A Blind AnalysisA Blind Analysis
You are not allowed to peek!You are not allowed to peek!
Prof. Donald Koetke
Senior Resea...
3/30/07 VU Colloquium 2
OutlineOutlineOutlineOutline
1. What is a “blind analysis”?
• What is a “bias”?
• Does “bias” = “s...
3/30/07 VU Colloquium 3
OutlineOutlineOutlineOutline
1. What is a “blind analysis”?
• What is a “bias”?
• Does “bias” = “s...
3/30/07 VU Colloquium 4
OutlineOutlineOutlineOutline
1. What is a “blind analysis”?
• What is a “bias”?
• Does “bias” = “s...
3/30/07 VU Colloquium 5
OutlineOutlineOutlineOutline
1. What is a “blind analysis”?
• What is a “bias”?
• Does “bias” = “s...
3/30/07 VU Colloquium 6
OutlineOutlineOutlineOutline
1. What is a “blind analysis”?
• What is a “bias”?
• Does “bias” = “s...
3/30/07 VU Colloquium 7
OutlineOutlineOutlineOutline
1. What is a “blind analysis”?
• What is a “bias”?
• Does “bias” = “s...
3/30/07 VU Colloquium 8
A Blind AnalysisA Blind AnalysisA Blind AnalysisA Blind Analysis
What is a “bias”?
Does “bias” = “...
3/30/07 VU Colloquium 9
A Blind AnalysisA Blind AnalysisA Blind AnalysisA Blind Analysis
1. You know what the answer “shou...
3/30/07 VU Colloquium 10
A Blind AnalysisA Blind AnalysisA Blind AnalysisA Blind Analysis
The goal of a “blind analysis” i...
3/30/07 VU Colloquium 11
A Blind AnalysisA Blind AnalysisA Blind AnalysisA Blind Analysis
1. What is a “blind analysis”?
A...
3/30/07 VU Colloquium 12
OutlineOutline
1. What is a “blind analysis”?
• What is a “bias”?
• Does “bias” = “systematic err...
3/30/07 VU Colloquium 13
HistoryHistoryHistoryHistory
Blind analysis begins in ~1930s with -
Medical research -- blind tes...
3/30/07 VU Colloquium 14
HistoryHistoryHistoryHistory
Blind analysis begins in ~1930s with -
Medical research -- blind tes...
3/30/07 VU Colloquium 15
HistoryHistoryHistoryHistory
Blind analysis begins in ~1930s with -
Medical research -- blind tes...
3/30/07 VU Colloquium 16
Medical research -- The double blind test!
HistoryHistoryHistoryHistory
Blind analysis begins in ...
3/30/07 VU Colloquium 17
Medical research -- The double blind test!
HistoryHistoryHistoryHistory
Blind analysis begins in ...
3/30/07 VU Colloquium 18
Medical research -- The double blind test!
HistoryHistoryHistoryHistory
Blind analysis begins in ...
3/30/07 VU Colloquium 19
HistoryHistoryHistoryHistory
Blind analysis has become the standard
methodology in clinical trial...
3/30/07 VU Colloquium 20
HistoryHistoryHistoryHistory
Ernest Rutherford (1934) --
“It seems to me that in some way it is r...
3/30/07 VU Colloquium 21
HistoryHistoryHistoryHistory
Gregor Mendel (1865) --
The classic case is Gregor Mendel’s
work on ...
3/30/07 VU Colloquium 22
HistoryHistoryHistoryHistory
Modern examples --
From nuclear and subnuclear physics ---
Reason: I...
3/30/07 VU Colloquium 23
HistoryHistoryHistoryHistory
3/30/07 VU Colloquium 24
HistoryHistoryHistoryHistory
3/30/07 VU Colloquium 25
B-meson lifetime ratio
The mean ratio has a χ2
of 4.5 for 13 degrees of freedom; Pχ=0.985
8 Major...
3/30/07 VU Colloquium 26
OutlineOutlineOutlineOutline
1. What is a “blind analysis”?
• What is a “bias”?
• Does “bias” = “...
3/30/07 VU Colloquium 27
An example of a “search” for an uncommon occurrence
A reaction that violates the Standard Model
c...
3/30/07 VU Colloquium 28
MEGA
Search for µ → eγ
Question: When and How are the
values of σ determined?
Signal: Ee = Eγ = 5...
3/30/07 VU Colloquium 29
MEGA
Search for µ → eγ
Blind Analysis: The boundaries are
determined before the analysis of
(most...
3/30/07 VU Colloquium 30
3/30/07 VU Colloquium 31
TWIST
High precision µ → eνµνe
ExamplesExamplesExamplesExamples
A search for physics beyond (not ...
3/30/07 VU Colloquium 32
Number
X = E/Emax
N(x) = a + bx
a,b from
theory
ExamplesExamplesExamplesExamples
Simulation = “Mo...
3/30/07 VU Colloquium 33
Muon decay spectrum
Current SM
η = -0.007 ± 0.013 0
ρ = 0.7518 ± 0.0026 3/4
δ = 0.7486 ± 0.0026 ±...
3/30/07 VU Colloquium 34
Energy
Cos(θ)
ExamplesExamplesExamplesExamples
Muon decay spectrum from Standard
Model
3/30/07 VU Colloquium 35
Energy
Cos(θ)
TWIST measured spectrum
ExamplesExamplesExamplesExamples
Energy
Cos(θ)
Standard Mod...
3/30/07 VU Colloquium 36
Energy
Cos(θ)
TWIST simulated spectrum
ρ,δ,
ξ,η
Energy
Cos(θ)
TWIST measured spectrum
ExamplesExa...
3/30/07 VU Colloquium 37
Energy
Cos(θ)
TWIST measured spectrum
ExamplesExamplesExamplesExamples
Energy
Cos(θ)
Standard Mod...
3/30/07 VU Colloquium 38
Energy
Cos(θ)
TWIST simulated spectrum
?
Energy
Cos(θ)
TWIST measured spectrum
ExamplesExamplesEx...
3/30/07 VU Colloquium 39
ExamplesExamplesExamplesExamples
Before you can open the black box:
• Get all computer codes work...
3/30/07 VU Colloquium 40
ExamplesExamplesExamplesExamples
ρo,δo,
ξo,ηo∆ρ = ρ’ - ρo
∆δ = δ’ - δo
∆ξ = ξ’ - ξo
∆η = η’ - ηo
...
3/30/07 VU Colloquium 41
ExamplesExamplesExamplesExamples
Let’s look at one of your experimentsLet’s look at one of your e...
3/30/07 VU Colloquium 42
ExamplesExamplesExamplesExamples
Present accepted value:
c = 299,792,458 m/s
c ≈ 3 x 108
m/s
A me...
3/30/07 VU Colloquium 43
ExamplesExamplesExamplesExamples
Present accepted value:
c = 299,792,458 m/s
c ≈ 3 x 108
m/s
A me...
3/30/07 VU Colloquium 44
OutlineOutlineOutlineOutline
1. What is a “blind analysis”?
• What is a “bias”?
• Does “bias” = “...
3/30/07 VU Colloquium 45
ReflectionsReflectionsReflectionsReflections
1. Guide to a blind analysis: If my answer
were to c...
3/30/07 VU Colloquium 46
ReflectionsReflectionsReflectionsReflections
4. It is not always possible to achieve perfect
“bli...
3/30/07 VU Colloquium 47
Thank
you
ReflectionsReflectionsReflectionsReflections
8. A blind analysis removes the
“comfort f...
3/30/07 VU Colloquium 48
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A Blind Analysis

  1. 1. A Blind AnalysisA Blind Analysis You are not allowed to peek!You are not allowed to peek! Prof. Donald Koetke Senior Research Professor of Physics Valparaiso University
  2. 2. 3/30/07 VU Colloquium 2 OutlineOutlineOutlineOutline 1. What is a “blind analysis”? • What is a “bias”? • Does “bias” = “systematic error”? • What is the special (subtle) bias? 2. What is the history of the blind analysis”? 3. What are examples of “blind analysis” in physics, astronomy, astrophysics, and, … ? 4. Some thoughts and reflections --
  3. 3. 3/30/07 VU Colloquium 3 OutlineOutlineOutlineOutline 1. What is a “blind analysis”? • What is a “bias”? • Does “bias” = “systematic error”? • What is the special (subtle) bias? 2. What is the history of the blind analysis”? 3. What are examples of “blind analysis” in physics, astronomy, astrophysics, and, … ? 4. Some thoughts and reflections --
  4. 4. 3/30/07 VU Colloquium 4 OutlineOutlineOutlineOutline 1. What is a “blind analysis”? • What is a “bias”? • Does “bias” = “systematic error”? • What is the special (subtle) bias? 2. What is the history of the blind analysis”? 3. What are examples of “blind analysis” in physics, astronomy, astrophysics, and, … ? 4. Some thoughts and reflections --
  5. 5. 3/30/07 VU Colloquium 5 OutlineOutlineOutlineOutline 1. What is a “blind analysis”? • What is a “bias”? • Does “bias” = “systematic error”? • What is the special (subtle) bias? 2. What is the history of the blind analysis”? 3. What are examples of “blind analysis” in physics, astronomy, astrophysics, and, … ? 4. Some thoughts and reflections --
  6. 6. 3/30/07 VU Colloquium 6 OutlineOutlineOutlineOutline 1. What is a “blind analysis”? • What is a “bias”? • Does “bias” = “systematic error”? • What is the special (subtle) bias? 2. What is the history of the blind analysis”? 3. What are examples of “blind analysis” in physics, astronomy, astrophysics, and, … ? 4. Some thoughts and reflections --
  7. 7. 3/30/07 VU Colloquium 7 OutlineOutlineOutlineOutline 1. What is a “blind analysis”? • What is a “bias”? • Does “bias” = “systematic error”? • What is the special (subtle) bias? 2. What is the history of the blind analysis”? 3. What are examples of “blind analysis” in physics, astronomy, astrophysics, and, … ? 4. Some thoughts and reflections --
  8. 8. 3/30/07 VU Colloquium 8 A Blind AnalysisA Blind AnalysisA Blind AnalysisA Blind Analysis What is a “bias”? Does “bias” = “systematic error”? What is the special (subtle) bias? “A prejudice in favor of or against” -- may be due to computer codes, equipment performance or setting, decisions/selections/cuts imposed, etc. Yes - if it causes a systematic shift in a result (This is not a “mistake” or “blunder”.) Experimenter bias in making decisions/choices to achieve a desired answer. Exampl es …
  9. 9. 3/30/07 VU Colloquium 9 A Blind AnalysisA Blind AnalysisA Blind AnalysisA Blind Analysis 1. You know what the answer “should be” - i.e., you know what the “accepted” answer is -- but your answer is different - outside of errors. What do you do? 2. You make a measurement and within errors it agrees with the “accepted” answer -- What do you do? You do an exper i ment and… Asymmetry!!
  10. 10. 3/30/07 VU Colloquium 10 A Blind AnalysisA Blind AnalysisA Blind AnalysisA Blind Analysis The goal of a “blind analysis” is to prevent the experimenter from (unconsciously - or consciously) making decisions in the analysis that would affect the result based on: • The predictions of a model or theory (e.g., the Standard Model for particle physics) • Previous measurements known to the experimenter • The experimenter’s intuition or other predisposition These are all examples of personal bias
  11. 11. 3/30/07 VU Colloquium 11 A Blind AnalysisA Blind AnalysisA Blind AnalysisA Blind Analysis 1. What is a “blind analysis”? A “blind analysis” is an analysis of measured data in which the final answer is kept hidden from the experimenters until all of the decisions about the analysis have been made: • Computer codes have been developed and tested • Decisions about the number of events (trials) needed have been made (cuts have been selected) • Apriori agreements are reached about what to do when the real answers from the experiment are revealed; no further analysis!
  12. 12. 3/30/07 VU Colloquium 12 OutlineOutline 1. What is a “blind analysis”? • What is a “bias”? • Does “bias” = “systematic error”? • What is the special (subtle) bias? 2. What is the history of the blind analysis”? 3. What are examples of “blind analysis” in physics, astronomy, astrophysics, and, … ? 4. Some thoughts and reflections --
  13. 13. 3/30/07 VU Colloquium 13 HistoryHistoryHistoryHistory Blind analysis begins in ~1930s with - Medical research -- blind tests! Patients don’t know whether they are getting -- a) the medicine/treatment, or, b) a placebo Patients are assigned to (a) or (b) ramdomly Therefore - the patients are “Therefore - the patients are “blindblind” to their treatment” to their treatmentTherefore - the patients are “Therefore - the patients are “blindblind” to their treatment” to their treatment They may i magi ne sympt oms or cur e, et c. , but onl y t he r esear cher / physi ci an knows i f t hese can be due t o t he medi ci ne/ t r eat ment .
  14. 14. 3/30/07 VU Colloquium 14 HistoryHistoryHistoryHistory Blind analysis begins in ~1930s with - Medical research -- blind tests! • Patients talk to medical researcher e.g., how are you feeling? is pain less or more? are the other problems? serious or not so serious? before or after you take the medicine? …etc. • Researcher hears what patient says • Researcher examines the patient • Researcher records all this as “data” Do you see aDo you see a problem here?problem here? Do you see aDo you see a problem here?problem here? c. f . , 1937 JAMA 26 June 2178/ 2.
  15. 15. 3/30/07 VU Colloquium 15 HistoryHistoryHistoryHistory Blind analysis begins in ~1930s with - Medical research -- blind tests! • Therefore, the medical researcher can (and will) unconsciously and unintentionally interpret and record the information (data) with this bias (knowledge). The patients are “The patients are “blindblind” to their treatment -” to their treatment - butbut,, the researcher isthe researcher is NOTNOT!! The patients are “The patients are “blindblind” to their treatment -” to their treatment - butbut,, the researcher isthe researcher is NOTNOT!! The solution is…
  16. 16. 3/30/07 VU Colloquium 16 Medical research -- The double blind test! HistoryHistoryHistoryHistory Blind analysis begins in ~1930s with - • The list of patients and their treatment is prepared and maintained by someone who is NOT participating in the research. The list is sealed in the “black box”. • The list can be retrieved from the “black box” only after all the analysis is completed. The patients are “The patients are “blindblind” to their treatment -” to their treatment - andand,, the researcher is “the researcher is “blindblind” to who is getting treated!” to who is getting treated! The patients are “The patients are “blindblind” to their treatment -” to their treatment - andand,, the researcher is “the researcher is “blindblind” to who is getting treated!” to who is getting treated! 1948 Am. Hear t Jr nl . , XXXVI , 529. 1950 Am. Jr nl . Med. , I X, 142/ 1.
  17. 17. 3/30/07 VU Colloquium 17 Medical research -- The double blind test! HistoryHistoryHistoryHistory Blind analysis begins in ~1930s with - Consider a simple analysis -- “Was the medicine effective?” • The data on all patients will indicate whether the medication was effective for each patient. • When this data analysis is complete (and free from mistakes) and any disagreement among the researchers have been settled and any concerns about bias have been removed, i.e., then (and only then) - • The “black box” can be opened and the list can be retrieved. • The data on all patients is now grouped into two groups: group (a) and group (b)
  18. 18. 3/30/07 VU Colloquium 18 Medical research -- The double blind test! HistoryHistoryHistoryHistory Blind analysis begins in ~1930s with - The simple analysis -- “Was the medicine effective?” • For what fraction of group (a) [fa] and group (b) [fb] was the medicine effective? • Do a statistical analysis to determine whether the difference in these two fractions is statistically significant - or whether it is consistent with a random occurrence. The result is now known! • The researchers agree to accept the results obtained and no further analysis of the data is permitted - unless there has been a blunder (mistake) - in which case fix the blunder and report both results and the nature of the “fix”.
  19. 19. 3/30/07 VU Colloquium 19 HistoryHistoryHistoryHistory Blind analysis has become the standard methodology in clinical trials. Blind analysis has been used in the physical sciences only in recent years. Physicists (and astronomers) are, of course -- -- Careful -- Quantitative -- Attentive to bias (systemtic errors) Why should they need a blind analysis?
  20. 20. 3/30/07 VU Colloquium 20 HistoryHistoryHistoryHistory Ernest Rutherford (1934) -- “It seems to me that in some way it is regrettable that we had a theory of the positive electron before the beginning of the experiments. Blackett* did everything possible not to be influenced by the theory, but the way of anticipating results must inevitably be influenced to some extent by the theory. I would have liked it better if the theory had arrived after the experimental facts had been established.” Ernest Rutherford, Proc. Solvay Conference, (Gauthier-Villars, Paris 1934), p 177. * Nobel prize in physics for discovering the positron (1948)
  21. 21. 3/30/07 VU Colloquium 21 HistoryHistoryHistoryHistory Gregor Mendel (1865) -- The classic case is Gregor Mendel’s work on inheritance. 84 degrees of freedom, giving a probability that he would have measured this well to be only 7x10-5 !! In every case the data agreed with the theoretical ratios within less than the standard errors. Taking the whole together, χ2 was 41.6 on
  22. 22. 3/30/07 VU Colloquium 22 HistoryHistoryHistoryHistory Modern examples -- From nuclear and subnuclear physics --- Reason: It’s the field in which the blind analysis techniques have been widely used - and - It is the field with which I am most familiar.
  23. 23. 3/30/07 VU Colloquium 23 HistoryHistoryHistoryHistory
  24. 24. 3/30/07 VU Colloquium 24 HistoryHistoryHistoryHistory
  25. 25. 3/30/07 VU Colloquium 25 B-meson lifetime ratio The mean ratio has a χ2 of 4.5 for 13 degrees of freedom; Pχ=0.985 8 Major experiments Over 2000 physicists Bottom line: The agreement appears to be too good!! HistoryHistoryHistoryHistory
  26. 26. 3/30/07 VU Colloquium 26 OutlineOutlineOutlineOutline 1. What is a “blind analysis”? • What is a “bias”? • Does “bias” = “systematic error”? • What is the special (subtle) bias? 2. What is the history of the blind analysis”? 3. What are examples of “blind analysis” in physics, astronomy, astrophysics, and, … ? 4. Some thoughts and reflections --
  27. 27. 3/30/07 VU Colloquium 27 An example of a “search” for an uncommon occurrence A reaction that violates the Standard Model conservation of lepton number If you do not find the reaction, you have not shown the Standard Model to be incorrect If you do find the reaction, you had better be very sure that you have got it right!!!
  28. 28. 3/30/07 VU Colloquium 28 MEGA Search for µ → eγ Question: When and How are the values of σ determined? Signal: Ee = Eγ = 52.8 MeV Boxes represent 2σ boundaries ExamplesExamplesExamplesExamples
  29. 29. 3/30/07 VU Colloquium 29 MEGA Search for µ → eγ Blind Analysis: The boundaries are determined before the analysis of (most of) the data! Signal: Ee = Eγ = 52.8 MeV Boxes represent 2σ boundaries ExamplesExamplesExamplesExamples
  30. 30. 3/30/07 VU Colloquium 30
  31. 31. 3/30/07 VU Colloquium 31 TWIST High precision µ → eνµνe ExamplesExamplesExamplesExamples A search for physics beyond (not included in) the Standard Model. pµ = 29.8 MeV/c Measure: pe(θ)
  32. 32. 3/30/07 VU Colloquium 32 Number X = E/Emax N(x) = a + bx a,b from theory ExamplesExamplesExamplesExamples Simulation = “Monte Carlo” Simulation of the experiment using a,b Nexp(x) = a’ + b’x Analyzed expimental data Find a’ & b’ by comparison of real data with simulated data Find a’ & b’ by comparison of real data with simulated data The detector system distorts the distribution
  33. 33. 3/30/07 VU Colloquium 33 Muon decay spectrum Current SM η = -0.007 ± 0.013 0 ρ = 0.7518 ± 0.0026 3/4 δ = 0.7486 ± 0.0026 ± 0.0028 3/4 Pµξ = 1.0027 ± 0.0079 ± 0.0030 1 )1(3)34( 3 2 )33( )(cos 0 2 2 x x x xx dxdx d −+−+−∝ Γ ηρ θ     −+−+ )34( 3 2 )1(cos xxP δθξμ ExamplesExamplesExamplesExamples
  34. 34. 3/30/07 VU Colloquium 34 Energy Cos(θ) ExamplesExamplesExamplesExamples Muon decay spectrum from Standard Model
  35. 35. 3/30/07 VU Colloquium 35 Energy Cos(θ) TWIST measured spectrum ExamplesExamplesExamplesExamples Energy Cos(θ) Standard Model spectrum Monte Carlo computer code ρ,δ, ξ,η
  36. 36. 3/30/07 VU Colloquium 36 Energy Cos(θ) TWIST simulated spectrum ρ,δ, ξ,η Energy Cos(θ) TWIST measured spectrum ExamplesExamplesExamplesExamples Problem! This spectrum is the S.M. spectrum -- nothing is hidden; the experimenter is not “blinded”. Compare spectra → ρ’,δ’,ξ’,η’ ρ’,δ’, ξ’,η’
  37. 37. 3/30/07 VU Colloquium 37 Energy Cos(θ) TWIST measured spectrum ExamplesExamplesExamplesExamples Energy Cos(θ) Standard Model spectrum Monte Carlo computer code ρo,δo, ξo,ηo Unknown spectrum ρo,δo,ξo,ηo are generated randomly, are encrypted, stored secretly, and used to generate the simulated data. Nobody knows what the offsets from ρ,δ,ξ,η are. ρo,δo,ξo,ηo are generated randomly, are encrypted, stored secretly, and used to generate the simulated data. Nobody knows what the offsets from ρ,δ,ξ,η are.
  38. 38. 3/30/07 VU Colloquium 38 Energy Cos(θ) TWIST simulated spectrum ? Energy Cos(θ) TWIST measured spectrum ExamplesExamplesExamplesExamples Compare spectra to get → ∆ρ, ∆δ, ∆ξ, ∆η ρ’,δ’, ξ’,η’ ∆ρ = ρ’ - ρo ∆δ = δ’ - δo ∆ξ = ξ’ - ξo ∆η = η’ - ηo
  39. 39. 3/30/07 VU Colloquium 39 ExamplesExamplesExamplesExamples Before you can open the black box: • Get all computer codes working and tested • Identify all sources of systematic error and evaluate the size of each one • Take all of the data you will need including data to help estimate the systematic errors • Be sure that the Monte Carlo programs accurately simulate your experiment or you will have false values • Analyze all of the data you intend to use to get the result ρo,δo, ξo,ηo
  40. 40. 3/30/07 VU Colloquium 40 ExamplesExamplesExamplesExamples ρo,δo, ξo,ηo∆ρ = ρ’ - ρo ∆δ = δ’ - δo ∆ξ = ξ’ - ξo ∆η = η’ - ηo Measure Calculate the results Compare with Standard Model predictions Write the paper
  41. 41. 3/30/07 VU Colloquium 41 ExamplesExamplesExamplesExamples Let’s look at one of your experimentsLet’s look at one of your experiments from PHYS-245from PHYS-245
  42. 42. 3/30/07 VU Colloquium 42 ExamplesExamplesExamplesExamples Present accepted value: c = 299,792,458 m/s c ≈ 3 x 108 m/s A measurement of the speed of light 1 2 θ T osc t = θ 2π T ⇒ c = D t D
  43. 43. 3/30/07 VU Colloquium 43 ExamplesExamplesExamplesExamples Present accepted value: c = 299,792,458 m/s c ≈ 3 x 108 m/s A measurement of the speed of light 1 2 θ T osc t = θ 2π T ⇒ c = D t D To =T +δT To co Blinded
  44. 44. 3/30/07 VU Colloquium 44 OutlineOutlineOutlineOutline 1. What is a “blind analysis”? • What is a “bias”? • Does “bias” = “systematic error”? • What is the special (subtle) bias? 2. What is the history of the blind analysis”? 3. What are examples of “blind analysis” in physics, astronomy, astrophysics, and, … ? 4. Some thoughts and reflections --
  45. 45. 3/30/07 VU Colloquium 45 ReflectionsReflectionsReflectionsReflections 1. Guide to a blind analysis: If my answer were to come out to be six standard deviations from the expected result, what would I do? Make the list, and then - do all of that bef or e you look at the answer! 2. A blind analysis is intended to guard against experimenter bias. It will not guard against fraud; that requires integrity and honesty. 3. A blind analysis is likely not the fastest way to an answer.
  46. 46. 3/30/07 VU Colloquium 46 ReflectionsReflectionsReflectionsReflections 4. It is not always possible to achieve perfect “blindness” -- e.g., drug testing. 5. Don’t need to plan everything in the analysis before beginning; just keep the answer hidden. 6. A blind analysis may not work for every experiment - but it is worth investigating before you begin. 7. In a blind analysis you want to hide the answer from anyone else who might want to offer advice that may be based on the answer.
  47. 47. 3/30/07 VU Colloquium 47 Thank you ReflectionsReflectionsReflectionsReflections 8. A blind analysis removes the “comfort factor” - knowing what answer you are getting so you can make changes, do more analysis, repeat measurements, etc., if the answer is not what you expect. But, that may not be the best science!But, that may not be the best science!But, that may not be the best science!But, that may not be the best science!
  48. 48. 3/30/07 VU Colloquium 48

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