Umbala we-Left Introduction Hypothesis testing 2.1 Introduction 2.2 Bayesian statistics 2.3 Test martingales 2.4 p-values 2.5 Optional Stopping and Peeking 2.6 Combining p-values and Optional Continuation 2.7 A/B testing Safe Tests 3.1 Introduction 3.2 Classical t-test 3.3 Safe t-test 3.4 χ2 -test 3.5 Safe Proportion Test Safe Testing Simulations 4.1 Introduction and 4.2 Python Implementation 4.3 Comparing the t-test with the Safe t-test 4.4 Comparing the χ2 -test with the safe proportion test Mixture sequential probability ratio test 5.1 Sequential Testing 5.2 Mixture SPRT 5.3 mSPRT and the safe t-test Online Controlled Experiments 6.1 Safe t-test on OCE datasets Vinted A/B tests and 7.1 Safe t-test for Vinted A/B tests 7.2 Safe proportion test for sample ratio mismatch Conclusion and References 5 I-Mixture sequential probability ratio test 5.1 Ukuhlolwa okuqhubekayo Njengoba isakhiwo se-A/B isizinda esidala, futhi kukhona izindlela zokufunda imiphumela ye-test [Joh+17]. Njengoba sikhona, oku kuholela isiphumo esizayo sokuphuma i-false-positive rate. Ukuze uthole isakhiwo yayo, amabhizinisi amabhizinisi amabhizinisi amabhizinisi amabhizinisi asebenza izindlela ze-statistical ezisebenzayo ngokushesha. Lolu hlobo se-statistics ibizwa ngokuthi i-sequential testing, noma i-mode-valid inference. I-sequential testing isekelwe nge-Wald's seminal paper on the subject, I-Sequential Tests of Statistical Hypotheses [Wal45]. I-Wald ibonise indlela yokufaka okokuqala yokufaka, ebizwa ngokuthi i Wald noWolfowitz zibonise ukuthi i-SPRT iyisisombululo se-sequential engcono ngenxa ye-power ye-statistical [WW48]. Kuye kubaluleke, kunjalo, ukuthi isakhiwo yayo se-test se-sequential ayinezingeni ne-safe tests. Imibuzo yayo isekelwe ekubunjini indawo ye-probability ratio eminyakeni ezintathu: ukulayisha i-H0, ukulayisha i-H0, noma ukuguqulwa kwe-sampling. Ngokungafani, i-t-test ye-safe iyisisombululo se-GROW [Pér+22], okungenza ukuthi i-E-variable E uzokukhula ngokukhawuleza lapho i-H0 ayinayo. Ukuphendula ukulayisha i-H0 kusetshenz 5.2 Ukulungiswa kwe-SPRT Ukukhishwa kwe-A/B test ye-sequential testing kubandakanya ukwandisa i-SPRT ukuze isebenza nge idatha ye-sampling ezimbili. Lokhu kwenziwa ngu-Johari et al. [Joh+17] owaqala inqubo ye-A/B test ebizwa ngokuthi i-mixture Sequential Probability Ratio test (mSPRT). Le test yatholakala kumakhasimende amakhulu zezobuchwepheshe afana ne-Uber ne-Netflix [SA23]. Njengoba ne-safe t-test, i-mSPRT isebenza kahle nge-granular, idatha ye-sequential. I-mSPRT ikakhulukazi efana ne-SPRT, ngokuvamile ngokuvumelana ukuthi i-parameter efana ne- θ0. Thina ucwanjiswa ngokuvumelana ne-mat Thola i-statistics ye-mSPRT emkhakheni yayo ye-martingale ukuze kulinganiswe ukusebenza nge-safe t-test. Umbhali: (1) U-Daniel Beasley Author: (1) U-Daniel Beasley U-Archiv iyatholakala ngaphansi kwe-ATTRIBUTION-NONCOMMERCIAL-SHAREALIKE 4.0 INTERNATIONAL. Okuzenzakalelayo Ngaphansi kwe-ATTRIBUTION-NONCOMMERCIAL-SHAREALIKE 4.0 INTERNATIONAL. available on arxiv I-Archive ye-Archive
