{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,21]],"date-time":"2026-02-21T07:42:44Z","timestamp":1771659764164,"version":"3.50.1"},"reference-count":12,"publisher":"Wiley","issue":"8","license":[{"start":{"date-parts":[[2001,4,6]],"date-time":"2001-04-06T00:00:00Z","timestamp":986515200000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Statistics in Medicine"],"published-print":{"date-parts":[[2001,4,30]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Two\u2010part models arise when there is a clump of 0 observations in a distribution of continuous non\u2010negative responses. Several methods for comparing two such distributions are available. These include the straightforward application of the <jats:italic>z<\/jats:italic>\u2010test (or <jats:italic>t<\/jats:italic>\u2010test), the Wilcoxon\u2013Mann\u2013Whitney rank sum test, the Kolmogorov\u2013Smirnov test, and three tests that use a 2 degree of freedom <jats:italic>\u03c7<\/jats:italic><jats:sup>2<\/jats:sup> test based on the sum of the test for equality of proportions and a conditional <jats:italic>\u03c7<\/jats:italic><jats:sup>2<\/jats:sup> test for the continuous responses. This conditional test may be the <jats:italic>z<\/jats:italic>\u2010test, the rank sum test, or the <jats:italic>\u03c7<\/jats:italic><jats:sup>2<\/jats:sup> corresponding to the Kolmogorov\u2013Smirnov test. This study compares the size and power of several of these methods. All tests have the appropriate distribution under the null hypothesis if the distribution of the continuous part has finite moments. If it does not, the <jats:italic>z<\/jats:italic>\u2010test has no power to detect any alternatives. It is found that the 2 d.f. tests are superior to the others when the larger proportion of 0 values corresponds to the population with the larger mean. If the reverse holds, the difference in the proportion of zeros reinforces the difference in means and some single\u2010part models (the rank sum or Kolmogorov\u2013Smirnov) do best. In those cases, the two\u2010part models are not far behind, although statistically significantly poorer with respect to power. Published in 2001 by John Wiley &amp; Sons, Ltd.<\/jats:p>","DOI":"10.1002\/sim.790","type":"journal-article","created":{"date-parts":[[2002,8,25]],"date-time":"2002-08-25T22:25:53Z","timestamp":1030314353000},"page":"1215-1234","source":"Crossref","is-referenced-by-count":95,"title":["Comparisons of two\u2010part models with competitors"],"prefix":"10.1002","volume":"20","author":[{"given":"Peter A.","family":"Lachenbruch","sequence":"first","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2001,4,6]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.2307\/1266044"},{"issue":"5","key":"e_1_2_1_3_2","first-page":"351","article-title":"Analysis of data with clumping at zero","volume":"18","author":"Lachenbruch PA","year":"1976","journal-title":"Biometrische Zeitschrift"},{"key":"e_1_2_1_4_2","series-title":"Health Insurance Experiment Series","volume-title":"A comparison of alternative models for the demand for medical care","author":"Duan N","year":"1982"},{"key":"e_1_2_1_5_2","first-page":"371","volume-title":"Epidemiologic Methods in the Study of Aging","author":"Lachenbruch PA","year":"1992"},{"key":"e_1_2_1_6_2","doi-asserted-by":"publisher","DOI":"10.1016\/0264-410X(96)00017-5"},{"key":"e_1_2_1_7_2","doi-asserted-by":"publisher","DOI":"10.1111\/j.0006-341X.1999.00645.x"},{"key":"e_1_2_1_8_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-6296(98)00030-7"},{"key":"e_1_2_1_9_2","doi-asserted-by":"publisher","DOI":"10.1002\/(SICI)1097-0258(19960315)15:5<477::AID-SIM217>3.0.CO;2-R"},{"key":"e_1_2_1_10_2","volume-title":"Introduction to the Theory of Nonparametric Statistics","author":"Randles RH","year":"1979"},{"key":"e_1_2_1_11_2","volume-title":"Stata Statistical Software: Release 6.0","author":"StataCorp.","year":"1999"},{"key":"e_1_2_1_12_2","volume-title":"Statistical Analysis: A Computer Oriented Approach","author":"Afifi AA","year":"1972"},{"key":"e_1_2_1_13_2","doi-asserted-by":"publisher","DOI":"10.1002\/sim.4780060110"}],"container-title":["Statistics in Medicine"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fsim.790","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/sim.790","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,11,18]],"date-time":"2023-11-18T07:45:39Z","timestamp":1700293539000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/sim.790"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2001,4,6]]},"references-count":12,"journal-issue":{"issue":"8","published-print":{"date-parts":[[2001,4,30]]}},"alternative-id":["10.1002\/sim.790"],"URL":"https:\/\/doi.org\/10.1002\/sim.790","archive":["Portico"],"relation":{},"ISSN":["0277-6715","1097-0258"],"issn-type":[{"value":"0277-6715","type":"print"},{"value":"1097-0258","type":"electronic"}],"subject":[],"published":{"date-parts":[[2001,4,6]]}}}