Cmpuaal Publc ealh Sac Fmula (Pa ) Ve: Mach 007 Old Fahed Decpve Sac Yu huld cme he cu aleady kwg he Sac Paamee P Emae Fmula Iepea Ne / Dcu Sum f quae σ df ( x x) N eay epea. Mea μ x x x A meaue f ceal lca; expeca Vaace σ A meaue f pead ; exped u quaed Sadad Deva σ A meaue f vaably, exped daa u. Me apppae f decpve pup. 5-p ummae ad bxpl - Yu huld cme he cu aleady kwg he Sac Fmula Iepea 5-p Summay Ne / Dcu Meda ha deph f Meda + A meaue f ceal Q0 Mmum lca Q F Quale Q Meda IQR Q3 Q A meaue f pead, Q3 Thd quale aka hge-pead Q4 Maxmum Iequale Rage ( IQR) Lwe Fece F ( ) l Uppe Fece F ( ) u F l Q. 5 F u Q3 +. 5 ( IQR) ( IQR) U deeme: Lwe de value Lwe ude value() Ud deeme: Uppe de value Uppe ude value() Accmpay decpve ac w/ EDA whe pble. Mea ad adad deva ae be whe dbu bell-haped a lea ymmecal. Aumg mal dbu, 68% f daa p le wh + adad deva fm he mea, 95% wh +. F he daa u Chebychev ule (a lea 75% f daa le wh + adad deva fm he mea). Whe cmpag de-by-de bxpl, dcu he lca (lk a bx, whke, ad meda), dcu pead (lk a IQR ), elave each he. Al dcu age (whke-pead), velap, ad ude value. The bx ca 50% f daa, daw fm Q Q3, ad he hegh f h bx he IQR (hgepead). The le de he bx Q (meda). The lwe whke daw fm Q he lwe de value. The uppe whke daw fm Q3 he uppe de value. Fece ae eve daw. Remembe pl d f ude value. Gd mehd cmpae gup, ep. whe dbu aymmecal. Page f 5 C:\daa\h67\fmula.dc
Cmpuaal Publc ealh Sac Fmula (Pa ) Ve: Mach 007 Teg MEANS -- alway epe cex f decpve ad EDA; emembe fallace f g. eg; emembe valdy aump ump dbual cd Te yphe Fmula Ne / Dcu Equal vaace e Sude Pled ( ecmmeded pacce) Uequal vaace e ( ehe-fhe pblem; Welch lu) ANOVA μ μ ( df )( ) ( df )( ) + p df + x x p a x x x x, df df + df Sadad e f he mea dffeece + x x ac x a x μ μ :... μ μ μ3 : fal (a lea e pp. mea dffe) df ' x x ( + ) ( ) ( ) + Vaace ewee gup k ( x x), df Vaace Wh gup k W W ( ), W dfw F ac F a W, df k, df W N k A cmm e fgeg quae he adad deva befe plg. Check e whehe vaace adad deva ae gve. Whe we pl he vaace, we uppe -ufmy f ad. Cd: depede ample, Nmaly, equal vaace Th e ca be ud whe equal vaace ae aumed aumed. Cde ug h e f yu pefmed a gfcace e f vaace ad ccluded heecedacy. Cd: depede ample, Nmaly ANOVA de ell yu whch mea dffe, yu mgh eed d p-hc cmpa. ANOVA ha all he lma f gfcace eg. Cd: depede ample, Nmaly, equal vaace Page f 5 C:\daa\h67\fmula.dc
Cmpuaal Publc ealh Sac Fmula (Pa ) Ve: Mach 007 P-hc Cmpa: The e ae pefmed fllwg ANOVA Te Lea Sgfcace Dffeece (LSD) fe Mehd K gup / Aump gup f each cmpa Numbe f cmpa: m k C Same a LSD Mehd yphe Fmula Ne / Dcu Example: f k 3 μ μ3 μ 3 Same a LSD Mehd a x x w +, whee j w j baed fm ANOVA x x j, df N k x x j F each P value baed ug LSD, p f p m Mulple e fe whch mea dffeece ae gfca. f. adju f he Pblem f Mulple Cmpa Lk a ummay ac ad EDA pu cmpa cex Teg VARIANCES Te F-a e Levee e K gup / Aump k gup k me gup yphe Fmula Ne / Dcu aume hee dffeece vaace (hmcedacy) : σ σ : σ σ : σ σ : fal σ 3... F a, whcheve lage Degee f feedm df, df Cmpue wh SP, had calcula Whe equal vaace ejeced, cde he fllwg mehd cmpae mea: EDA, decpve/ummay ac, uequal vaace -e. Keep he umea ad he dema paae. The lage vaace ge he umea ad u he df f h pacula gup. Page 3 f 5 C:\daa\h67\fmula.dc
Cmpuaal Publc ealh Sac Fmula (Pa ) Ve: Mach 007 Scaepl Ac Lk f Addal e Deeme X X (explaay; depede) ad Y Y (ep; depede) Label axe wh vaable ame ad u Judge Lk a cae pl. Ca ed be decbed wh a Wach f ela ha ae cuved, U haped, hew -lea. Leay agh le? I dffcul a egh f aca vually ( depede A Lk a he dec f he lpe (pve, egave, he cale f he pl) Dec fla) Oule may be mpa flueal Lk f P ude cae clud (.e., wh lage edual) Oule Cela Sac Sum f quae Cela Ceffce Teg Paamee ρ P Emae 0 : ρ 0 v. : ρ 0 Fmula xx ( x x) ( y y) [ ( x x)( y y) ] xx, a / df Ne / Dcu xx quafe he pead f vaable X quafe he pead f vaable Y quafe he exe whch w vaable g gehe The egh f he cela he ablue value f, ad deped he applca. Geeal gudele: weak f <0.3, mdeae f 0.3< <0.7, g f >0.7 The ceffce f deema ( ) he pp f Y vaably ha ca be explaed by chage X. Null hyphe aume cela. If we ejec, he we ae ayg ha gfca, ad X ad Y ae celaed. Iepea wk be f hee a lea elahp, ad feece/eg ρ aume ha X ad Y ae bvaae mal Page 4 f 5 C:\daa\h67\fmula.dc
Cmpuaal Publc ealh Sac Fmula (Pa ) Ve: Mach 007 Lea Rege Sac Slpe Ceffce: Iecep Ceffce Rege Mdel Cfdece Ieval f β Sgfcace Te Paamee β P Emae b Fmula XY b XX α a a y bx y ˆ a + bx whee ŷ he pedced Y a level x, a he ecep emae ad b he lpe emae b ± (, α )( b ) Y x whee b he adad e f he lpe xx Y x adad e f he ege Redual Mea Squae Cmpue b ad/ Y x wh SP ( edu d by had) 0: β 0 v 0: β 0 Null hyphe clam ppula lpe 0 ( aca ) Y X U e ANOVA, a decbed Lab Wkbk Ne The lpe dcae pedced chage Y pe u chage X (key ac) Y-ecep he value he Y-ax whe X equal 0 (eeded ach he le; fe epeed. Dbual cd: Leay bewee X ad Y Idepedece f each bvaae bva Nmaly f he edual Equal vaace f he edual Valdy cd (gd f, gd ample, cfudg) ump dbual cd. A few addal geeal cmme: Iepea a wh udeadg wha yu hpe accmplh. Make yu ac vald ad meagful! Cfdece eval ae uually me u ha gfcace e becau f he ably emae effec ze. Udead each ep, ju he cclu. Sep ae:. yphe aeme,.te ac, 3. P value 4.Cclu. The P value a meaue f evdece aga 0 (ypcal hehld: 0.0, 0.05, ad 0.0) bu pvde fma abu he egh, dec, mpace f he elahp. U cmpuaal l whe avalable. D feel cmpelled calculae eveyhg by had. Page 5 f 5 C:\daa\h67\fmula.dc