Resolved: All Data Are Wrong (by definition)

Most data analysis focuses on the analysis and presentation of data, as if the data are somehow divine. Most people remain blissfully unaware of the fact that all data has to be sourced and that sourcing requires the application of a measurement process. The measurement process always introduces discrepancies between the expected result and the actual result. This talk presents examples of bad data presentation and then shows you how to make measurement discrepancies explicit.

Transcript

1. Resolved: All Data Are Wrong
   (by definition)
   Dr. Neil Gunther
   Performance Dynamics
   Distributed Systems Meetup Online
   Pune, INDIA
   April 11 2020
   SM
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2. Abstract
   “In God we Trust, all others must bring data” is a quote usually attributed to the famous proponent of
   data-driven decisions, William Edwards Deming. His unique viewpoint (c.1950) was that data analysis is
   essential for achieving superior performance in all facets of manufacturing. Today, the SARS-COV-2 pandemic
   has highlighted the importance of data-driven decisions in the effort to combat its devastating impact until a
   vaccine becomes available. Deming’s approach, however, though necessary, is not sufficient. Put more bluntly,
   how do I know the data you are bringing is any good? Early Covid-19 data was manipulated by the Chinese
   government. Russia has since been accused of the same thing. But, even if the data have not been doctored,
   that doesn’t mean you should treat data as sacrosanct — no matter the context. The illusion that data are divine
   comes, in part, from the naive acceptance of the way measured values are reported. For example, a %cpu of
   72.2, is commonly seen in various O/S performance tools. This pristine numerical representation gives the
   illusion of a divine source: an illusion that is especially rampant in distributed performance monitoring
   applications. In reality, data are devilish and thus need to be ‘waterboarded’ to extract the truth. In this talk, I’ll
   show you how.
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3. Introduction
   Outline
   1 Introduction
   2 Measurement Basics
   3 Bad Data Examples
   4 How to Express Errors
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4. Introduction
   Things I’ve Tweeted about data
   All data are wrong ... by definition
   Treating data as divine is a sin
   Measurement is much more than just sucking up data from various repositories
   You can’t trust Data Scientists with data because they never learnt to make measurements
   Measurement is a process, not a number
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5. Introduction
   Typical performance data
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6. Introduction
   Types of data
   Linux ‘top’ shows both
   Continuous data: These data have fractional values (usually ≥ 0)
   Represented by positive reals
   Decimal point, R≥0
   Examples: %CPU column, timestamp
   Discrete data: These data are whole numbers (usually ≥ 0)
   Counts represented by positive integers
   Cardinals +0, Z+
   Examples: memory pages, packets
   Won’t be considering:
   Categorical data
   Nominal data
   Ordinal data
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7. Measurement Basics
   Outline
   1 Introduction
   2 Measurement Basics
   3 Bad Data Examples
   4 How to Express Errors
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8. Measurement Basics
   Measure twice ...
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9. Measurement Basics
   ... cut once
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10. Measurement Basics
    No perfect measurement
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11. Measurement Basics
    Cut me some slack
    The expected value is never identical to the actual value
    How much slack should be allowed between the expected (pencil line) and
    actual (saw cut)?
    Construction: Woodframe tolerance 1/8" (USA) or 2 mm ISO (EU).
    Your Income: It’s tax season. How accurate are the amounts on your income
    tax filing? Try asking your CPA.
    GFC 2008: How many mortgages went into default? How much real money
    was actually lost? These are BANKS! How could they not
    know?
    We don’t have any “building code” tolerances in the IT world.
    Generally done (if at all) on an ad hoc design basis.
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12. Bad Data Examples
    Outline
    1 Introduction
    2 Measurement Basics
    3 Bad Data Examples
    4 How to Express Errors
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13. Bad Data Examples
    Superluminal neutrino data
    Sept 2011: OPERA/LHC Italian team announces neutrinos vν
    > c
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14. Bad Data Examples
    Superluminal neutrino data
    Sept 2011: OPERA/LHC Italian team announces neutrinos vν
    > c
    Big deal: Implies Einstein was wrong coz SRT is badly broken
    Extremely difficult measurements
    “It only takes ONE experiment to prove me wrong”
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15. Bad Data Examples
    Superluminal neutrino data
    Sept 2011: OPERA/LHC Italian team announces neutrinos vν
    > c
    Big deal: Implies Einstein was wrong coz SRT is badly broken
    Extremely difficult measurements
    “It only takes ONE experiment to prove me wrong”
    Data check: 6σ confidence level
    1 in a BILLION chance that these data are a fluke
    5σ (1 in a million) is sufficient for particle physics (e.g., Higgs boson)
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16. Bad Data Examples
    Superluminal neutrino data
    Sept 2011: OPERA/LHC Italian team announces neutrinos vν
    > c
    Big deal: Implies Einstein was wrong coz SRT is badly broken
    Extremely difficult measurements
    “It only takes ONE experiment to prove me wrong”
    Data check: 6σ confidence level
    1 in a BILLION chance that these data are a fluke
    5σ (1 in a million) is sufficient for particle physics (e.g., Higgs boson)
    Dec 2011: OPERA team withdraws paper
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17. Bad Data Examples
    Superluminal neutrino data
    Sept 2011: OPERA/LHC Italian team announces neutrinos vν
    > c
    Big deal: Implies Einstein was wrong coz SRT is badly broken
    Extremely difficult measurements
    “It only takes ONE experiment to prove me wrong”
    Data check: 6σ confidence level
    1 in a BILLION chance that these data are a fluke
    5σ (1 in a million) is sufficient for particle physics (e.g., Higgs boson)
    Dec 2011: OPERA team withdraws paper
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18. Bad Data Examples
    Superluminal neutrinos disappear
    Unlocked: vν
    > c Locked: vν
    < c
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19. Bad Data Examples
    Superluminal neutrinos disappear
    Unlocked: vν
    > c Locked: vν
    < c
    OPERA team manager also disappeared
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20. Bad Data Examples
    Hubble’s bubble 1929
    The most important scatter plot in history (1 pc = 3.3 ly)
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21. Bad Data Examples
    Hubble’s trouble 1929
    1 Linear regression model ˆ
    y = 423.94 x1
    (through origin, c = 0)
    regressand ˆ
    y: recession velocity (km/sec)
    regressor x1
    : enormous distance to the “stars”
    2 Slope (rise/run) =⇒ expansion rate H0
    (inverse time units)
    3 Inverted slope =⇒ time the universe has been expanding
    4 Edwin double checked and “corrected” the slope (in wrong direction!)
    H0
    465.18 km/s/Mpc (Hubble’s constant)
    Tuniv
    2 billion years
    5 Tearth > 3 billion yrs in 1929 ... 4.5 billion yrs today
    6 Oops! What do you do?
    Toss it (data says you’re wrong)
    Publish (possibly destroy your career)
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22. Bad Data Examples
    Hubble’s win 2003
    Data comes from the Devil; models come from God (H0
    70 today)
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23. Bad Data Examples
    Counting is easy
    Can’t have errors ... right?
    But might get entangled
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24. Bad Data Examples
    CERN LHC paper
    “ATLAS Collaboration” is a proxy for the entire experimental team
    Too many authors to fit under the paper title
    But exactly how many?
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25. Bad Data Examples
    CERN authors
    Author list is 15 appended pages!
    Article limit is 4 pages
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26. Bad Data Examples
    CERN authors
    Author list is 15 appended pages!
    Article limit is 4 pages
    More than 3000 authors !!!
    · · · · · · · · ·
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27. Bad Data Examples
    Just write a progam (right?)
    Author counts Sources or error:
    PDF has to be parsed as text
    Comma separators, new lines, etc.
    Weird numbers for author affiliation
    Different programs get different counts
    What about the tea lady?
    Streaming counts Sources or error:
    Is counter or sensor working correctly?
    Is event being triggered correctly?
    Is the count being transported reliably?
    Is count being accumulated correctly?
    Are statistics (quantiles, histrograms, etc.)
    What is the error margin?
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28. Bad Data Examples
    Load average — mangled metrics
    [njg]~% uptime
    11:28 up 2:50, 3 users, load averages: 0.91 1.09 1.08
    Load average is the original performance tool (c.1965)
    Measures run-queue length in Unix/Linux OS
    Not your average kind of average (low-pass filter)
    In Solaris 2.0 and 2.2 kernel code for LA was modified
    Sun Microsystems never told anyone
    Remained broken until Solaris 2.3
    If you used it for sys admin or capacity planning ... good luck!
    Software is so malleable
    You need to regression test your vendor perf tools
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29. How to Express Errors
    Outline
    1 Introduction
    2 Measurement Basics
    3 Bad Data Examples
    4 How to Express Errors
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30. How to Express Errors
    All data has errors
    1 Data has to be sourced
    2 The source is usually some form of measuring instrument(ation)
    3 Measuring always introduces errors (wrongness)
    4 All data are wrong
    5 The real question is:
    How big is that wrongidity?
    How much wrongidityness can you tolerate? (SLAs)
    Out of sight, out of mind
    A widespread problem today is that most people doing data analysis are far
    removed from the sources of data and the type of measurement processes
    that generated those data. Blissfully unaware of the measurement aspect, the
    whole notion of errors never enters their mind. Data appear divine.
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31. How to Express Errors
    Expressing measurement error
    Need more that one sample measurement
    1 Take n data samples
    2 Take the sample mean (usual average)
    3 Take the sample standard deviation around that mean
    4 Compute the standard error (divide std dev by
    √
    n)
    5 Write the result as mean ± std error
    6 Range around the mean quantifies the error margin
    7 Rule of thumb:
    Relative error:
    std error
    mean
    × 100
    A standard error of around ±5% is typical and acceptable
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32. How to Express Errors
    Example
    times.ms plot(times.ms, type="h", col="blue", xlab="Sample", ylab="Time (ms)")
    # data analysis
    mu sd se cat(sprintf("Reported value: %.2f \u00b1 %.2f ms\n", mu, se))
    abline(h=mu, col="red")
    abline(h=mu + se, col="red", lty="dashed")
    abline(h=mu - se, col="red", lty="dashed")
    Reported value: 9.87 ± 0.32 ms
    0 20 40 60 80 100
    5 10 15
    Sample
    Time (ms)
    0 20 40 60 80 100
    5 10 15
    Sample
    Time (ms)
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33. How to Express Errors
    Other error representations
    See slide 17 for error bars on Hubble data
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34. How to Express Errors
    Covid-19 curves (Added)
    Financial Times daily SIR curves don’t show any error bars (but could)
    Appear each day on Twitter
    Created by John Burn-Murdoch @jburnmurdoch
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35. How to Express Errors
    Confidence intervals
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36. How to Express Errors
    Significant digits
    Guerrilla CaP book Chap. 3
    Can’t have more digits reported than
    the smallest resolution of the measuring
    instrument
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37. How to Express Errors
    Accuracy vs. precision
    Also in Chap. 3
    Archery targets
    Distance from bullseye
    analogous to accuracy
    Clustering analogous to
    precision
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38. How to Express Errors
    Hubble’s data
    Hubble didn’t have a
    precision problem
    He had an accuracy
    problem
    His data was way off the
    bullseye
    Systematic error in 1920s
    telescope optics
    Likely suspected that or
    wouldn’t have published
    But made it worse by
    “correcting” the slope
    Despite all that, his linear
    model survived
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39. How to Express Errors
    

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40. How to Express Errors
    Check. Check. Then check again!
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41. How to Express Errors
    Waterboading your data
    0 100 200 300 400
    0 100 200 300 400 500
    Measured Throughput
    Offered load
    TPS
    0 100 200 300 400
    0 100 200 300 400
    Measured Response Time
    Offered load
    ms
    0 100 200 300 400
    0 100 200 300 400
    Running Threads
    Offered load
    Active threads
    Use Little’s law N = X ∗ R
    X and R are measured directly
    N: offered load on DVR side
    X ∗ R: actual load on SUT side
    N = X ∗ R !?
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42. How to Express Errors
    Summary
    All data are wrong. Why?
    Measurement is a process
    That process introduces errors (systematic, random, etc.)
    Need to see error margin to decide acceptability
    Check ... check .... and check again
    Measurements are repesented by numbers (but not math)
    Numbers like 72 or 72.37 are not sufficient
    Require 72.37 ±0.21 to indicate error explicitly
    Don’t exceed sigfigs
    Need (i) sample mean ˆ
    µ and (ii) sample standard deviation ˆ
    σ
    Measure n samples (1-shots are meaningless)
    Standard error: ˆ
    σ/
    √
    n
    Reported value: ˆ
    µ ± ˆ
    σ/
    √
    n (as above)
    But reporting errors does not guarantee meaningfulness (remember those neutrinos)
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43. How to Express Errors
    Wanna know more?
    1. Guerrilla book 2. Online training
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44. Comments and/or Questions?
    Performance Dynamics
    Castro Valley, California
    www.perfdynamics.com
    Training
    Twitter
    Facebook
    Blog
    info@perfdynamics.com
    +1-510-537-5758
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