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. *Svewed graphs > pull mean \n direction o¢ the svew » the sam syromertie gtaphs? Mean and Median Will be appro x Measutes of Spread 4 Range (max-min) & Non-resistany Couriers misiead range) x 5H SUMMary se min . quortie\ (Q\) = 25° percentile eo medial + quartive 3 (Q3): 75" percentile « Max x Bi Summary Graphical Display + box and Whistler plor - Anterquarile range (\ar)> @3-G (ves\sian4) TT Aix enh ch M Os x Calculating an Ovil\ier + any Thing, Kad FAS OUSIAE > Modified Box + Whnsve bs @y~ 19 (NOR) Plot by ay* 1-5 (VOR) ° ‘ a Ly standard Deviation % Measures he average A\stance of every obSeYVA\\on from ‘he Mean [si = *VOTIONCE (na) (4-3)? + (v;-k) 4... 4 yn)? N-\ N= H of Aata pornas X= mean value of Xi Xe each values of data x * The Empivicay Rule .. Symbois =) x = Sampte mean by Sa = SOME Stondard deviation b mM: Popriation Mean 4 0 * population Standard deviation * Nocma\ Disiribuhons - peated ¥ symmernc, Singie - PEalted, and & + 68/95/49.) Rule x Namal 4 N(m,o) = formal Ly 68% of data \ies 745%, oF Aata \\es 2 SY¥d. dey V 44.1% of dato \ies 2 sta dey Noma) Density Curve \ 7 = S . YER oa & ES g B4y, \s%s M300 M-IO M-T OY MPO MIM- M130 X = -a2 -) 9 AY 42 +3 2 ¥ the Standard normal Distribution is the Norma Distribution With mean o And Std dev | 3 = X-M oO jo find Probabitity P( 2 +) or P(2 >8) use Norm caf be-shaved, determined oy “ \ Std. dev away fom the mean (mM +0) away Com the mean (+26) Away Fom Mean (4 +30) -m\e rE east be Norma) an\y populations can Assessing Norma\iyy ( Y Pop deportures From \ ® Mistogram and Check for ty Method) = move Normatity Method 2+ Malle A Normal probabvirity elot ( from oo | Chaprer 3 f i Normal POPUIAKIeN) X Scatter Plots 4 Correlation ey Varvopves Study (y * Yesponse varjavie = measures tne outcome of a ¥ (y) * €xPlonatory Vatiabie = LESPonge YOuvabie (x) Ly Scatter Plor = form Plan avory > \inear or . Strength : Ly Rela Wonships . Positive ASSOC OL ON = No Ly cove \ation (r) = Measures a \\near Yelaran Ship between 2 Yr ii ey no ASsocl\ation + WACaton OF YC data S\splay fox Owe chon = Non\inear Wear oy Higher x Neqaive OSsociation = Shron ma) \ow x, “Mowledae of Xi-x Sx y's Behavior Ane OF Neither? ) Mighery Nai y x ‘eveasing Or \inear > Sampve Comes Ages IN a May Nelo explain or Predich Cha CY 2 Quaniitative VOvabies POSihive, Negative, Aecteasing gwes Strength and AWection oF QvVantivative Vari aves I) * P0Si4ive y= Pos tive x Negatwe v= Association Negative Association \ sid dev Slope (b) = ¢ (57/54) \ndicates dnat a Change i NF Corvesponds 40 0 Change of Wr sid dey in y . +/- | X when the vatiabies are perfectly covetared (r= t/ ) the predicted vesponse, J, Changes precisely the same Yn Std dev units as x Changes “OS € \S wealer, y Moves \ess in Vesponse to Changes in xX 2 Ly Ane coefF\cieny of determination , : (fo error) in y that 1s of yy on xX. \t Is \s the "% of variation , explained by the least Squares Fearession ® Measure of how Successeul \wne was In ex Planing the Tesponre y \s unexplained the leavession the vest of the vanation * bounded From 0 to\ * LF Yeally good, OF trash LG Residvat Cevvor) > Ane Aiefevence between an observed VO\ve of the Vesponse n Voryabie and the value predicted by the Yegvession line ¥ k Yesidua\ = yes (observed preaiciea) K Ves\dual Ploia determines ie dhe \inear model \s Appropriate veavession line Orpears as a hors 2onia\ \\ne Yhrougn ine origin X SUM of Yes\duvals =O X \oow fore = Tandom Scattey “NO Pattern * Consistent band Width HAT where is 9 CUYVe | Pattern, of INCease/ decrease \® bond width, then the \\near model \s tie La~ye(l) AY prcathy extremes Yes\dvals (doesnr4 appropiate Ly outers \n the y ditection and Nave large Wt Qenera\ patyern) Ly \nf\vential POINIS = Extremes ‘nN the DKOSH Cally Changes {h x Aivection , removing them e€ Yesiduals L, Associaton + Correlation # Causation \)) Causation ®— 6 Z) Common Yesponse > observed association between * and y Ani \S due lo a third lurking variable (2). gray be no 2h between xX and y, but both vespond yo z Q® ® No 2) Cofounding > both the explanatory X and the Namieing “27 ate Vmpact no, Ahe vesponse Ys and we Cannot distinguish between Mne eects of Fhe 2 apes ha Choprer 4 x Vocab Ls popviation = the enitie group of Indwiduals La Census = atiemet 10 Qother dala from Me enttye Zopviation Ls sample = subset/por\ion of the Populanon Yoot dato \s actwally Ob\ained From , used fo Mawe Conclusions about the population Ly gorameter (p, rr) = 0 # that describes the population el Categorical PrOoporrion «th? quantitative mean 3 Ly Shatistics (f,%) = a # dhat describes the Sample, used to estimate the parameter Ly Probiems with Sampting oF the Popelaq v) under coverage ~ occurs when Some members Cannot be chosen \n O@ Sample : ; those that are Tepresen 4+ tan contribute fo brat ¢ are similar in Some Way of Selecilon uc, Non - Sem pling Errors > noy an error in the method ch, lost In the mat i») PFOCE ES ING error+ data entry error, CRU glitch, ecd, or their 2) Non-Yesponse error > farture to Contact the subject, Vefusal to participate (yin 3) Response errors Subject provides False information lying, MiStaven Yeeoection , Confusion, €4¢-) Ly 9 bservational Study + observe/interview subjects + Measure Variables C ° An tevest Without Attempting to ifluence ¥ Experiments = Aelibevarery ‘Mipose a tHeaimeni on units in ordev to MEASUVeE Yesponse , the Prreose 1S to Study the Weaimeny dhe "€sponse/benavioy of dine the e€ect of In Causing a Change in Subject lL Weatmeny = exrerimenjay Condition tral Is \Mplemented by the expevimentor and 4s to the Subjects “Pp nSA 4 factors = explanatory Vanlable “> \evels= va\ues of Yhe explanarovy Variable k ON\y A Contro\ied exPer Ment studies can?t) CaN Show Causation (observationa & Completely Randomized Design (ceo) Ty: Yeal Weatmen} ra (7/3) P< SRS Compave = a Yesponse TZ" contol Jioup (nya) ‘n’ experymenial unis Principres of Exgernmentat Design = 1) Randomiation — Assign UNS Tandomiy 40 tNeatment Sroup- this i] Ne\ps Create Tovgnry equivaleny Qtoups of experimental unyts by balancing he effects Of otner Variabwies amoung. the Heatmens Qroups 2) Repiication > Conduct the experiment on 3) contro (eloanite the e€ects of Weep other VOVVOble Many Subsects/units (n) Vuriing Varvaples | and Pray Mgnt Flect the Yesponse the Groups (contro) Group = No treatment, Same for all Placebo) * SAatstical Stanifeance = OPServed efter 45 So \arge thay ay Wavid Vorely have GCcurved by Chance , thevefove . the explanatory Vaviabive must have causeg it. — Errors ') Widden Bias > EK PETIMenN\s Tey on are ieated the fact thay ali Subyects equally Ly Dovbie blind ex Peviments - Mether the Subject Know who has Ly S' Nave vind = he/she Evalvator ot the Yecieved whith Yeatment Subject doesn’ Know Which tY €atimeny Vecltves | buy CVAIUAtoY does LY RefUsSaiss yetye to Participate 2) NOn-adhereys > Participants den'+ follow expevimenta) Pletocol 4) Drop- outs — Hced'y Whiews Subyects leaves Study (side effects health problemr | dies, ete.) / S Blow a « group of experimental units that are SimMiar in ways Vay ave expected to affect the Yesponce to tWeatment VW (x73) ~, a (412) —— Compare xe — ay (x/3) —? eis Compove men + ~ (=) NN blocre nF ; oO Women -* Campave x Sin ’ —— To (4) —. woren 4, (e es Mutually Exc\usiwve 4 2 events (A1B) ave Mutvayt y &¥clusive (dis yoint) \f they have no OUI Cone ¢ Some time / Con Nevev ocey ay the \ Common nd log ether Le A+B ave Aisjaint — P(Aand B) =0 4 P(A or B) = BA) 4 PCB) x COmPleMentary A AAe y Pp the entive Sample SPace * OrSyoint—> do oy Nave up the entive sampre space Complementary A\s joint O® x Mersecing Evenrs x Comainment P(A) s v © 4 YMGENS the UMlon of OMY Collection of events \s the event that OA least one of Ihe events occurs 4 the “Mon of A ond Bis the Probability of A,B, w boy * P(Ayg) = P(A) + (gy - P(ANB) (union, or) (inter Section, and) L, Conditiona| Probabrisy + \ndependence * the Provabiity we Assign io an event can Change owe Know MMOL Some Other eveny oy COMMON, has occured 4 Conditiona Preba wii ty whe Probabitity that \ eveny that another event 5 happens aiven OWNeoay \nowh to have Nappened ‘ (Bla) > Conditionay L, Probatitity “% Oiven a» bs ina the Probabvity of B gyven thay A has Oued already ovds = IF, = PCAN) Intersection "ey wen, Why * POBIA) > ane PC A) condition that events A o X geneval multiplication rule > the Probabiiity B both occur can be Cound using Wis Ly Pf ang) ~ P(A) PCB\ A) L n No effecy 0° \nde pendence Wo tne occurence of ane event hos the chance thay the Other event wi\l happen * PCA\B)= P(A) ond P(BIA) = p(B) X Mutt plication tule for inde ove NO erendeny B both pendent events 9 \F A ana B Events, then the Probability that A and P(ANB) = P(A): P(B) OCCUY \¢ ¥ Intersection =0 + \€ events ave Metvally exclusive 4 PlAnR)=0 ® Miersectyon = Product * if events ave independent SP (ANB) = PLA - PCB) Ls Aripte Union * P(A UBUc) = PIA) + Plays prc) - PCA AB) - PLAN) - P(BNc) * P(ANBACc) L> pCa) = P(ANB) + PlAN BR) Chapter 6 * TONAOM Variable = a VANAble Whose of a Valve is Tandon Phenomenon A Numerical outcome i x Aiscvete Yondom VOrlable = x has Values . The PiObab,\, X and they a Countable YY distribution of x CONV spond ing Probabilitves ( Wowwe | xs | xa ts | xg remy Te. Ve Le Los Rumber of possibte sts the values of d Mest add up to \) LL avles L, Trans forming 4 Combining Random Vari ywatlon x adding /subtracting O Constant 10 each obse location Ly odds %a° 10 Measures of Center * of spread Ly coes nod Change shaper or measures nstant * MUN prying /Aviding tach observation by a Co ocailon by b ly multipnes/adivides measures Of Center + loc rd (an, std dey) 4 multiplies / divides Measures of aprend fronge, by bv by does oi Change Shape X Rules For Means dom Ly \F yr ars 15 a \\near tansformation of the rande nstants Naviaple xX, Where © and b are real Numbered Cons E khan... \) the Probability Aistri bution of y has the Same Shape os the Probabiihy distibutian of x 2) My= Maroy = at bMy 3) Fev any 2 yandom Variables, X and y, if T= x+y then the expected Value of T IS E(q)- Mn? Mary * MA gay = My + My x Rules for var; ances Ly \e Y= Ara 1S O linear tans formation of tne vandowm VOYIOe x, Wheve i a an ab ave Yea\ Num ') Garx=\b\O% 3 Tory = BO, heved Constants | then. 2) Me variance of The Sum Of Several \nNdependent yandom Vaviguies ‘S the sum of 2 2 2 3) xy e Oy 4 Oy : £ x Kand y Mus} be j o x-y= Ovx + O'y Indeperden} ] the, Variances not X variances add, Std dey do no =) Vauiances only add Qo ort oy 45 Ly Binomial Random Variavies (2 ovrcomes) * Criteria \) Dinory> theve ave 2 ovlcome,y Success and falluve 2) Yneve 15 for each tal, (p= Success) oO Cixed Nomber, ¢ 3) the Wn absevvations Classified as n, of attempts /obsevvations/ais Ave independent a ke a \nomial Fandom Variabie Ly xs humbey of Suceesses in ‘n? attempts “Sx javes on Values 29,1,8,.0.m% with Parameters 1m, p S 4 chectl : oS Nong as the \0%%_ condition \s satisfied x nf’on . Ly to cheew For Normality (in order to “D ye up) Xx Np2lo & n(\-p)2\o « Sample Means os the sample mean, K sqs of sive 1 drown dev O, then. is Mx=mM 4+ Ane Sampling Aisiiibution Uy suppose thar ¥ is the mean of from a large population with mean as cot Oe z * the mean of the sompling distri bution uk ge ¥ Yhe std dev of the sampling aystieurion of X \s On > TR ks long as the \o% condition is Met A \€ the popoiation distribution Is nermal, then the sampling Aistribulion oF Xs fermat (no matter whal nis) Ly Ane Probavility of KX af an SRS has mock MyCch much less Vora itity Yhen the Probability of just x Ly The Central Limit Therom (CLT) * Yegardless of the distribution Of the population, the Sampling Aistniburen oF Means/averages tends to novma\, Move and Move so as the sample size nm increases ¥ Non-Normal populations spawn novmal SAMPIing Aisi butions ¥ CLT> when n is Norge, ine sampung A\StVibution of the Samp\e Mean X is approx normal by YA N(M,e) 9 22 Yor 4b xX*#NO 7 = XM CVn 1€ n>30 L+ n>307 \n avdey to do Normal With sompres frown Non-norma\ Calculations Populanians x when nd 30 Ly mae Wistooram * loow for departuves VE OON LIS FA no outers From hovmalt ty or skeuneds Chapter § - Confidence Intervals TAS (Gar U RD Ha: cn re can Wandie some skewnes: Ly Confidence intervals ave used tO eSHIMATE the Value of a Parameter rom o Sample Statistic Ls confidence levels (10%, 19 %, AV) 
