Sequential Confidence Intervals for Comparing Two Proportions with Applications in A/B Testing
This article addresses the use of fixed-width confidence intervals (FWCIs) for comparing two independent Bernoulli populations in A/B testing scenarios. Two sequential estimation procedures are proposed: one for estimating the difference in log probabilities of success and the other for log odds rat...
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| Format: | Article |
| Language: | English |
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MDPI AG
2025-01-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/13/1/161 |
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| author | Jun Hu Lijia Zheng Ibtihal Alanazi |
| author_facet | Jun Hu Lijia Zheng Ibtihal Alanazi |
| author_sort | Jun Hu |
| collection | DOAJ |
| description | This article addresses the use of fixed-width confidence intervals (FWCIs) for comparing two independent Bernoulli populations in A/B testing scenarios. Two sequential estimation procedures are proposed: one for estimating the difference in log probabilities of success and the other for log odds ratios. Both methods showcase great efficiency, as established via theoretical analysis and Monte Carlo simulations. The practical utility of these methods is demonstrated through two real-world applications: analyzing retention rates in mobile game Cookie Cats and evaluating the effectiveness of online advertising. |
| format | Article |
| id | doaj-art-f4b7c31b68d14bd8b125d6453fc26d8d |
| institution | Kabale University |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-f4b7c31b68d14bd8b125d6453fc26d8d2025-01-10T13:18:27ZengMDPI AGMathematics2227-73902025-01-0113116110.3390/math13010161Sequential Confidence Intervals for Comparing Two Proportions with Applications in A/B TestingJun Hu0Lijia Zheng1Ibtihal Alanazi2Department of Mathematics and Statistics, Oakland University, Rochester, MI 48309-4486, USADepartment of Health Policy, Stanford University School of Medicine, Stanford, CA 94305, USADepartment of Mathematics and Statistics, Oakland University, Rochester, MI 48309-4486, USAThis article addresses the use of fixed-width confidence intervals (FWCIs) for comparing two independent Bernoulli populations in A/B testing scenarios. Two sequential estimation procedures are proposed: one for estimating the difference in log probabilities of success and the other for log odds ratios. Both methods showcase great efficiency, as established via theoretical analysis and Monte Carlo simulations. The practical utility of these methods is demonstrated through two real-world applications: analyzing retention rates in mobile game Cookie Cats and evaluating the effectiveness of online advertising.https://www.mdpi.com/2227-7390/13/1/161A/B testingBernoulli proportionsfixed-width confidence intervalmobile gamingonline advertisingsequential estimation |
| spellingShingle | Jun Hu Lijia Zheng Ibtihal Alanazi Sequential Confidence Intervals for Comparing Two Proportions with Applications in A/B Testing Mathematics A/B testing Bernoulli proportions fixed-width confidence interval mobile gaming online advertising sequential estimation |
| title | Sequential Confidence Intervals for Comparing Two Proportions with Applications in A/B Testing |
| title_full | Sequential Confidence Intervals for Comparing Two Proportions with Applications in A/B Testing |
| title_fullStr | Sequential Confidence Intervals for Comparing Two Proportions with Applications in A/B Testing |
| title_full_unstemmed | Sequential Confidence Intervals for Comparing Two Proportions with Applications in A/B Testing |
| title_short | Sequential Confidence Intervals for Comparing Two Proportions with Applications in A/B Testing |
| title_sort | sequential confidence intervals for comparing two proportions with applications in a b testing |
| topic | A/B testing Bernoulli proportions fixed-width confidence interval mobile gaming online advertising sequential estimation |
| url | https://www.mdpi.com/2227-7390/13/1/161 |
| work_keys_str_mv | AT junhu sequentialconfidenceintervalsforcomparingtwoproportionswithapplicationsinabtesting AT lijiazheng sequentialconfidenceintervalsforcomparingtwoproportionswithapplicationsinabtesting AT ibtihalalanazi sequentialconfidenceintervalsforcomparingtwoproportionswithapplicationsinabtesting |