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- 1. LeanUXDenver 2012 L6σ LeanUX Multivariate Testing Using Design of Experiments (DOE) Scott Leek Sigma Consulting Resources, LLC LeanUXDenver September 21, 2012© 2012 Sigma Consulting Resources, LLC 1
- 2. Purpose L6σ Objectives • Strategies and tactics for testing theories, advantages and disadvantages • Fundamental approach and iterative nature of experimentation • Properties of a good experimental design • Basic DOE terminology • Design types and uses • Full factorial designs • Concepts • How to • Example • Fractional factorial designs© 2012 Sigma Consulting Resources, LLC 2
- 3. LeanUX Notional Scenario L6σ Objective Test landing experience factors to increase landing page conversion rate© 2012 Sigma Consulting Resources, LLC 3
- 4. LeanUX Approaches L6σ Strategy Retrospective (Passive Observation) Methods Buttons Measurements Observe Effect Effect Layout Offers Colors Search for Cause© 2012 Sigma Consulting Resources, LLC 4
- 5. LeanUX Approaches L6σ Strategy Prospective (Experimentation) Methods Materials Measurements …To Create Effect Effect People Machines Environment Change One or More Factors…© 2012 Sigma Consulting Resources, LLC 5
- 6. LeanUX Tactics L6σ Options • Historical data • One factor at a time • All factors at the same time • A/B Testing • Design of Experiments (DOE)/Multivariate Testing (MVT)© 2012 Sigma Consulting Resources, LLC 6
- 7. LeanUX Tactics L6σ Historical Data Description Analyze historical (retrospective) data to find correlations and/or build predictive models (ANOVA, Regression, GLM, et cetera). Conversion Probability Load Time© 2012 Sigma Consulting Resources, LLC 7
- 8. LeanUX Tactics L6σ Historical Data Advantages Disadvantages Timely and efficient use of data Large data sets Logistically simple Background variables uncontrolled Effective predictive models Potential lurking variables Interactions can be problematic Factor testing range too narrow Important factors not tested Errors in the data, incomplete data© 2012 Sigma Consulting Resources, LLC 8
- 9. LeanUX Tactics L6σ Proving Cause “To ﬁnd out what happens to a system when you interfere with it, you have to interfere with it (not just passively observe it).” George E. P. Box© 2012 Sigma Consulting Resources, LLC 9
- 10. LeanUX Tactics L6σ One Factor At A Time Description Start from baseline factor settings and change one factor. If the result is better retain the change, if not, return to the baseline. Repeat with the next factor. Factor 1 Factor 2 Factor 3 Factor 4 Factor 5© 2012 Sigma Consulting Resources, LLC 10
- 11. LeanUX Tactics L6σ One Factor At A Time Baseline for five factors Change factor 1 If improved retain change, change factor 2 If not improved do not retain change, change factor 3© 2012 Sigma Consulting Resources, LLC 11
- 12. LeanUX Tactics L6σ One Factor At A Time Advantages Disadvantages Fast and simple to execute Confounded by random variation Little planning required Logistically problematic You can get lucky No information on main effects No information on interactions Factor combinations not tested Background variables uncontrolled Potential lurking variables© 2012 Sigma Consulting Resources, LLC 12
- 13. LeanUX Tactics L6σ All Factors At The Same Time Description Start from baseline factor settings and change multiple (or all) factors simultaneously. Baseline for five factors Change multiple factors© 2012 Sigma Consulting Resources, LLC 13
- 14. LeanUX Tactics L6σ All Factors At The Same Time Advantages Disadvantages Fast and simple to execute Effects are confounded Little planning required Logistically problematic You can get lucky Factor combinations not tested Background variables uncontrolled Potential lurking variables© 2012 Sigma Consulting Resources, LLC 14
- 15. LeanUX Tactics L6σ A/B Testing Description A simple designed experiment randomly exposing users to either a control (A) or a treatment (B). The treatment can vary one factor on a landing page, or vary the multiple factors in the landing experience. Revenue Landing Landing Page 1 Page 2© 2012 Sigma Consulting Resources, LLC 15
- 16. LeanUX Tactics L6σ A/B Testing Advantages Disadvantages Relatively simple Limited number of comparisons Efficient use of data Limited information on main effects Effective results No information on interactions Protect against lurking variables Increased probability of Type I error* Plan for background variables * Pairwise comparisons of seven factors, two at a time, results in 21 tests (7!/(2 ! × 5 !)). Assuming 95% confidence the probability of a Type I error increases to 66% (1 - (0.9521)) from 5% (1 - (0.95)).© 2012 Sigma Consulting Resources, LLC 16
- 17. LeanUX Tactics L6σ Design of Experiments (DOE) Description Similar to A/B testing but multiple factors are tested simultaneously allowing for precise estimates of main effects and interaction effects. Yes Discount Field Photo Offering Graphic No Icon Small Large Button Size© 2012 Sigma Consulting Resources, LLC 17
- 18. LeanUX Tactics L6σ Design of Experiments (DOE) Advantages Disadvantages Relatively simple Can be logistically complicated* Efficient use of data Requires planning and discipline Effective results Protect against lurking variables Plan for background variables Estimates for main effects Estimates for interaction effects Predictive model * Crook, Thomas, Frasca, Brian, Kohavi, Ron, LongBotham, Roger, “Seven Pitfalls to Avoid when Running Controlled Experiments on the Web,” http://www.exp-platform.com/Pages/ExPpitfalls.aspx.© 2012 Sigma Consulting Resources, LLC 18
- 19. Design of Experiments (DOE) L6σ LeanUX Experimentation Knowledge Current Decision/ State UX UX Action Data Data Theory Theory Theory…© 2012 Sigma Consulting Resources, LLC 19
- 20. Design of Experiments (DOE) L6σ Properties of a Good Experimental Design* 1. Actionable well-defined objective(s) 2. Conducted sequentially to build knowledge 3. Variation in the response variables can be allocated to factors, background variables, and lurking variables 4. Experiments are conducted over as wide a range of conditions as possible to improve confidence (degree of belief) 5. As simple as possible while satisfying the first four properties * Adapted from Moen, Ronald D., Nolan, Thomas W., Provost, Lloyd P., (1991): Improving Quality Through Planned Experimentation, McGraw-Hill, New York.© 2012 Sigma Consulting Resources, LLC 20
- 21. Design of Experiments (DOE) L6σ Terms • Response Variable – also called a dependent variable, or overall evaluation criterion (OEC). A response variable is a measure that the experiment is trying to maximize, minimize, or optimize – e.g., click-through rate, dwell time, et cetera. • Factor – also called an independent variable (variant). Factors are changed in a planned way during the experiment to observe the affect on the response – e.g., button position, headline type, offer graphic, et cetera. • Level – a setting for a factor that can be qualitative or quantitative – e.g., button position of top or bottom, offer graphic of icon or photo, response time, et cetera.© 2012 Sigma Consulting Resources, LLC 21
- 22. Design of Experiments (DOE) L6σ Terms • Background Variable – a variable that potentially affects the response variable but is not of interest to study as a factor – e.g., browser type, server response time, volumes, time (day, week, month, year), et cetera. Background variables are managed in one of three ways: holding constant, blocking, or measuring. • Lurking Variable – a variable potentially affecting the response variable that is unknown at the time the experiment is planned. Lurking variables are mitigated through randomization.© 2012 Sigma Consulting Resources, LLC 22
- 23. Design of Experiments (DOE) L6σ Terms • Experimental Unit – the smallest unit receiving different combinations of factor levels (treatments) – e.g., people, batches, projects, parts, et cetera. • Run (Test or Trial) – a set of factor level combinations (treatments) tested in the experiment – e.g., button size = large, offering graphic = icon, discount field = yes. • Effect – the change in the response variable when factor levels are changed – e.g., conversion rates increase when the offering graphic is a photo of a person versus an icon. There are main effects and interaction effects.© 2012 Sigma Consulting Resources, LLC 23
- 24. Design of Experiments (DOE) L6σ Design Types & Uses Knowledge Low High Design Fractional Response Screening Full Factorials Type Factorials Surface # of Factors >5 5 – 10 2–8 2–8 Identify Identify main Identify main Optimize factor Purpose important effects + some effects + settings factors interactions interactions© 2012 Sigma Consulting Resources, LLC 24
- 25. Design of Experiments (DOE) L6σ Design Types & Uses Knowledge Low High Design Fractional Response Screening Full Factorials Type Factorials Surface # of Factors >5 5 – 10 2–8 2–8 Identify Identify main Identify main Optimize factor Purpose important effects + some effects + settings factors interactions interactions© 2012 Sigma Consulting Resources, LLC 25
- 26. Design of Experiments (DOE) L6σ 2k Full Factorial Designs • The experimental trials are performed for all possible combinations of factor levels. • Full factorial designs are frequently called nk designs n = number of factor levels k = number of factors • A common factorial design is the 2k design, simple and powerful. • Disadvantages of the 2k design include possible non- linear relationships and the number of trials can increase quickly.© 2012 Sigma Consulting Resources, LLC 26
- 27. 2k Full Factorial Designs L6σ Why 2k Designs? # of Factors (k) 2k 3k 2 4 9 3 8 27 4 16 81 5 32 243 6 64 729 7 128 2,187 8 256 6,561 2k designs require significantly fewer trials as the number of factors increases.© 2012 Sigma Consulting Resources, LLC 27
- 28. 2k Full Factorial Designs L6σ Risks? Conversion Probability Relationship may be non-linear Basic 2k design assumes a linear relationship Lo Hi Load Time Options for dealing with non-linear relationships: add center points, add factor levels, or use Response Surface Methodology.© 2012 Sigma Consulting Resources, LLC 28
- 29. 2k Full Factorial Designs L6σ Factors & Levels Factor Level Small Button Size Large Icon Offering Graphic Photo Yes Discount Field No Three factors, each at two levels = 23 = 8 trials (runs) in the full factorial design.© 2012 Sigma Consulting Resources, LLC 29
- 30. 2k Full Factorial Designs L6σ Notation & Standard Order Standard Button Offering Discount Standard Button Offering Discount Order Size Graphic Field Order Size Graphic Field 1 Small Icon No 1 - - - 2 Large Icon No 2 + - - = 3 Small Photo No 3 - + - 4 Large Photo No 4 + + - 5 Small Icon Yes 5 - - + 6 Large Icon Yes 6 + - + 7 Small Photo Yes 7 - + + 8 Large Photo Yes 8 + + +© 2012 Sigma Consulting Resources, LLC 30
- 31. 2k Full Factorial Designs L6σ Visualizing the Experimental Space • A cube helps visualize the experimental space with 3 factors • Each corner represents one of the 23 = 8 trials (runs) • A Full Factorial design covers the entire experimental space Button Size = Large Offering Graphic = Photo Discount Field = Yes Yes Discount Field Photo Offering Graphic No Icon Small Large Button Size = Small Offering Graphic = Icon Button Size Discount Field = No© 2012 Sigma Consulting Resources, LLC 31
- 32. Design of Experiments (DOE) L6σ Steps (1 – 4 of 10) 1. Define the objective(s) 2. Summarize relevant background information 3. Identify the response variable(s) 4. Identify the factors and levels© 2012 Sigma Consulting Resources, LLC 32
- 33. LeanUX DOE L6σ Plan 1. Objective(s) Test landing page factors to increase conversion rate 2. Background Information A series of prior experiments concluded that there are 3 significant factors out of the 8 tested 3. Response Variable(s) Conversion rate 4. Factors Levels Button Size Small Large Offer Graphic Icon Photo Discount Field No Yes© 2012 Sigma Consulting Resources, LLC 33
- 34. Design of Experiments (DOE) L6σ Controlling Background Variables • Hold constant • Measure and include as a covariate • Run the experiment in Blocks (groups of experimental units receiving similar treatments)© 2012 Sigma Consulting Resources, LLC 34
- 35. Design of Experiments (DOE) L6σ Steps (5 – 7 of 10) 5. Identify the background variables and method of control 6. Select the design including replication 7. Randomize trials (runs)© 2012 Sigma Consulting Resources, LLC 35
- 36. LeanUX DOE L6σ Plan 5. Background Variable(s) Method of Control Browser Type Measure Operating System Measure Time (Day, Week, Month, Year) Measure (could run in blocks) 6. Design and Replication 23 Full Factorial = 8 trials x 2 Replicates = 16 trials 7. Randomization Users randomly assigned to treatments. All assignments are re-directs. The assignment and redirecting process will be tested offline.© 2012 Sigma Consulting Resources, LLC 36
- 37. Design of Experiments (DOE) L6σ Replication • Repetition of experimental treatments so that experimental error (common cause variation) can be estimated • A 23 Full Factorial 8-run design with 2 replicates requires 16 trials (runs) • All trials, including replicates should be randomized • Include replication if resources allow (estimate error, estimate response variability, calculate statistical significance)© 2012 Sigma Consulting Resources, LLC 37
- 38. Design of Experiments (DOE) L6σ Randomization • Creating a random sequence to run the experimental trials (runs) or randomly assign users to treatments • Random means the probability of each event is equal Standard Order Random Order * Crook et al recommend conducting A/A testing prior to experimentation to validate the randomization process. See Crook, Thomas, Frasca, Brian, Kohavi, Ron, LongBotham, Roger, “Seven Pitfalls to Avoid when Running Controlled Experiments on the Web,” http://www.exp-platform.com/Pages/ExPpitfalls.aspx.© 2012 Sigma Consulting Resources, LLC 38
- 39. Design of Experiments (DOE) L6σ Why Randomize? • The response of interest is conversion rate. • The graph depicts the conversion rate over a typical day. • Why did the conversion rate trend down over the course of a day?© 2012 Sigma Consulting Resources, LLC 39
- 40. Design of Experiments (DOE) L6σ Why Randomize? • A new landing page is tested against a control, but assignments are not randomized • The control is tested during the first half of the day and the treatment is tested during the second half of the day Treatment Control© 2012 Sigma Consulting Resources, LLC 40
- 41. Design of Experiments (DOE) L6σ Why Randomize? • Tested randomly throughout the day the effect of the lurking variable is averaged over both the treatment or control • Randomization provide protection against lurking variables and is known as the “experimenter’s insurance”© 2012 Sigma Consulting Resources, LLC 41
- 42. Design of Experiments (DOE) L6σ Steps (8 – 10 of 10) 8. Conduct the experiment and collect data 9. Analyze data 10. Draw conclusions and action plans© 2012 Sigma Consulting Resources, LLC 42
- 43. Design of Experiments (DOE) L6σ Conducting the Experiment • During the experiment plan to collect information about events and outcomes that are not part of the experimental plan© 2012 Sigma Consulting Resources, LLC 43
- 44. Analyzing a 2k Design L6σ Model • The analysis of a 2k design results in a model Y = b1X1 + b2X2 + + bnXn + e • A full factorial design begins by examining all possible terms that might be included in a model, for example, in a 23 design there are three main effects (A, B, C), three two factor interaction effects (AB, AC, BC), and one three factor interaction (ABC) • The “e” term represents the model error or residual© 2012 Sigma Consulting Resources, LLC 44
- 45. Design of Experiments (DOE) L6σ Analyzing a 2k Design 1. Test the model Data errors and lurking variables Assumptions 2. Identify significant main and interaction effects 3. Create appropriate graphical summaries© 2012 Sigma Consulting Resources, LLC 45
- 46. Analyzing a 2k Design L6σ Test for Data Errors & Lurking Variables • A simple time series plot is used to look for obvious data errors (missing values, outliers caused data entry) • Test for lurking variables by examining the time series plots for trends or time related cycles or patterns© 2012 Sigma Consulting Resources, LLC 46
- 47. Analyzing a 2k Design L6σ Residuals • All models contain residual, or “left over” variation that is not explained by the terms (factors) in the model Residual = Observed - Predicted Button&Size Offer&Graphic Discount&Field Conversion&Rate Predicted Residual Large Photo No 23 26 .3 Small Photo No 20 20.5 .0.5 Large Photo Yes 20 19 1 Small Icon No 13 10.5 2.5 Small Photo Yes 21 19.5 1.5 Large Icon Yes 10 9 1 Large Photo No 29 26 3 Large Photo Yes 18 19 .1 Small Icon Yes 5 6.5 .1.5 Small Photo Yes 18 19.5 .1.5 Small Icon No 8 10.5 .2.5 Small Photo No 21 20.5 0.5 Large Icon Yes 8 9 .1 Large Icon No 15 16 .1 Small Icon Yes 8 6.5 1.5 Large Icon No 17 16 1© 2012 Sigma Consulting Resources, LLC 47
- 48. Analyzing a 2k Design L6σ Residual Assumptions • An independent random variable that is normally distributed with a mean of 0 • Constant variance over the range of experimental conditions • Stable over time • Not correlated to the factors© 2012 Sigma Consulting Resources, LLC 48
- 49. Analyzing a 2k Design L6σ Testing Assumptions© 2012 Sigma Consulting Resources, LLC 49
- 50. Design of Experiments (DOE) L6σ Analyzing a 2k Design ✔1. Test the model Data errors and lurking variables Assumptions 2. Identify significant main and interaction effects and assess the quality of the model 3. Create appropriate graphical summaries© 2012 Sigma Consulting Resources, LLC 50
- 51. Analyzing a 2k Design L6σ Significant Effects • Main Effect – the change in the response variable that results when a factor level is changed. • Interaction Effect – the change in the response variable that results when a factor level is changed and the effect is a function of the level of a second factor.© 2012 Sigma Consulting Resources, LLC 51
- 52. Analyzing a 2k Design L6σ Main Effect 18.25 Discount Field Effect 13.5 - 18.25 = -4.75 13.5© 2012 Sigma Consulting Resources, LLC 52
- 53. Analyzing a 2k Design L6σ Main Effect The average change (increase or decrease) in the response variable when changing a factor level from low (high) to high (low). Main Effect = (Average High (+) Level) – (Average Low (-) Level) Discount Field Main Effect = #19.5+19.0 + 9.0 + 6.5 & − # 20.5+ 26.0 +16.0 +10.5 & = # 54 & − # 73 & = 13.5 −18.25 = −4.75 ! $ ! $ ! $ ! $ " 4 % " 4 % "4% "4% Discount Field Yes (+) Discount Field No (-)© 2012 Sigma Consulting Resources, LLC 53
- 54. Analyzing a 2k Design L6σ Interaction Effect Conversion declines when a discount field is added, the amount of the decline depends on the button size.© 2012 Sigma Consulting Resources, LLC 54
- 55. Analyzing a 2k Design L6σ Interaction Effect The average change in the response variable when a factor level is changed from a low to a high level, and the effect depends on the level of another factor. (! 19 + 9 $ ! 26 +16 $+ (! 19.5 + 6.5 $ ! 20.5 +10.5 $+ Discount Field Button Size Interaction Effect = *# &−# &- − *# &−# &- )" 2 % " 2 %, )" 2 % " 2 %, [14 − 21] − [13−15.5] −4.5 = = = −2.25 2 2 2 Discount Field Yes (+), Large Button (+) Discount Field No (-), Large Button (+) Discount Field Yes (+), Small Button (-) Discount Field No (-), Small Button (-)© 2012 Sigma Consulting Resources, LLC 55
- 56. Analyzing a 2k Design L6σ Significant Effects • Effects (main or interaction) are deemed significant based upon a statistical hypothesis test (e.g., t-test) that results in a p-value • The p-value is the probability of a Type I error (alpha, level of confidence); commonly, if p < 0.05 the Null Hypothesis is rejected and the Alternative Hypothesis is accepted: Null Hypothesis (H0): AverageControl – AverageTreatment = 0 Alternative Hypothesis (H0): AverageControl – AverageTreatment ≠ 0 • Most software creates a table with a variety of statistics (effect, coefficient, t-statistic, p-value, et cetera) related to each effect, some software provide charts that graphically identify significant effects© 2012 Sigma Consulting Resources, LLC 56
- 57. Analyzing a 2k Design L6σ Significant Effects • Three factors are statistically significant: Button Size, Offer Graphic, and Discount Field. • None of the interactions are significant. P-value = 0.05 t-Statistic© 2012 Sigma Consulting Resources, LLC 57
- 58. Analyzing a 2k Design L6σ Significant Effects Factorial Fit: Conversion Rate versus Button Size, Offer Graphic, ... Estimated Effects and Coefficients for Conversion Rate (coded units) Term Effect Coef SE Coef T P _ Constant 15.875 0.5995 26.48 0.000 Button Size 3.250 1.625 0.5995 2.71 0.027 Offer Graphic 10.750 5.375 0.5995 8.97 0.000 Discount Field -4.750 -2.375 0.5995 -3.96 0.004 Button Size*Offer Graphic -0.750 -0.375 0.5995 -0.63 0.549 Button Size*Discount Field -2.250 -1.125 0.5995 -1.88 0.097 Offer Graphic*Discount Field 0.750 0.375 0.5995 0.63 0.549 Button Size*Offer Graphic* -0.750 -0.375 0.5995 -0.63 0.549 Discount Field S = 2.39792 PRESS = 184 R-Sq = 93.11% R-Sq(pred) = 72.44% R-Sq(adj) = 87.08% • Effect = change in the response variable when factor is changed from a low level to a high level. • Coefficient = If factors are coded, the coefficient is half the value of the effect. • t-Statistic is the statistical test to determine the p-value and statistical significance. • P-value: if < 0.05 the factor is statistically significant (p-value = probability of a Type I error).© 2012 Sigma Consulting Resources, LLC 58
- 59. Analyzing a 2k Design L6σ Assessing Model Quality Factorial Fit: Conversion Rate versus Button Size, Offer Graphic, ... Estimated Effects and Coefficients for Conversion Rate (coded units) Term Effect Coef SE Coef T P _ Constant 15.875 0.5995 26.48 0.000 Button Size 3.250 1.625 0.5995 2.71 0.027 Offer Graphic 10.750 5.375 0.5995 8.97 0.000 Discount Field -4.750 -2.375 0.5995 -3.96 0.004 Button Size*Offer Graphic -0.750 -0.375 0.5995 -0.63 0.549 Button Size*Discount Field -2.250 -1.125 0.5995 -1.88 0.097 Offer Graphic*Discount Field 0.750 0.375 0.5995 0.63 0.549 Button Size*Offer Graphic* -0.750 -0.375 0.5995 -0.63 0.549 Discount Field S = 2.39792 PRESS = 184 R-Sq = 93.11% R-Sq(pred) = 72.44% R-Sq(adj) = 87.08% • S = standard deviation of the residuals. • PRESS = predicted sum of the squares. • R-Sq = simple R2. • R-Sq(pred) = R2 for model predictions. • R-Sq(adj) = R2 adjusted, used with more than one factor to compare various models.© 2012 Sigma Consulting Resources, LLC 59
- 60. Assessing Model Quality L6σ The R2 Statistic • R2 is the percent of variation in the response explained by the factor(s) R2 = Explained _Variation *100 Total_Variation Total Variation (100%) % Explained© 2012 Sigma Consulting Resources, LLC 60
- 61. Analyzing a 2k Design L6σ Significant Effects & Assessing Model Quality • After assessing the the initial model, remove insignificant terms and rerun the model© 2012 Sigma Consulting Resources, LLC 61
- 62. Design of Experiments (DOE) L6σ Analyzing a 2k Design ✔1. Test the model Data errors and lurking variables Assumptions ✔2. Identify significant main and interaction effects and assess the quality of the model 3. Create appropriate graphical summaries© 2012 Sigma Consulting Resources, LLC 62
- 63. Design of Experiments (DOE) L6σ Main Effects Plot© 2012 Sigma Consulting Resources, LLC 63
- 64. Design of Experiments (DOE) L6σ Interaction Plot© 2012 Sigma Consulting Resources, LLC 64
- 65. Design of Experiments (DOE) L6σ Cube Plot© 2012 Sigma Consulting Resources, LLC 65
- 66. Design of Experiments (DOE) L6σ Prediction Equation • The prediction equation includes a constant (overall average) in the equation. • The coefficients for discrete factors are the amount added or subtracted from the overall average. • The coefficients for continuous factors are slopes if they are not coded. • Whether an effect is added or subtracted depends on whether the effect is negative or positive, and how the factor was coded (e.g., no= –1, yes= +1). Conversion = 15.875 + (Button Size * 1.625) + (Offer Graphic * 5.375) + (Discount Field * -2.375) Large Button, Photo, No Discount Conversion = 15.875 + (1 * 1.625) + (1 * 5.375) + (-1 * -2.375) = 25.25© 2012 Sigma Consulting Resources, LLC 66
- 67. Design of Experiments (DOE) L6σ Conclusions & Action Plans • Summarize findings in simple language • Present how conclusions have been (or will be) validated • Use simple graphical displays to communicate important concepts • Make recommendations concrete and actionable • The appropriate action may include conducting another experiment© 2012 Sigma Consulting Resources, LLC 67
- 68. Design of Experiments (DOE) L6σ Reducing Experimental Trials Fractional Factorial Designs© 2012 Sigma Consulting Resources, LLC 68
- 69. Design of Experiments (DOE) L6σ Reducing the Size of a Factorial Design Standard Button Offering Discount Order Size Graphic Field 1 - - - Yes 2 + - - 3 - + - 4 + + - Discount Field Photo 5 - - + 6 + - + Offering No Icon 7 - + + Graphic Small Large 8 + + + Button Size If only 4 trials can be run (half of the full factorial) which 4 trials should be chosen?© 2012 Sigma Consulting Resources, LLC 69
- 70. Fractional Factorial Designs L6σ Selecting the Half Fraction Standard Button Offering Discount Order Size Graphic Field 1 - - - Yes 2 + - - 3 - + - 4 + + - Discount Field Photo 5 - - + 6 + - + Offering No Icon 7 - + + Graphic Small Large 8 + + + Button Size The Discount Field is only tested at the “no”(-) level resulting in no measure of the effect of the Discount Field.© 2012 Sigma Consulting Resources, LLC 70
- 71. Fractional Factorial Designs L6σ Selecting the Half Fraction Standard Button Offering Discount Order Size Graphic Field 1 - - - Yes 2 + - - 3 - + - 4 + + - Discount Field Photo 5 - - + 6 + - + Offering No Icon 7 - + + Graphic Small Large 8 + + + Button Size The effects of Discount Field (yes, +) and Offering Graphic (icon, -) are confounded (Discount Field (yes) and Offering Graphic (icon) are always tested together, as are Discount Field (no) and Offering Graphic (photo))© 2012 Sigma Consulting Resources, LLC 71
- 72. Fractional Factorial Designs L6σ Selecting the Half Fraction Standard Button Offering Discount Order Size Graphic Field 1 - - - Yes 2 + - - 3 - + - 4 + + - Discount Field Photo 5 - - + 6 + - + Offering No Icon 7 - + + Graphic Small Large 8 + + + Button Size • Each factor makes two comparisons for each of the 3 factors (balanced) • Covers the most experimental space using four trials • Collapses into a full factorial if one of the factors is found not significant© 2012 Sigma Consulting Resources, LLC 72
- 73. Fractional Factorial Designs L6σ Selecting the Half Fraction Standard Button Offering Discount Order Size Graphic Field 1 - - - Yes 2 + - - 3 - + - 4 + + - Discount Field Photo 5 - - + 6 + - + Offering No Icon 7 - + + Graphic Small Large 8 + + + Button Size • This will also work.© 2012 Sigma Consulting Resources, LLC 73
- 74. Fractional Factorial Designs L6σ Notation 2k factorial designs us the following notation: 2 k-p R Where k = number of factors p = fraction of the design (p=1=½ fraction, p=2=¼ fraction) R = resolution© 2012 Sigma Consulting Resources, LLC 74
- 75. Fractional Factorial Designs L6σ Confounding • Reducing the number of runs improves efficiency. The cost is a reduction in the quantity of information provided, this is due to confounding. • Confounding means that effects are mixed up. How the effects are confounded depends on the resolution of the Fractional Factorial design. • Fractional Factorial designs are structured to create confounding with higher order interactions (typically not common). • Using the Conversion Rate example the 23-1III results in the following confounding: • Button Size + (Offering Graphic * Discount Rate) • Offering Graphic + (Button Size * Discount Rate) • Discount Rate + (Button Size * Offering Graphic) • The 23-1III is not a very useful design due to its resolution.© 2012 Sigma Consulting Resources, LLC 75
- 76. Fractional Factorial Designs L6σ Resolution • Resolution is a measure of the degree of confounding. • The higher the resolution the more likely important main effects, and two factor interactions will be confounded with very higher order interactions. • A full factorial design is full resolution. Resolution Confounding Main effects + 2-factor (and higher) interactions III 1+2 Main effects + 3-factor (and higher) interactions 1+3 IV 2-factor interactions + 2-factor (and higher) interactions 2+2 Main effects + 4-factor (and higher) interactions 1+4 V 2-factor interactions + 3-factor (and higher) interactions 2+3© 2012 Sigma Consulting Resources, LLC 76
- 77. Fractional Factorial Designs L6σ Resolution© 2012 Sigma Consulting Resources, LLC 77
- 78. Fractional Factorial Designs L6σ Design Types & Resolution Knowledge Low High Design Fractional Response Screening Full Factorials Type Factorials Surface # of Factors >5 5 – 10 2–8 2–8 Identify Identify main Identify main Optimize factor Purpose important effects + some effects + settings factors interactions interactions Resolution III IV+ Full Full© 2012 Sigma Consulting Resources, LLC 78
- 79. 25-1 Fractional Factorial Design L6σ Factors & Levels Factor Level Small Button Size Large Icon Offering Graphic Photo Yes Discount Field No Blue Background Gray G Format Heading H Format© 2012 Sigma Consulting Resources, LLC 79
- 80. 25-1 Fractional Factorial Design L6σ Factors & Levels Five factors with full factorial = 32 runs and the half factorial = 16© 2012 Sigma Consulting Resources, LLC 80
- 81. 25-1 Fractional Factorial Design L6σ Analysis Confounding Structure These Effects Are Confounded With These Effects Overall Average Button Size * Offering Graphic * Discount Field * Background * Heading Button Size Offering Graphic * Discount Field * Background * Heading Offering Graphic Button Size * Discount Field * Background * Heading Discount Field Button Size * Offering Graphic * Background * Heading Background Button Size * Offering Graphic * Discount Field * Heading Heading Button Size * Offering Graphic * Discount Field * Background Button Size * Offering Graphic Discount Field * Background * Heading Button Size * Discount Field Offering Graphic * Background * Heading Button Size * Background Offering Graphic * Discount Field * Heading Button Size * Heading Offering Graphic * Discount Field * Background Offering Graphic * Discount Field Button Size * Background * Heading Offering Graphic * Background Button Size * Discount Field * Heading Offering Graphic * Heading Button Size * Discount Field * Background Discount Field * Background Button Size * Offering Graphic * Heading Discount Field * Heading Button Size * Offering Graphic * Background Background * Heading Button Size * Offering Graphic * Discount Field© 2012 Sigma Consulting Resources, LLC 81
- 82. Design of Experiments (DOE) L6σ Other Issues • Statistical control and process predictability • Sample representativeness (bias) • Power (ability to detect a difference) and sample size • “Exercise the experimentation system” (A/A) testing • Significant differences in browser redirects© 2012 Sigma Consulting Resources, LLC 82
- 83. Design of Experiments (DOE) L6σ Summary • DOE is a planned approach to testing, designs have a known number of trials that can be budgeted • Important main/interaction effects identified • Multiple factors evaluated simultaneously • Background variables managed by controlling, measuring, or blocking • Lurking variables mitigated by randomization • Replication enables estimation of experimental error • Prediction equations • The number of trials in full factorial designs can be reduced with fractional factorials© 2012 Sigma Consulting Resources, LLC 83
- 84. Design of Experiments (DOE) L6σ References Box, E. P. George, Hunter, William G., Hunter, J. Stuart, (1978): Statistics for Experimenters, John Wiley & Sons, New York. Crook, Thomas, Frasca, Brian, Kohavi, Ron, LongBotham, Roger, “Seven Pitfalls to Avoid when Running Controlled Experiments on the Web,” http://www.exp-platform.com/Pages/ExPpitfalls.aspx. Kohavi, Ron, Longbotham, Roger, “Unexpected Results in Online Controlled Experiments,” http://www.informatik.uni-trier.de/~ley/db/indices/a-tree/k/Kohavi:Ron.html. Kohavi, Ron, Henne, Randal M., Sommerfield, Dan, “Practical Guide to Controlled Experiments on the Web: Listen to Your Customers not the HiPPO,” http://exp-platform.com/hippo.aspx. Moen, Ronald D., Nolan, Thomas W., Provost, Lloyd P., (1991): Improving Quality Through Planned Experimentation, McGraw-Hill, New York.© 2012 Sigma Consulting Resources, LLC 84

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