# A/B Testing - Design, Analysis and Pitfals

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1. A/B Testing – Design, Analysis and Pitfalls slavabo@gmail.com 2. Business Package Test 3. Additional Advertising Test 4. Agenda ã Design the Experiment ▫ 2 main…
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• 1. A/B Testing – Design, Analysis and Pitfalls slavabo@gmail.com
• 4. Agenda • Design the Experiment ▫ 2 main questions – how many users and how long to run the test ▫ Define reasonable number of KPIs ▫ Pay attention on seasonality/weekdays effect • Analyze the Experiment ▫ Statistical methods for checking significance ▫ Non-parametric methods ▫ Outliers/bots/fraud • Data-driven culture • Pitfalls • Open Discussion
• 5. Design • Test Duration & Sample Size ▫ Duration needs to be defined before the experiment is started! ▫ Depends on distribution of main KPIs  80% have Binomial Distribution (Conversion Rate, CTR, etc…) + CLT can help.  20% other (count events, revenue).  Power calculations for defining N (size) and t (duration) OR use rules of thumb.  General rule – the less difference you want to catch the more data you’ll need to collect.
• 6. Design ▫ Example – # of searches per user (SweetIM)  Poisson assumption for count events  Not appropriate when variance >> mean  NB was found appropriate  Power limitation of NB
• 7. Statistical Power and Sensitivity 50% 55% 60% 65% 70% 75% 80% 85% 90% 95% 0.5% 1,001,243 1,133,747 1,276,816 1,433,622 1,608,696 1,808,942 2,045,743 2,340,142 2,738,670 3,386,960 1.0% 251,556 284,847 320,792 360,188 404,175 454,485 513,980 587,946 688,074 850,953 1.5% 112,359 127,228 143,284 160,880 180,527 202,998 229,572 262,609 307,332 380,083 2.0% 63,516 71,922 80,998 90,945 102,052 114,755 129,777 148,453 173,734 214,860 2.5% 40,853 46,259 52,097 58,494 65,638 73,808 83,470 95,482 111,743 138,194 3.0% 28,511 32,284 36,358 40,823 45,809 51,511 58,254 66,637 77,985 96,446 3.5% 21,051 23,837 26,845 30,142 33,823 38,033 43,011 49,201 57,580 71,210 4.0% 16,197 18,341 20,655 23,192 26,024 29,264 33,094 37,857 44,304 54,791 4.5% 12,861 14,564 16,401 18,416 20,665 23,237 26,279 30,060 35,180 43,507 5.0% 10,470 11,855 13,351 14,991 16,821 18,915 21,391 24,470 28,637 35,416 5.5% 8,696 9,846 11,089 12,451 13,971 15,710 17,767 20,324 23,785 29,415 6.0% 7,343 8,315 9,364 10,514 11,798 13,267 15,003 17,162 20,085 24,839 6.5% 6,288 7,120 8,018 9,003 10,103 11,360 12,847 14,696 17,199 21,270 7.0% 5,449 6,170 6,948 7,801 8,754 9,844 11,132 12,735 14,903 18,431 7.5% 4,770 5,401 6,083 6,830 7,664 8,618 9,746 11,148 13,047 16,135 8.0% 4,213 4,771 5,373 6,032 6,769 7,612 8,608 9,847 11,524 14,252 8.5% 3,750 4,247 4,783 5,370 6,026 6,776 7,663 8,766 10,259 12,687 9.0% 3,362 3,807 4,287 4,814 5,402 6,074 6,869 7,858 9,196 11,373 9.5% 3,032 3,434 3,867 4,342 4,872 5,478 6,196 7,087 8,294 10,258 10.0% 2,750 3,114 3,507 3,938 4,419 4,969 5,619 6,428 7,523 9,303 Sensitivity Statistical Power Sample size as a function of sensitivity and statistical power; Negative Binomial parameter α =0.31, average and length of the test 𝑡 = 30, 𝜇 = 0.69
• 8. Design • Define Reasonable Number of KPIs ▫ It’s impossible to conclude based on 20 KPIs • Project your KPI on Main Business (Lead) Indicators • Consider Weighted KPIs or GPI (General Performance Indicator) • Seasonality ▫ Weekends may have different user behavior than Weekdays ▫ Holidays can be unpredictable • 7-days rule of thumb
• 9. Analysis • Statistical Parametric Methods • Non-Parametric Methods • Permutation Tests • Outliers/Bots/Fraud
• 10. Analysis • Statistical Parametric Methods ▫ Use confidence intervals based on KPI distribution ▫ T-test, Chi-square test, etc will work, but…  T-test assumes normal distribution of statistic  Chi-square can be weak when low frequencies are observed ▫ Try Hypothesis testing based on KPI distribution – it’s not simple but worse it
• 11. • Can be used as a generalization of Poisson in over dispersed cases (Var >> Mean). • Has been used before in other domains to analyze the count data (genetics, traffic modeling). • Fits well the real distribution. 0 100 200 300 400 500 0.000.050.100.150.200.25 Number of search Frequency Real data Fitted NB Fitted Poisson
• 12. Analysis • Non-parametric tests ▫ When it’s hard to estimate the distribution ▫ As Q&A for parametric tests • Mann-Whitney, Kolmogorov-Smirnov ▫ Pros:  Can be appropriate for unknown or not Normal distributions  More robust than t-test ▫ Cons  Less sensitive and have less power than parametric test (median as a parameter)  Assume that both samples come from the same distribution  Assume normal distribution in large samples
• 13. Analysis • Permutations tests 1. Calculate test statistic 2. Shuffle and resample 2 random groups 3. Calculate again test statistic 4. Compare to your original statistic, if is more extreme ->k=+1 5. Return on step 2 N times 6. Calculate the probability to get a result, more extreme than your original k/N - this is your P-value
• 14. Analysis • Check for outliers ▫ Plot your data on daily/hourly level ▫ Descriptive statistics can help (variance) • Try to filter bots and crawlers ▫ It is almost impossible to filter all non-human activity on the web. ▫ Automatic bots and crawlers can bias the results and drive to wrong conclusions. • Continuous A/A test for sanity check for the whole system ▫ What difference you observe between A groups and is it insignificant? ▫ Technical and tracking issues
• 15. Data-Driven Culture • Avoid HiPPO that is not supported by data Highest Paid Person’s Opinion • Be clear about your KPI & how they affect your business • Fight your ego – numbers don’t lie • 80%-90% of tests won’t give positive result • Learn from failed tests
• 16. Pitfalls • Picking an easy-to-beat KPI without relation to lead business metrics ▫ Example – focusing on increase click-through rate for banners/buttons and ignoring other metrics like user retention or revenue. • Using incorrect statistical methods or violate the assumptions ▫ Example 1 – assuming that KPI has Normal distribution without actually checking it. ▫ Example 2 – Using online significance calculators without understanding the data distribution
• 17. Pitfalls • Combining ratios from different proportions over time -Simpson’s Paradox ▫ Example: • Ignoring outliers and bots | not plotting data on a timeline ▫ Example: One outlier can change the test results
• 18. Pitfalls • Starting test without validation (A/A test as a solution) • Change control group during the test (solution- change them both!) • Technical issues with experiment group ▫ Example – redirect , cash, new technology • Running your experiment “until it will reach significant difference” • Not “anchoring” users to one group only (also cookie problems)
• 19. Reference ▫ How Not To Run An A/B Test ▫ http://www.evanmiller.org/how-not-to-run-an-ab-test.html ▫ Microsoft Experimentation Platform ▫ http://www.exp-platform.com/Pages/ExPpitfalls.aspx ▫ Simpson’s Paradox ▫ http://vudlab.com/simpsons/

Nov 23, 2017

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