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• Philip Tellis

•                           .com
• philip@lognormal.com
• @bluesmoon
• geek paranoid speedfreak
• http://bluesmoon.info/




    Boston #WebPerf Meetup / 2012-08-14   The Statistics of Web Performance Analysis   1
I’m a Web Speedfreak




Boston #WebPerf Meetup / 2012-08-14   The Statistics of Web Performance Analysis   2
We measure real user website performance




Boston #WebPerf Meetup / 2012-08-14   The Statistics of Web Performance Analysis   3
This talk is about the Statistics we learned while building it




  Boston #WebPerf Meetup / 2012-08-14   The Statistics of Web Performance Analysis   4

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Report on financial statement for five years using trend, comparative & comm...
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satyendra.upreti2011@gmail.com
The Statistics of Web Performance Analysis

            Philip Tellis / philip@lognormal.com


             Boston #WebPerf Meetup / 2012-08-14




 Boston #WebPerf Meetup / 2012-08-14   The Statistics of Web Performance Analysis   5
0
                             Numbers



Boston #WebPerf Meetup / 2012-08-14   The Statistics of Web Performance Analysis   6
Accurately measure page performance∗




Boston #WebPerf Meetup / 2012-08-14   The Statistics of Web Performance Analysis   7
Be unintrusive




     If you try to measure something accurately, you will change
                          something related
                                                                       – Heisenberg’s uncertainty principle




       Boston #WebPerf Meetup / 2012-08-14   The Statistics of Web Performance Analysis                       8

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And one number to rule them all




Boston #WebPerf Meetup / 2012-08-14   The Statistics of Web Performance Analysis   9
What do we measure?




    • Network Throughput
    • Network Latency
    • User perceived page load time




      Boston #WebPerf Meetup / 2012-08-14   The Statistics of Web Performance Analysis   10
We measure real user data




Boston #WebPerf Meetup / 2012-08-14   The Statistics of Web Performance Analysis   11
Which is noisy




Boston #WebPerf Meetup / 2012-08-14   The Statistics of Web Performance Analysis   12

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1
                        Statistics - 1



Boston #WebPerf Meetup / 2012-08-14   The Statistics of Web Performance Analysis   13
Disclaimer




   I am not a statistician




      Boston #WebPerf Meetup / 2012-08-14   The Statistics of Web Performance Analysis   14
1-1  Random Sampling



Boston #WebPerf Meetup / 2012-08-14   The Statistics of Web Performance Analysis   15
Population



                        All possible users of your system




       Boston #WebPerf Meetup / 2012-08-14   The Statistics of Web Performance Analysis   16

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Sample



                    Representative subset of the population




         Boston #WebPerf Meetup / 2012-08-14   The Statistics of Web Performance Analysis   17
Bad sample



                                   Sometimes it’s not




      Boston #WebPerf Meetup / 2012-08-14   The Statistics of Web Performance Analysis   18
How to randomize?




                                                                                   http://xkcd.com/221/




      Boston #WebPerf Meetup / 2012-08-14   The Statistics of Web Performance Analysis                    19
How to randomize?




      • Pick 10% of users at random and always test them

                                               OR

      • For each user, decide at random if they should be tested

   http://tech.bluesmoon.info/2010/01/statistics-of-performance-measurement.html




         Boston #WebPerf Meetup / 2012-08-14   The Statistics of Web Performance Analysis   20

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Select 10% of users - I




       if($sessionid % 10 === 0) {
          // instrument code for measurement
       }

     • Once a user enters the measurement bucket, they stay
       there until they log out
     • Fixed set of users, so tests may be more consistent
     • Error in the sample results in positive feedback




       Boston #WebPerf Meetup / 2012-08-14   The Statistics of Web Performance Analysis   21
Select 10% of users - II




       if(rand() < 0.1 * getrandmax()) {
          // instrument code for measurement
       }

     • For every request, a user has a 10% chance of being
       tested
     • Gets rid of positive feedback errors, but sample size !=
       10% of population




       Boston #WebPerf Meetup / 2012-08-14   The Statistics of Web Performance Analysis   22
How big a sample is representative?




                                     Select n such that
                                     σ
                                1.96 √n ≤ 5%µ




       Boston #WebPerf Meetup / 2012-08-14   The Statistics of Web Performance Analysis   23
1-2     Margin of Error



Boston #WebPerf Meetup / 2012-08-14   The Statistics of Web Performance Analysis   24

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Standard Deviation

     • Standard deviation tells you the spread of the curve
     • The narrower the curve, the more confident you can be




       Boston #WebPerf Meetup / 2012-08-14   The Statistics of Web Performance Analysis   25
MoE at 95% confidence




                                       σ
                                 ±1.96 √n




      Boston #WebPerf Meetup / 2012-08-14   The Statistics of Web Performance Analysis   26
MoE & Sample size




   There is an inverse square root correlation between sample size
                         and margin of error




       Boston #WebPerf Meetup / 2012-08-14   The Statistics of Web Performance Analysis   27
1-3   Central Tendency



Boston #WebPerf Meetup / 2012-08-14   The Statistics of Web Performance Analysis   28

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Boston #WebPerf Meetup / 2012-08-14   The Statistics of Web Performance Analysis   29
One number




    • Mean (Arithmetic)
       • Good for symmetric curves
       • Affected by outliers


                Mean(10, 11, 12, 11, 109) = 30




      Boston #WebPerf Meetup / 2012-08-14   The Statistics of Web Performance Analysis   30
One number




    • Median
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       • Not trivial to pull out of a DB


              Median(10, 11, 12, 11, 109) = 11




      Boston #WebPerf Meetup / 2012-08-14   The Statistics of Web Performance Analysis   31
One number




    • Mode
       • Not often used
       • Multi-modal distributions suggest problems


                Mode(10, 11, 12, 11, 109) = 11




      Boston #WebPerf Meetup / 2012-08-14   The Statistics of Web Performance Analysis   32

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Other numbers




    • A percentile point in the distribution: 95th , 98.5th or 99th
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                P95th (10, 11, 12, 11, 109) = 12




      Boston #WebPerf Meetup / 2012-08-14   The Statistics of Web Performance Analysis   33
Other means




    • Geometric mean
        • Good if your data is exponential in nature
          (with the tail on the right)


           GMean(10, 11, 12, 11, 109) = 16.68




      Boston #WebPerf Meetup / 2012-08-14   The Statistics of Web Performance Analysis   34
Wait... how did I get that?




                N
                    ΠN xi — could lead to overflow
                     i=1

               ΣN loge (xi )
                i=1
                    N
          e                       — computationally simpler




       Boston #WebPerf Meetup / 2012-08-14   The Statistics of Web Performance Analysis   35
Wait... how did I get that?




                N
                    ΠN xi — could lead to overflow
                     i=1

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                i=1
                    N
          e                       — computationally simpler




       Boston #WebPerf Meetup / 2012-08-14   The Statistics of Web Performance Analysis   35

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Wait... how did I get that?




                N
                    ΠN xi — could lead to overflow
                     i=1

               ΣN loge (xi )
                i=1
                    N
          e                       — computationally simpler




       Boston #WebPerf Meetup / 2012-08-14   The Statistics of Web Performance Analysis   35
Wait... how did I get that?




                N
                    ΠN xi — could lead to overflow
                     i=1

               ΣN loge (xi )
                i=1
                    N
          e                       — computationally simpler




       Boston #WebPerf Meetup / 2012-08-14   The Statistics of Web Performance Analysis   35
Other means




    And there is also the Harmonic mean, but forget about that




      Boston #WebPerf Meetup / 2012-08-14   The Statistics of Web Performance Analysis   36
...though consequently




   We have other margins of error
    • Geometric margin of error
          • Uses geometric standard deviation
     • Median margin of error
        • Uses ranges of actual values from data set
     • Stick to the arithmetic MoE
       – simpler to calculate, simpler to read and not incorrect




       Boston #WebPerf Meetup / 2012-08-14   The Statistics of Web Performance Analysis   37

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...though consequently




   We have other margins of error
    • Geometric margin of error
          • Uses geometric standard deviation
     • Median margin of error
        • Uses ranges of actual values from data set
     • Stick to the arithmetic MoE
       – simpler to calculate, simpler to read and not incorrect




       Boston #WebPerf Meetup / 2012-08-14   The Statistics of Web Performance Analysis   37
2
                        Statistics - 2



Boston #WebPerf Meetup / 2012-08-14   The Statistics of Web Performance Analysis   38
2-1         Distributions



Boston #WebPerf Meetup / 2012-08-14   The Statistics of Web Performance Analysis   39
Let’s look at some real charts




Boston #WebPerf Meetup / 2012-08-14   The Statistics of Web Performance Analysis   40

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Sparse Distribution




       Boston #WebPerf Meetup / 2012-08-14   The Statistics of Web Performance Analysis   41
Log-normal distribution




       Boston #WebPerf Meetup / 2012-08-14   The Statistics of Web Performance Analysis   42
Bimodal distribution




       Boston #WebPerf Meetup / 2012-08-14   The Statistics of Web Performance Analysis   43
What does all of this mean?




Boston #WebPerf Meetup / 2012-08-14   The Statistics of Web Performance Analysis   44

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Distributions




     • Sparse distribution suggests that you don’t have enough
       data points
     • Log-normal distribution is typical
     • Bi-modal distribution suggests two (or more) distributions
       combined




       Boston #WebPerf Meetup / 2012-08-14   The Statistics of Web Performance Analysis   45
In practice, a bi-modal distribution is not uncommon




Boston #WebPerf Meetup / 2012-08-14   The Statistics of Web Performance Analysis   46
Hint: Does your site do a lot of back-end caching?




Boston #WebPerf Meetup / 2012-08-14   The Statistics of Web Performance Analysis   47
2-2               Filtering



Boston #WebPerf Meetup / 2012-08-14   The Statistics of Web Performance Analysis   48

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Boston Web Performance Meetup, April 22, 2014 The very first requirement of a great user experience is actually getting the bytes of that experience to the user before they they get fed up and leave. In this talk we'll start with the basics and get progressively insane. We'll go over several front-end performance best practices, a few anti-patterns, the reasoning behind the rules, and how they've changed over the years. We'll also look at some great tools to help you. Schedule: 6:30, pizza 7:15: talk

httpnetworkfrontend
Outliers




                                                        • Out of range data points
                                                        • Nothing you can fix here
                                                        • There’s even a book about
                                                           them




       Boston #WebPerf Meetup / 2012-08-14   The Statistics of Web Performance Analysis   49
Outliers




                                                        • Out of range data points
                                                        • Nothing you can fix here
                                                        • There’s even a book about
                                                           them




       Boston #WebPerf Meetup / 2012-08-14   The Statistics of Web Performance Analysis   49
Outliers




                                                        • Out of range data points
                                                        • Nothing you can fix here
                                                        • There’s even a book about
                                                           them




       Boston #WebPerf Meetup / 2012-08-14   The Statistics of Web Performance Analysis   49
Outliers




                                                        • Out of range data points
                                                        • Nothing you can fix here
                                                        • There’s even a book about
                                                           them




       Boston #WebPerf Meetup / 2012-08-14   The Statistics of Web Performance Analysis   49

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mmm... beacons
mmm... beaconsmmm... beacons
mmm... beacons

The document appears to be a presentation on measuring real user experiences using Real User Monitoring (RUM) and analyzing the data. It discusses using RUM tools like Boomerang to collect data on user behavior and performance in real-time. The presentation then examines specific metrics collected like user patience, cache behavior, and how quickly new software versions are distributed based on the RUM data.

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Part I of RUM Distillation 101. Part II is by Jonathan Klein available here: http://www.slideshare.net/jnklein/uxfest-performance-a

uxfestperformancerum
DNS problems can cause outliers




     • 2 or 3 DNS servers for an ISP
     • 30 second timeout if first fails
     • ... 30 second increase in page load time
     • Maybe measure both and fix what you can
     • http://nms.lcs.mit.edu/papers/dns-ton2002.pdf




       Boston #WebPerf Meetup / 2012-08-14   The Statistics of Web Performance Analysis   50
Band-pass filtering




       Boston #WebPerf Meetup / 2012-08-14   The Statistics of Web Performance Analysis   51
Band-pass filtering




     • Strip everything outside a reasonable range
         • Bandwidth range: 4kbps - 4Gbps
         • Page load time: 50ms - 120s
     • You may need to relook at the ranges all the time




       Boston #WebPerf Meetup / 2012-08-14   The Statistics of Web Performance Analysis   51
IQR filtering




       Boston #WebPerf Meetup / 2012-08-14   The Statistics of Web Performance Analysis   52

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Extending Boomerang
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The document discusses Boomerang, an open source tool for measuring real user performance on websites. It measures load times, bandwidth usage, latency and other metrics. Additional functionality can be added through plugins. The presentation encourages developers to use Boomerang to analyze user behavior, identify performance issues, and continuously improve sites based on real user data. It provides several examples of insights that can be gained, such as how performance varies by country, browser, and internet connection speed.

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Abusing JavaScript to measure Web Performance, or, "how does boomerang work?"
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The document is a presentation about abusing JavaScript to measure web performance. It discusses using JavaScript to measure network latency, TCP handshake time, network throughput, DNS lookup time, IPv6 support and latency, and other performance metrics. It provides code examples for measuring each metric in JavaScript and notes challenges to consider. The presentation encourages the use of the open source Boomerang library for accurate performance measurement.

webperfboomerangnetwork
IQR filtering




                  Here, we derive the range from the data




       Boston #WebPerf Meetup / 2012-08-14   The Statistics of Web Performance Analysis   52
Further Reading




   lognormal.com/blog/2012/08/13/analysing-performance-data/




      Boston #WebPerf Meetup / 2012-08-14   The Statistics of Web Performance Analysis   53
Summary




    • Choose a reasonable sample size and sampling factor
    • Tune sample size for minimal margin of error
    • Decide based on your data whether to use mode, median
      or one of the means
    • Figure out whether your data is Normal, Log-Normal or
      something else
    • Filter out anomalous outliers




      Boston #WebPerf Meetup / 2012-08-14   The Statistics of Web Performance Analysis   54
• Philip Tellis

•                           .com
• philip@lognormal.com
• @bluesmoon
• geek paranoid speedfreak
• http://bluesmoon.info/




    Boston #WebPerf Meetup / 2012-08-14   The Statistics of Web Performance Analysis   55

Recommended for you

Abusing JavaScript to Measure Web Performance
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While building boomerang, we developed many interesting methods to measure network performance characteristics using JavaScript running in the browser. While the W3C's NavigationTiming API provides access to many performance metrics, there's far more you can get at with some creative tweaking and analysis of how the browser reacts to certain requests. In this talk, I'll go into the details of how boomerang works to measure network throughput, latency, TCP connect time, DNS time and IPv6 connectivity. I'll also touch upon some of the other performance related browser APIs we use to gather useful information. I will NOT be covering the W3C Navigation Timing API since that's been covered by Alois Reitbauer in a previous Boston Web Perf talk.

webperfbostonmeetup
Rum for Breakfast
Rum for BreakfastRum for Breakfast
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The document discusses analyzing real user monitoring (RUM) data to gain insights into website performance and user behavior. It describes building plugins to collect navigation and timing data from browsers. Various statistical techniques for analyzing the data are covered, including log-normal distributions, filtering outliers, sampling, and correlating metrics like page load time and bounce rates. The analysis of an example 8 million page dataset suggests very fast or slow page loads are associated with higher bounce rates, and thresholds for user-unfriendly performance are proposed based on bounce rates exceeding 50%.

webperfperformanceinsights
Analysing network characteristics with JavaScript
Analysing network characteristics with JavaScriptAnalysing network characteristics with JavaScript
Analysing network characteristics with JavaScript

This document contains slides from a presentation about using JavaScript to analyze network performance. It discusses how to measure latency, TCP handshake time, network throughput, DNS lookup time, IPv6 support and latency, and private network scanning using JavaScript. Code examples are provided for measuring each of these network metrics by making image requests and timing the responses. The presentation emphasizes that accurately measuring network throughput requires requesting resources of different sizes and accounting for TCP slow start. It also notes some challenges around caching and geo-located DNS results.

networkingsecurityjavascript
Thank you




Boston #WebPerf Meetup / 2012-08-14   The Statistics of Web Performance Analysis   56
Photo credits




     • http://www.flickr.com/photos/leoffreitas/332360959/ by leoffreitas
     • http://www.flickr.com/photos/cobalt/56500295/ by cobalt123
     • http://www.flickr.com/photos/sophistechate/4264466015/ by Lisa
       Brewster




       Boston #WebPerf Meetup / 2012-08-14   The Statistics of Web Performance Analysis   57
List of figures




     • http://en.wikipedia.org/wiki/File:Standard_deviation_diagram.svg
     • http://en.wikipedia.org/wiki/File:Normal_Distribution_PDF.svg
     • http://en.wikipedia.org/wiki/File:KilroySchematic.svg
     • http://en.wikipedia.org/wiki/File:Boxplot_vs_PDF.png




       Boston #WebPerf Meetup / 2012-08-14   The Statistics of Web Performance Analysis   58

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The Statistics of Web Performance Analysis

  • 1. • Philip Tellis • .com • philip@lognormal.com • @bluesmoon • geek paranoid speedfreak • http://bluesmoon.info/ Boston #WebPerf Meetup / 2012-08-14 The Statistics of Web Performance Analysis 1
  • 2. I’m a Web Speedfreak Boston #WebPerf Meetup / 2012-08-14 The Statistics of Web Performance Analysis 2
  • 3. We measure real user website performance Boston #WebPerf Meetup / 2012-08-14 The Statistics of Web Performance Analysis 3
  • 4. This talk is about the Statistics we learned while building it Boston #WebPerf Meetup / 2012-08-14 The Statistics of Web Performance Analysis 4
  • 5. The Statistics of Web Performance Analysis Philip Tellis / philip@lognormal.com Boston #WebPerf Meetup / 2012-08-14 Boston #WebPerf Meetup / 2012-08-14 The Statistics of Web Performance Analysis 5
  • 6. 0 Numbers Boston #WebPerf Meetup / 2012-08-14 The Statistics of Web Performance Analysis 6
  • 7. Accurately measure page performance∗ Boston #WebPerf Meetup / 2012-08-14 The Statistics of Web Performance Analysis 7
  • 8. Be unintrusive If you try to measure something accurately, you will change something related – Heisenberg’s uncertainty principle Boston #WebPerf Meetup / 2012-08-14 The Statistics of Web Performance Analysis 8
  • 9. And one number to rule them all Boston #WebPerf Meetup / 2012-08-14 The Statistics of Web Performance Analysis 9
  • 10. What do we measure? • Network Throughput • Network Latency • User perceived page load time Boston #WebPerf Meetup / 2012-08-14 The Statistics of Web Performance Analysis 10
  • 11. We measure real user data Boston #WebPerf Meetup / 2012-08-14 The Statistics of Web Performance Analysis 11
  • 12. Which is noisy Boston #WebPerf Meetup / 2012-08-14 The Statistics of Web Performance Analysis 12
  • 13. 1 Statistics - 1 Boston #WebPerf Meetup / 2012-08-14 The Statistics of Web Performance Analysis 13
  • 14. Disclaimer I am not a statistician Boston #WebPerf Meetup / 2012-08-14 The Statistics of Web Performance Analysis 14
  • 15. 1-1 Random Sampling Boston #WebPerf Meetup / 2012-08-14 The Statistics of Web Performance Analysis 15
  • 16. Population All possible users of your system Boston #WebPerf Meetup / 2012-08-14 The Statistics of Web Performance Analysis 16
  • 17. Sample Representative subset of the population Boston #WebPerf Meetup / 2012-08-14 The Statistics of Web Performance Analysis 17
  • 18. Bad sample Sometimes it’s not Boston #WebPerf Meetup / 2012-08-14 The Statistics of Web Performance Analysis 18
  • 19. How to randomize? http://xkcd.com/221/ Boston #WebPerf Meetup / 2012-08-14 The Statistics of Web Performance Analysis 19
  • 20. How to randomize? • Pick 10% of users at random and always test them OR • For each user, decide at random if they should be tested http://tech.bluesmoon.info/2010/01/statistics-of-performance-measurement.html Boston #WebPerf Meetup / 2012-08-14 The Statistics of Web Performance Analysis 20
  • 21. Select 10% of users - I if($sessionid % 10 === 0) { // instrument code for measurement } • Once a user enters the measurement bucket, they stay there until they log out • Fixed set of users, so tests may be more consistent • Error in the sample results in positive feedback Boston #WebPerf Meetup / 2012-08-14 The Statistics of Web Performance Analysis 21
  • 22. Select 10% of users - II if(rand() < 0.1 * getrandmax()) { // instrument code for measurement } • For every request, a user has a 10% chance of being tested • Gets rid of positive feedback errors, but sample size != 10% of population Boston #WebPerf Meetup / 2012-08-14 The Statistics of Web Performance Analysis 22
  • 23. How big a sample is representative? Select n such that σ 1.96 √n ≤ 5%µ Boston #WebPerf Meetup / 2012-08-14 The Statistics of Web Performance Analysis 23
  • 24. 1-2 Margin of Error Boston #WebPerf Meetup / 2012-08-14 The Statistics of Web Performance Analysis 24
  • 25. Standard Deviation • Standard deviation tells you the spread of the curve • The narrower the curve, the more confident you can be Boston #WebPerf Meetup / 2012-08-14 The Statistics of Web Performance Analysis 25
  • 26. MoE at 95% confidence σ ±1.96 √n Boston #WebPerf Meetup / 2012-08-14 The Statistics of Web Performance Analysis 26
  • 27. MoE & Sample size There is an inverse square root correlation between sample size and margin of error Boston #WebPerf Meetup / 2012-08-14 The Statistics of Web Performance Analysis 27
  • 28. 1-3 Central Tendency Boston #WebPerf Meetup / 2012-08-14 The Statistics of Web Performance Analysis 28
  • 29. Boston #WebPerf Meetup / 2012-08-14 The Statistics of Web Performance Analysis 29
  • 30. One number • Mean (Arithmetic) • Good for symmetric curves • Affected by outliers Mean(10, 11, 12, 11, 109) = 30 Boston #WebPerf Meetup / 2012-08-14 The Statistics of Web Performance Analysis 30
  • 31. One number • Median • Middle value measures central tendency well • Not trivial to pull out of a DB Median(10, 11, 12, 11, 109) = 11 Boston #WebPerf Meetup / 2012-08-14 The Statistics of Web Performance Analysis 31
  • 32. One number • Mode • Not often used • Multi-modal distributions suggest problems Mode(10, 11, 12, 11, 109) = 11 Boston #WebPerf Meetup / 2012-08-14 The Statistics of Web Performance Analysis 32
  • 33. Other numbers • A percentile point in the distribution: 95th , 98.5th or 99th • Used to find out the worst user experience • Makes more sense if you filter data first P95th (10, 11, 12, 11, 109) = 12 Boston #WebPerf Meetup / 2012-08-14 The Statistics of Web Performance Analysis 33
  • 34. Other means • Geometric mean • Good if your data is exponential in nature (with the tail on the right) GMean(10, 11, 12, 11, 109) = 16.68 Boston #WebPerf Meetup / 2012-08-14 The Statistics of Web Performance Analysis 34
  • 35. Wait... how did I get that? N ΠN xi — could lead to overflow i=1 ΣN loge (xi ) i=1 N e — computationally simpler Boston #WebPerf Meetup / 2012-08-14 The Statistics of Web Performance Analysis 35
  • 36. Wait... how did I get that? N ΠN xi — could lead to overflow i=1 ΣN loge (xi ) i=1 N e — computationally simpler Boston #WebPerf Meetup / 2012-08-14 The Statistics of Web Performance Analysis 35
  • 37. Wait... how did I get that? N ΠN xi — could lead to overflow i=1 ΣN loge (xi ) i=1 N e — computationally simpler Boston #WebPerf Meetup / 2012-08-14 The Statistics of Web Performance Analysis 35
  • 38. Wait... how did I get that? N ΠN xi — could lead to overflow i=1 ΣN loge (xi ) i=1 N e — computationally simpler Boston #WebPerf Meetup / 2012-08-14 The Statistics of Web Performance Analysis 35
  • 39. Other means And there is also the Harmonic mean, but forget about that Boston #WebPerf Meetup / 2012-08-14 The Statistics of Web Performance Analysis 36
  • 40. ...though consequently We have other margins of error • Geometric margin of error • Uses geometric standard deviation • Median margin of error • Uses ranges of actual values from data set • Stick to the arithmetic MoE – simpler to calculate, simpler to read and not incorrect Boston #WebPerf Meetup / 2012-08-14 The Statistics of Web Performance Analysis 37
  • 41. ...though consequently We have other margins of error • Geometric margin of error • Uses geometric standard deviation • Median margin of error • Uses ranges of actual values from data set • Stick to the arithmetic MoE – simpler to calculate, simpler to read and not incorrect Boston #WebPerf Meetup / 2012-08-14 The Statistics of Web Performance Analysis 37
  • 42. 2 Statistics - 2 Boston #WebPerf Meetup / 2012-08-14 The Statistics of Web Performance Analysis 38
  • 43. 2-1 Distributions Boston #WebPerf Meetup / 2012-08-14 The Statistics of Web Performance Analysis 39
  • 44. Let’s look at some real charts Boston #WebPerf Meetup / 2012-08-14 The Statistics of Web Performance Analysis 40
  • 45. Sparse Distribution Boston #WebPerf Meetup / 2012-08-14 The Statistics of Web Performance Analysis 41
  • 46. Log-normal distribution Boston #WebPerf Meetup / 2012-08-14 The Statistics of Web Performance Analysis 42
  • 47. Bimodal distribution Boston #WebPerf Meetup / 2012-08-14 The Statistics of Web Performance Analysis 43
  • 48. What does all of this mean? Boston #WebPerf Meetup / 2012-08-14 The Statistics of Web Performance Analysis 44
  • 49. Distributions • Sparse distribution suggests that you don’t have enough data points • Log-normal distribution is typical • Bi-modal distribution suggests two (or more) distributions combined Boston #WebPerf Meetup / 2012-08-14 The Statistics of Web Performance Analysis 45
  • 50. In practice, a bi-modal distribution is not uncommon Boston #WebPerf Meetup / 2012-08-14 The Statistics of Web Performance Analysis 46
  • 51. Hint: Does your site do a lot of back-end caching? Boston #WebPerf Meetup / 2012-08-14 The Statistics of Web Performance Analysis 47
  • 52. 2-2 Filtering Boston #WebPerf Meetup / 2012-08-14 The Statistics of Web Performance Analysis 48
  • 53. Outliers • Out of range data points • Nothing you can fix here • There’s even a book about them Boston #WebPerf Meetup / 2012-08-14 The Statistics of Web Performance Analysis 49
  • 54. Outliers • Out of range data points • Nothing you can fix here • There’s even a book about them Boston #WebPerf Meetup / 2012-08-14 The Statistics of Web Performance Analysis 49
  • 55. Outliers • Out of range data points • Nothing you can fix here • There’s even a book about them Boston #WebPerf Meetup / 2012-08-14 The Statistics of Web Performance Analysis 49
  • 56. Outliers • Out of range data points • Nothing you can fix here • There’s even a book about them Boston #WebPerf Meetup / 2012-08-14 The Statistics of Web Performance Analysis 49
  • 57. DNS problems can cause outliers • 2 or 3 DNS servers for an ISP • 30 second timeout if first fails • ... 30 second increase in page load time • Maybe measure both and fix what you can • http://nms.lcs.mit.edu/papers/dns-ton2002.pdf Boston #WebPerf Meetup / 2012-08-14 The Statistics of Web Performance Analysis 50
  • 58. Band-pass filtering Boston #WebPerf Meetup / 2012-08-14 The Statistics of Web Performance Analysis 51
  • 59. Band-pass filtering • Strip everything outside a reasonable range • Bandwidth range: 4kbps - 4Gbps • Page load time: 50ms - 120s • You may need to relook at the ranges all the time Boston #WebPerf Meetup / 2012-08-14 The Statistics of Web Performance Analysis 51
  • 60. IQR filtering Boston #WebPerf Meetup / 2012-08-14 The Statistics of Web Performance Analysis 52
  • 61. IQR filtering Here, we derive the range from the data Boston #WebPerf Meetup / 2012-08-14 The Statistics of Web Performance Analysis 52
  • 62. Further Reading lognormal.com/blog/2012/08/13/analysing-performance-data/ Boston #WebPerf Meetup / 2012-08-14 The Statistics of Web Performance Analysis 53
  • 63. Summary • Choose a reasonable sample size and sampling factor • Tune sample size for minimal margin of error • Decide based on your data whether to use mode, median or one of the means • Figure out whether your data is Normal, Log-Normal or something else • Filter out anomalous outliers Boston #WebPerf Meetup / 2012-08-14 The Statistics of Web Performance Analysis 54
  • 64. • Philip Tellis • .com • philip@lognormal.com • @bluesmoon • geek paranoid speedfreak • http://bluesmoon.info/ Boston #WebPerf Meetup / 2012-08-14 The Statistics of Web Performance Analysis 55
  • 65. Thank you Boston #WebPerf Meetup / 2012-08-14 The Statistics of Web Performance Analysis 56
  • 66. Photo credits • http://www.flickr.com/photos/leoffreitas/332360959/ by leoffreitas • http://www.flickr.com/photos/cobalt/56500295/ by cobalt123 • http://www.flickr.com/photos/sophistechate/4264466015/ by Lisa Brewster Boston #WebPerf Meetup / 2012-08-14 The Statistics of Web Performance Analysis 57
  • 67. List of figures • http://en.wikipedia.org/wiki/File:Standard_deviation_diagram.svg • http://en.wikipedia.org/wiki/File:Normal_Distribution_PDF.svg • http://en.wikipedia.org/wiki/File:KilroySchematic.svg • http://en.wikipedia.org/wiki/File:Boxplot_vs_PDF.png Boston #WebPerf Meetup / 2012-08-14 The Statistics of Web Performance Analysis 58