Fundamentals of Biostatistics SIXTH EDITION Bernard Rosner Harvacs University 24 Baamole 2a Exorple 22 Descriptive Statistics Introduction ef sep aking 3a In Ae Het Fad ve so real sss Ue fn Be acme fy Tg ath ta 1 er ral hasteve, this pred is fee impenrie wnd, oFea b L Ner pra, (Son er abtean veal yt asf Hata bh Pe Cancer Nurtlon Snr nesses hase ym hat ronson sei Preven cancer Te es ns they, ilary urs ner te ete cal ‘ova remmunaplon avy 201 Ipapitaed ganner caves nd 2D reas Fight Be wea ome nol be ats ae a 4 RO HME eS fied wont ei the hen gee Sree si ore mets sone Wt Sed Lestat eal re they are cll? efor ay formal meant to anew his esto car be de he ve ensumption amiang ses ane! carols wet be eee. Conder Fyre 21, The br pruphs show ually tit she contals lave a bigher stan consumpsion un te cases do, partial at consumption leds exceeding the Recoramendad Daily Alscunes RDA, Pulmenaty Disease Medical issetcchers have often suspscied tke: passive smokere—peaple who ihenesles do nol sake Rul whe lie oF wer In an exon rent whe thers smoks might nace patie? pulncary function asa ras In 1980 a esearch gloup im san Diego pulsed nels necting thal pase smoke rid Indeed have sglficaly Inter paleo fuel than chara no “oot he didn ork ina enn fi suring ene, he Authors metared “ha carn mcngsite "0; cine svatiens in he nike ai Feninens if ave trinane tl sen len ir srhin peed inser pare nar i she ee 2 oman ange ve ne ore a the dak the els are easel a wae jot He 27 2 atusdhenr 7 Figure 2.1 Baty vitsminnA consumption among concer caste and contots Figue 22 olerty shows i the CO serumzatlons i the te winking ee ens zeal the sare ean Ln Ue da bt vasge wl nthe le of se ‘hiya he: ener again ae tha Nerking day saver at 7p Graphic iggy Lastanehe-mon-iaut aoe of hes ties ti whieh 61a "uweh disp dota Lo giv the nearer ehue at In the pine a een the ata 26d syst nts as where a moet caok tthe data he el ‘af Ivete sais, ght ¢ athe. ds pie sll a eh fait Imgertant Ia conveying Use fil walt of segs = tn pubeatwe ‘Une ue of ther primary erat mca eles wl rn hn tm ne alge ce the ne OF otRSs tt be ev cee many a Hee desi stall grssemsad ‘Sow wakes a ace graphic once display? The main yioins sta th tale shuld be a8 ethcoatained ay posse fu stoskd 9 ulestndase ie ur sein tae eat. These albus ezguie ene being. The eaycans dni ded {ecm yeh show be eal ace ane Ihe sitll les sed Uae a s 22 Neon evhan-moneside sorcenaton (= standatd amon by te of day 1 prem antear ‘teate should bes: dened. The quanlty of mates prsented a eu po Tanti nar zaps ace corsucte, hen cate msl fe ken te deploy nelthr 300 lang a4 oo few azo. tne sam? Is Lue o! buat mete ‘Man ansthss ae va lable summarizing da. a bach nue‘ and grape leven Ins caper hse methods are sume ved and Laee sents and Hee tis te Measures of Location Tae baie pre ol tsi 1 a ate a lve Cansides arm ea a rye eek teteme cryin eM ibe pp a3, vores eh ln San pee. Revi at Ue sap aoIomh ene pp a Ssheinieieuecor sumtssonecan be race ale Pui the ane Table 2 etae th:s quetiom en) be ateceed, the data eMUS he sum a8 free an posable, beczuse she maunbet a sample inl len Inge and kes ey lo ose a of ae serail ysture By Toosing a i ta dats nt ont, De type Pesan seul fo soarariny sata define lg rch, srl of Hs samo Uhistye or measure ga auvasute of Toca, The Arithmetic Mean flow tu cee Use idle ut somple msy sein obi, bat she swore yn thi, aout she lesson ius itbouamtes Stepaee te sareple fn as of ale set st Toedeaz anf. burr aa pavate hasnt im Sa lege, Califor, ding owl peice thi sainple fie In ple 2. (ue measure 4 lesen for 88 ale he elec ream coogi ‘onl te acer. The arte nies ean 4: same rcs ast. Pace by 1 earithmelie aaa i the sun ot all re obser cereariens I item aaa er a sion divige Dy Oho nurcr of The spa © sigs} in Doin ien 2.1 ¢samanales ign The esprsinn = simply short ay ol wing ts quality (9 =~ ssa Bane sper ene a £8 chen RISEN tal HP ‘Sample of hinheights ig} of ve-botn rant: born at a iva hosptat in Sum Diego, Caifamis during a I-eeh peed 0 Example 23 seuton example 24 , Maedche Ejay te Gre gnvesty sur aation signs sta ae stm Ia ns uremallon 13 estplsof the ae Carsten can be Esto: Pant ‘tesuaurien, tes 16 mp tal sn ema rh sane se. hag a steerer inne wink the tet ees thee nee oe see et se 2 frass sand dake nes funy rat be nenasetrive ot kaon epee sat ste ne pt Forme, thy it tn Tole.” aye es bea prt ane wg fg geet ta 1255 g shor the ator cut at re yell WOK g Dues stance, Peso sireighos uel lay tam Pheer cm ral 4 ipockl be She tive she arc ie Is pose Feet Sve fork cue of tae ape ts ws Uo cme se uf te atts rc Te antaasts iu poor sucesso Testo fa tae ts os Pe, Incas eas sot elect the cenreet Yar sumple. Neves, earache. ieaytir the rant dey eset carne of cerca ‘eine, The Median An ahotoatize mazsuce 9 ceasem. paps second 3 sopvlanty to tke a re tear i he medlan er, mare srseely Ce sample medlan, Suppese tec ie nshserasions a sample. I Cac absense eer froye smallest lates, ‘Ren she Teed ie defined as foe The sore mein it cry re" Poy test obsenate rh) 9 mie wurgect ths [fey ame 8 ae ang sbserations ct even ‘The eotuuste (ns ches Getactions ite eeange am eval amber of simple sont bates afche ample ring. Te mui Sins erently wee, ‘is estn and ee. bocause 5 uupussble to achieve ths gal with ue Ueter=, Getonrion. Samples wie aod simple se mave a unicue cena so--~ forte inp Sor sorepes oe 7 the aot Ingest un th cent Fpl th see Shee? pena arsnaler thas. cara? point a lyst Samples wrth a even aero "Eze have na erigue cesialpeint, ahd the mice seo valace real bs aee.aged Thus. et sarees of 70 § Ue court ane fe Gages site soule e aver) lta une sete, because mete ths stn! pr {Soryeae Psat Ho He aan Tale 2 Fis, cage saunter sein Sin plein = ayseage nr 6 ast “1D ange surat Infectious Diaesce Comins cit fibue 2 whic mets wha ae ‘vet kam om saan of al pats entering sel lpia iw 8 emo, Pernsytvuaia.one gre day: Compute the neac whiteblco! tenet Sample 0 adnierion whte-blood courts (2 1600) forall patents ercerng 3 hospi in Allentown, PA, on a siven dy 12 CHAP C8 ae Dew Skestee Soliton, # Fes ome bee aye ast Kos $75 520,12; ARs ress me splenic De ie He epson SEC ab Ise mute soma Mie sau ke mein isha is inoenebe Re ey aR al ves tn piu ihe sce paisa ae 2.2 hal # te ca er ssnvratne torte) a ne mud elt ein meer, hee the ite go wal, oll) Cheverly, (ae a nelle mea oral re ait fe (278 i He org sale U1 Uy eat ty The i ke a gle ners ae eee my hy elle pete suey lege usin He ata namie ales oP re Camparson af the Arthmatia Mean and the Median In irtaia is spmmetca, to tk sss pene cf the et gah ike src spe aoion ove te sons, Aun ecaphe of ib ten capes Be esgly petunia the eon oF pwac et prconn 4s PS ‘tall 3» 5-year sony wotkers maven wera gee 2.38 Figure2.3 Graphic splays cf) symmenic (6) positively skewed, ard ie} negatiol skewed dsr tions Example27 Tahte2a Exarpte 20 22+ Mesan!Locaen 1 Ina cheributnn pamtlvay skews! kee 39 the rt) chem pois ate thee naan roe he ss Seo the cl i eal value a pois bon the oie, An ora ef suc a Hitooton i he bse ute mmber of youn uf ur coasrave sive 1OC} use mcg a glow oF era ages 20-29 sea ‘a 2.26, Sina, c'lihciosis negatively eerred head to eli ther ‘ints below hs wre” tend 3p father om de reds nabs aie than Points above th: wien. a etaeple of sch a de haron fs Ihe albu of Felvehumidics nerve 2 Husa liste a: the ame lite ay ove a a bet of aye tnsttersr tha des ace aoe cae lo VND arch a ese Let uals on dev ens gan 250. Tr manysacyies elses ae3sbsn Me a HAR. ean ar eS radian can or wel 9s Neen Cision ln 3c, 0 ‘etic dsibatons the athe ann i apie ye Sai he ia sudan tor ngaie'y semis Yautions heretic naan lel Er hesler Tha Mode Ache wily el evs testo: the ase ‘Toe mode 's the most Sequel occusng velue amens 3: zhe cs-wauens tm aml Gynceol2ey Canstder Ibe spl 9 Gn: interval ere auscesiee mene pees fora xroup 9 9 calege one ago HPT hse In fale 2.8. ef Fascy cour gives eure acon ahi epied wash of se veel he Tarn che mo 2, bean tl ne, Paquet vat ‘Sample time intervals hetwoon succession menatwal porns days) of calegrrage women Compu ths mode of tne disuibutlon ¢ 12kie 22 he modes HUG, hocatse IL accu see fee Thct any oer ehis-Houd, “ eramploz8 Satin Soe viento hago ute than gre mle “n fat, oe wey acto af uso is utlons 8 ths monToe ol wes prseet, A oution th O° ‘vale io elles uaegodali so mde, hirnlal Mese mees, tiwandal; A 30 teak, “Comnpte the made ofthe atl 1 Tae 2. ‘here ne mode, bosats all he values eccut ext anes. Examp'c 2.9 musiats a commen probleme wi the mode: Nota Useful rrusute of locaben there tgs muenbs: of posINe a ues, eae fick ec- fate mnequenty Tn such sues the muceil besa fr Gn Ue center ef te fmipce on ln ex sins cate wll uct ae Hxainake 2.9, The mode enet vend indies wee because ie matbomatieal properues as genset Inter, And ia most common suualone tis tne a te abate, The Geometric Mean vane 1s9es of abovaeny date, spectical'y dala > the frm a? soncenteations af fine substance i analner, ae aetased by svi eluion technqacs, ca be sx rete rien At nu plo Ze at eens eMule ey aes of 2; thal Pat aes Caos eva the fasm 2,2 =O. Far sOmEconstanl 19 See fe ss deta lable 3. aquest sal inna sensi AN ‘iin € nas wna fv N. enantio patents (2. Hoe whet ‘hen yin papain snare fra) nn F 1 lay, yaa se sever, hl hy hae ese ps le Mca? te cay poe was Tilia tie bags teesienteatonn The spear have heer that suivesive pesuible cinent-aP ine iter ya censor Hist, A HN) Woy tt Woy e Mowe = tog eT ty 2k ey 2 1g? Tlan, te og egreerttne am eal are Ese ct lle ge he Salty lista yr ok ae skeen terse ve Te fatlaetc nes con them be comme me ey ese: Hak Diate.ton of minimal hor oancerrston Jac? ut pence fr gonotenoese