected to
the use of p-values and significant testing.
● Disagree with fixing α and act only if p-value is
less than that.
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Cox’s Formulation
● Fisher’s method - significance testing
● Neyman-Pearson Formulation - hypothesis testing
● Hypothesis testing is used for refining the scientist’s
views of reality by eliminating unnecessary parameters
or for deciding between two differing models of reality.
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Box’s Approach
● Agreed with Cox’s formulation
● Data from one experiment is compared to other
experiments
● Using the newer studies, scientist always return to older
studies to refine their interpretation
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Box’s Approach: Example
Manufacturer
EVOP
Modifying humidity, speed, sulfur and temperature
Little change in paper strength.
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Box’s Approach: Example
Slight differences
Fisher’s analysis of variance
New experiment!
Average strength across all runs has been increased slightly
New run with another slight increase in strength
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Cochran’s observational studies● The city of Baltimore - if public housing had an effect on the social attitudes
and progress of poor people● Following Fisher's methods - take a group of people, whether they had
applied for public housing or not, and randomly assign some of them to public housing and refuse it to the others.
● Observational study - following families who went into public housing and those who did not
● Once the parameters of all these effects had been estimated, the remaining differences in effect would be used to determine the effect of public housing on social attitudes
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Cochran’s observational studies
Cochran's methods : to estimate the underlying effect of treatment, taking into account the effect of imbalances in the assignment of treatment to patients.
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Rubin’s Model
● Each patient is assumed to have a possible response to each of the treatments.
● We can set up a mathematical model in which there is a symbol in the formula for each of those possible responses. Rubin derived conditions on this mathematical model that are needed to estimate what might have happened had the patient been put on the other treatment.
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Problem with Cochran and Rubin’s Model
● Cochran and Rubin methods are highly model specific - they will not produce correct answers unless the complicated mathematical models they use come close to describing reality; require the analyst to devise a mathematical model that will match reality in all or most of its aspects.
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Conclusion● No mathematical model is perfect
● Need to know what we are looking for to design a good
model for it