Study your flashcards anywhere!

Download the official Cram app for free >

  • Shuffle
    Toggle On
    Toggle Off
  • Alphabetize
    Toggle On
    Toggle Off
  • Front First
    Toggle On
    Toggle Off
  • Both Sides
    Toggle On
    Toggle Off
  • Read
    Toggle On
    Toggle Off
Reading...
Front

How to study your flashcards.

Right/Left arrow keys: Navigate between flashcards.right arrow keyleft arrow key

Up/Down arrow keys: Flip the card between the front and back.down keyup key

H key: Show hint (3rd side).h key

A key: Read text to speech.a key

image

Play button

image

Play button

image

Progress

1/179

Click to flip

179 Cards in this Set

  • Front
  • Back
Statistics & Research Design
Research Design
Qualitative Research
Rsrch is th systmtc study nd nvstgatn of a phnmnon n ordr 2 revl, anlyz, nd estblsh fcts, prncpls, nd thrys. Varius mthds of rsrch cn b ctgrzd as Qualitative or Quantitative. Qultatv rsrch cndctd 2 obtn a holstc dscrptn of th qlty of r/s, actns, situatns, or othr phnmona. Qultatv rsrch uses a nturlstc, cntxtual apprch, mphszes undrstndng nd ntrprtn, nd is prmrly nductv of natur. Nvstgtr's prspctv is an mprtnt elmnt of th ntir rsrch prcss. Prtcpnt nd nonprtcpnt obsrvtn, ntrvus, nd dcumnt anlys r strtgys usd by qultv rsrchrs.
Statistics & Research Design
Research Design
Quantitative Research
Quntv rsrch is cndctd 2 obtn numrcl data on varbls. Quntv rsrch mks use of mprcl mthds nd ststcl prcdrs, mphszes predctn, gnrlzblty, nd causlty, nd is prmrly dedctv. Altho, th nvstgtr's prspctv may b rflctd n th purps of th study, it is mnmzd n th anlys nd ntrprtn of th data. Quntv rsrch cn b ethr nonxprmntl or xprmntl. Nonxprmntl (dscrptv) rsrch is cndctd 2 cllct data on varibls rthr thn 2 tst hypths abt r/s btwn thm. Corrltnl rsrch, rchvl rsrch, cse stdes, nd srvys r ordnrly nonxprmntl. Xprmntl rsrch is cndctd 2 tst hypths abt th effcts of 1 or mre IVs on 1 or mre DVs. Xprmntl rsrch is mphszd on th psych lcnsng exm, nd it is th focus of ths sctn of the study mat'ls.
Statistics & Research Design
Research Design
Planning and Conducting Research
Ntails svrl bsic steps: Dvlpng an Idea n2 a Testabl Hypths: Onc nvstgtr idntfyd an issu 2 stdy, nvtgtr translts issu n2 a tstbl rsrch qustn or hypths abt th r/s btwn varbls. Chuzng Apprpriat Rsrch Dsgn: Nvstgtr chuz an apprpriat rsrch strtgy nd spcfc rsrch dsgn. Selctng a Sampl: Nvstgtr idntfys th trgt popltn, dtrmns hw smpl wil b slctd frm popltn, nd thn slcts smpl. Cndctng stdy: Nvstgt cndcts th stdy nd cllcts nd rcrds th data 4 latr anlys. Anlyzng Obtnd Data: aftr cllctng rlvnt data, nvstgtr anlyzs data usng apprpriat dscrptv nd nfrntl ststcl tchnqs. Rprtng th Rslts: Nvstgtr prpares rprt of rsrch rslts.
Statistics & Research Design
Identifying and Defining
Relevant Variables
A varibl is any chrctrstc, bhvr, evnt, or othr phenmon tht is cpbl of varyng, or xstng n at lst 2 dffrnt states, cndtns, or lvls. Whn chrctrstc rstrctd 2 sngl state or cndtn, it is clld Constant.
Statistics & Research Design
Identifying and Defining
Relevant Variables
Independent & Dependent Variables
A varible is an Indpndnt Varibl (IV) whn th varibl is blevd 2 affct or altr status on anthr varibl (dpndnt varibl). A varibl is Dpndnt (DV) whn status on tht varibl sems 2 "depend on" status on anthr varibl (indpndnt varibl). Th IV) oftn rfrd 2 as th tx or ntrvntn nd is symblzd w/th lttr X.
Statistics & Research Design
Defining & Measuring Variables
Onc a stdy's IVs nd DVs hv bn id'd, thy must b oprtnly dfnd - i.e., thy must b dfnd n trms of th mthd or prcss tht wil b usd 2 ID or meas thm. Whnvr obsrvtn is 2 b usd 2 ID or meas a bhvr, an mprtnt dcisn is how 2 rcrd or meas bhvr. 1 mthd is 2 obtn a narrtv rcrd of th bhvr as it actuly ocurs, w/th rcrd tkng th frm of a dtaild wrttn dscrptn or an audio nd/or vsul rcrdng. Content Analysis, wch nvolvs orgnzng th data n2 catgres cn thn b usd 2 smmrz nd ntrprt th nfo cntaind n th narrtv rcrd.
Statistics & Research Design
Defining & Measuring Variables
Protocol Analysis
Protcl anlys cn b vud as a typ of cntnt anlys. It is usd by psychlgst ntrstd n cgntv prcsses (heeded cgntns) tht undrly solvng a prblm. Sbjct's vrblztns r rcrded, nd th protcl (rcrd) is latr coded n trms of rlvnt catgres sch as ntntns, cgntns, plnng, nd evluatns.
Statistics & Research Design
Defining & Measuring Variables - Interval Recording & Event Sampling
An altrntv 2 obtng a cmplt rcrd of a bhvr is 2 lk @ spcfc aspcts of it by usng a systmtc mthd 4 smplng nd rcrdng th frquncy or durtn of th bhvr nd/or ratng th bhvr n trms of its qultv chrctrstcs. Mthds of bhvrl smplng nclud ntrvl rcrdng nd evnt smplng. Interval Recording nvolvs obsrvng a bhvr 4 a period of tme tht hs bn divded n2 equl ntrvls (e.g. a 30-min period tht hs bn divded n2 15-sec ntrvls) nd rcrdng whthr or not th bhvr ocurs durng ea ntrvl. Intrvl rcrdng is esp usfl 4 stdyng cmplx ntrctns nd bhvrs tht hv no clr bgnng or end sch as laughng, tlkng, or plyng. Event Sampling (rcrdng) ntails obsrvng a bhvr ea tme it ocurs. Ths tchnq gud 4 stdyng bhvrs tht ocur nfrquntly, tht hv a lng durtn, or tht lv a prmnt rcrd or othr prduct (e.g., a cmpltd wrksht or tst). Situational Sampling is an altrntv to bhvrl smplng nd usd whn gol of stdy is 2 obsrv a bhvr n a # of sttngs. Situatnl smplng hlps ncres th gnrlzblty of a stdy's fndngs. Sequential anlys ntails codng bhvr squncs rthr thn isoltd bhvrl evnts nd usd 2 stdy cmplx socl bhvrs.
Statistics & Research Design
Quasi-Experimental vs True Experimental Research
Experimental research
Xprmntl rsrch is clssfd as ethr tru xprmntl or quasi xprmntl. Altho all xprmntl rsrch is chrctrzd by sum dgre of xprmntl cntrl, or ablty 2 cntrl xprmntl cndtns nd varibls, only TRU Xprmntl Rsrch prvids th amt of cntrl ncssry 2 cnclud tht obsrvd variblty in a DV is actuly causd by variblty n an IV. Ths is b/c, whn cndctng a tru xprmntl stdy, an nvstgtr is nt only abl 2 cntrl th xprmntl cndtns nd dtrmn wch lvls of th IV 2 nclud n th stdy, but most mprtnt is abl 2 rndmly assgn sbjcts 2 dffrnt tx grps (i.e., dffrnt lvls of th IV). RANDOM ASSIGNMENT of sbjcts 2 grps, or "rndmztn" hlps nsur tht any obsrvd dffrncs btwn grps on th DV r actully du 2 th effcts of th IV.
Statistics & Research Design
Quasi-Experimental vs True Experimental Research
Quasi-Experimntal Research
Quasi-xprmntl rsrch nvolvs nvstgtng th effcts of an IV on a DV but duz nt prvid an nvstgtr w/same dgre of xprmntl cntrl. Most mprtnt, n quasi xprmntl rsrch, xprmntr cnnt cntrl th assgnmnt of sbjcts 2 tx grps bt, nsted must use intact (pre-xstng) grps or a sngl tx grp.
Statistics & Research Design
Sampling Techniques
Anthr erly stp n cndctng a rsrch stdy is 2 spcfy th pop of ntrst nd th mthd tht wil b usd 2 slct a smpl frm tht pop. 2 mxmz th gnrlzblty of a stdy's rslts, th smpl mst b rsprsntv of th pop frm wch it is drwn n trms of chrctrstcs rlvnt 2 th rsrch stdy. Th bst wy 2 nsur tht a smpl is rprsntv of th pop is 2 use a systmtc smplng (slctn) tchnq. Std smplng tchnqs nclud: Simple Random Sampling, Stratified Random Sampling, and Cluster Sampling.
Statistics & Research Design
Sampling Techniques
Simple Random Sampling
Whn usng the Rndm Smplng mthd, evry mbr of th pop hs an equl chnc of bng ncluded n smpl, nd th slctn of 1 mbr frm th pop hs no effct on th slctn of anthr. Rndm smplng rduces prblty tht a smpl wil b biasd n sum way, esp whn th smpl sz is lrg.
Statistics & Research Design
Sampling Techniques
Stratified Random Sampling
Whn th pop of ntrst vares n trms of spcfc "strata" (chrctrstcs) tht r rlvnt 2 th rsrch hypths, an nvstgtr cn use strtfd rndm smplng 2 nsur tht ea strtm is rprsntd n th smpl. Ths nvolvs dvdng th pop n2 th apprpriat strta nd rndmly slctng sbjcts frm ea strtum. Typcl strta nclud gndr, ag, educ lvl, SES, nd racl, ethnc, or cultrl bckgrnd.
Statistics & Research Design
Sampling Techniques
Cluster Sampling
Cluster Smplng entails slctng units (clstrs) of indvs rthr thn indvs nd ethr ncludng all indvs n thos units n th rsrch stdy or rndmly slctng indvs frm ea unit (th lattr tchnq is clld multistage cluster sampling). Clstr smplng usfl whn it is nt pssbl 2 ID or obtn accss 2 th ntir pop of ntrst.
Statistics & Research Design
Sampling Techniques
Random Assignment vs Random Selection
Rndm assgnmnt allws an nvstgtr 2 b mre crtn tht an obsrvd effct on th DV ws actuly causd by th IV, whl Random Selection nabls th nvstgtr 2 gnrlz th fndngs frm th smpl 2 th pop. It is rndm assgnmnt tht dstngushs tru xprmntl rsrch frm quasi-xprmntl rsrch.
Statistics & Research Design
Methods of Control in Experimental Research
Whn cndcting xprmntl rsrch, nvstgtr is usuly attmptng 2 answr 2 bsic qustns: Is ther a r/s btwn th IV and DV? If so, is the r/s a causl one? A stdy's dsgn allws the nvstgtr to cntrl 4 three fctrs tht cn caus varibilty n th stdy's DV: th IV, systmtc eror, and rndm eror (eror du 2 rndm flctuatns n sbjcts, xprmntl cndtns, mthds of msmnt, etc). Nvstgtr wnts 2 chuz a rsrch dsgn tht 1) mxmzes variblty n th DV tht is du 2 th IV; 2) cntrl variblty tht is du 2 xtrneus varibls; nd 3) mnmzes variblty causd by rndm eror.
Statistics & Research Design
Methods of Control in Experimental Research Maximizing Variabilty Due to thw Independent Vavriables
Tru xprmntl rsrch nhnces a rsrchr's ablity 2 mxmz variblty du 2 th IV (xprmntl) varibl by allwng nvestgtr 2 mk th lvls of th IV as dffrnt as pssbl so tht its effcts on th DV cn b dtectd.
Statistics & Research Design
Methods of Control in Experimental Research
Controlling Variability Due to Extraneous Variables
Xtraneus (cnfoundng) varibls is a sorc of SYSTEMTIC EROR. It is a varibl tht is irrlvnt 2 th purps of th rsrch stdy but cnfounds its rslts b/c it hs a systmc effct on (crrlts w/) th DV. Tchnqs usd 2 cntrl th effcts of xtraneus varibls nclud: Rndm assgnmnt of subjcts 2 tx grp (Rndmztn); Holdng th xtrneus varibl cnstnt; Matchng subjcts on th xtraneus varibl, Bldng th xtrneus varibl nto th study ("Blocking"), nd Statistical Cntrl of th Xtrneus varibl.
Statistics & Research Design
Methods of Control in Experimental Research
Randomization
An nvstgtr cn equlz th effcts of all knwn nd unknwn varibls by rndmly assgnng sbjcts 2 th dffrnt lvls of th IV. Th rndm assgnmnt of sbjcts is cnsdred th most "pwrful" mthd of xprmntl cntrl nd is th prmry chrctstc tht sets tru xprmntl rsrch aprt frm othr typs of rsrch.
Statistics & Research Design
Methods of Control in Experimental Research - Holding the Extraneous Varible Constant
An nvstgtr cn elmnat th effcts of an xtrneus varibl by slctng sbjcts hu r homgnus w/rspct 2 tht varibl. Prmry shrtcmng of ths mthd of cntrl is tht it lmts th gnrlzblty of th rsrch rslts.
Statistics & Research Design
Methods of Control in Experimental Research
Matching Subjects on the Extraneous Varible
Anthr wy 2 nsur tht grps r equvlnt is 2 mtch sbjcts n trms of thr status on th varibl nd thn rdnmly assgn mtchd sbjcts 2 one of th tx grps. Mtchn is usfl whn smpl sz is too smll 2 guarnt tht rndm assnmnt wil equlz th grp w/rgrd 2 th xtrneus varibl.
Statistics & Research Design
Methods of Control in Experimental Research
Building th Extraneous varible into the Study (Blocking).
An xtrneus varibl cn b cntrlld by ncludng it n th study as an addtl IV so tht its effcts on th DV cn b ststcly anlyzd. Whn usng ths tchnq, subjcts r nt indvlly mtchd bt r blckd (grpd) on th bsis of thr status on the xtrneus varibl. Sbjcts n ea blck r thn rndmly assgnd 2 one of th tx grps.
Statistics & Research Design
Methods of Control in Experimental Research
Statistical Control of the Extraneous Varible
Whn an nvstgtr hs nfo on ea subjct's status (scor) on xtrneus varibl, nvstgtr cn use th ANCOVA (anlys of covrianc) or othr ststcl technq 2 rmov variblty n th DV tht is du 2 th xtrneus varibl. Th ANCOVA cntrls an xtrneus varibl (th covriat) by equlzng all sbjcts w/rgrd 2 thr status on tht varibl. Ststcl cntrl is a usfl mthd in quasi-xprmntl rsrch n wch sbjcts cnnt b rndmly assgnd 2 tx grp.
Statistics & Research Design
Methods of Control in Experimental Research
Minimizing Random Error
Xprmntl rsrch (esp 4 tru xprmntl rsrch) hlps an nvstgtr mnmz th effcts of rndm (unprdctbl) flctutns n sbjcts, cndtns, nd measrng ntsrmnts by allwng nvstgtr 2 cntrl xprmntl cndtns nd prcdurs. 2 mnmz th effcts of rndm eror, an nvstgtr cn mk sur tht sbjcts do nt bcum fatigd durng cors of th stdy, tht th exprmnt sttng is fre frm dstrctns nd fluctns n envrnmntl cndtns, nd tht all measurng dvces r rlibl.
Statistics & Research Design
Methods of Control in Experimental Research
Main Goal of this Section
An important goal 4 chuzng a rsrch dsgn is 2 pck a dsgn tht mnmzes th effcts of both systmtc nd rdmn eror. Svrl ways 2 cntrl systmtic error (error du 2 xtrneus varibls) hv bn dscrbd. Be sur 2 knw the dffrncs btwn thm
Statistics & Research
Internal & External Validity
Bsic qustns 4 rsrch: "Is ther a r/s btwn the IV and the DV?" "If so, is th r/s a causl one?" "Cn th r/s btwn IVs nd DVs b gnrlzd 2 othr peop, settngs, times, nd opertns?" A rsrch stdy is said 2 hav ntrnl vldty 2 th xtnt tht it prvids accurt answrs 2 th frst 2 rsrch qustns nd xtrnl vldty 2 th dgre tht it prduces an accurt answr 2 th 3rd qustn.
Statistics & Research
Threats to Internal Validity
Internal Validity allws nvstgtr 2 dtrmn if thr is a causl r/s btwn IVs nd DVs. Intrnl vldty thretnd whnvr nvstgtr cnnt cntrl th 3 sorcs of variblty: if nvstgtr cnnt maxmz th effcts of th IV, th effcts of xtrneus varibl, nd/or minmz th effcts of rndm eror, th nvstgtr cnnt b crtn whthr obsrvd varblty (or lck of variblty) n th DV is attrbtbl 2 the IV or 2 sum othr fctr. 7 genric xtrneus varibls tht, if nt cntrlld, cn thrtn a stdy's ntrnl vldty: Maturation, History, Testing, Instrumentation, Statistical Regression, Selection, Attrition (Morality) nd Interaction with Selection.
Statistics & Research
Threats to Internal Validity
Maturation
Maturation rfrs 2 any biolgcl or psycholgcl chng tht ocurs w/in sbjct's durng th cors of a stdy as a fnctn of time, is not rlvnt 2 th rsrch hypths, nd affcts th status of most or all sbjcts on th DV n a systmtc way. Fatig, brdom, hngr, nd physcl nd ntllctul grwth r all potntl maturational effcts th cn lmit ntrnl vldty. Th bst wy 2 cntrl maturtn is 2 nclud mre thn 1 grp n stdy nd rndmly assgn sbjcts 2 grps. Snc sbjcts n all grps shud b sucptbl 2 th sm maturtnl effcts, any obsrvd dffncs btwn thm cn b attrbutd 2 th IV rthr thn 2 maturtn. Altrntvly, a sngl-grp time-series dsgn cn b usd. Ths dsgn nvolvs measrng th DV svrl tims @ rglr ntrvls b4 nd aftr intrvntn appld. Altho multpl msrmts of DV do nt elimnt maturtnl effcts, thy prvid nfo tht allws nvstgtr 2 dtect thm.
Statistics & Research
Threats to Internal Validity
History
Hstry thrtns a stdy's ntrnl vldty whn xtrnl evnts systmtcly affcts th status of sbjcts on th DV. Hstrcl evnts r most lkly 2 b a prblm whn a stdy ncluds only 1 grp nd th evnt ocurs at th same tme th IV is appld. N ths situatn, any dffcrnc n DV prfrmnc b4 an aftr th ntrvntn is appld mit b du 2 hstry rthr thn th IV. Hstry is cntrlld by ncludng mre thn 1 grp n th stdy nd rndmly assgng sbjcts 2 grps. Ths prcdr hlps nsur tht sbjcts n all grps r abt = n trms of xposur 2 xtrnl evnts so tht nvstgtr is bttr abl 2 cnclud tht obsrvd dffnc btwn grps actuly du 2 IV.
Statistics & Research
Threats to Internal Validity
Testing
B/c tkng a tst cn altr a prsn's prfrmnc on the tst whn it is readmnstrd, tstng cn thrtn a stdy's ntrnl vldty whnvr xposur 2 a tst mit altr sbjct's prfrmnc on sbsqunt tsts (whn pretst affcts sbjcts' scors on th poststs). Ths thret cn b cntrld by admntrng th DV meas only onc, by dsgng th meas n a way tht mnmzes memry nd prctc effcts, or by ncludng at lst 2 grps n th stdy.
Statistics & Research
Threats to Internal Validity Intrumentation
Chng n th acurcy or snstvty of measrng dvces or prcdrs durng th cors of a stdy cn cnfund th stdy's rslts. If ratrs acurcy mprvs ovr tme, any chng n sbjcts' pretst nd postst prfrmnc mit b du 2 ratr's ncresd acurcy rthr thn 2 th effcts of th IV. Nstrmntn cntrld by ncludng mre thn 1 grp n th stdy nd nsurng tht all grps r sbjct 2 sam nstrmntn effcts by usng sam measrng dvces nd prcdrs w/all sbjcts nd mkng sur tht measrng dvces nd prcdrs dont chng durng cors of th stdy.
Statistics & Research
Threats to Internal Validity Statistcal Regression
Th tndncy of xtrem scors n a meas 2 "rgrss" (move) twrd th mean whn th meas is radmnstrd 2 th sam grp is clld ststcl rgrssn. Ststcl rgrssn thretns ntrnl vldty whnvr sbjcts hv bn slctd b/c of thr xtrem status on th DV (or rltd meas). Ths thrt 2 ntrnl vldty is avoided by nt ncludng only xtrem scorers n th stdy. Selctn is oftn a prblm whn ntact grps r usd. It is cntrld by rndmly assgng sbjcts 2 grps or whn rndm assgnmnt is not pssbl, by admnstrng a pretst 2 sbjcts 2 dtrmn if th grps dffr initly w/rgrd 2 th DV.
Statistics & Research
Threats to Internal Validity
Attrition (Morality)
Attrtn poses a thret ntrnl vldty whn sbjcts hu drop out of 1 grp dffr n ways from sbjcts hu drop of othr grps. Attritn dffclt 2 cntrl, but pretstng cn hlp dtrmn if drpouts nd non-drpouts dffr w/rgrd 2 thr status on th DV.
Statistics & Research
Threats to Internal Validity Interactions with selection
Whn grps r intly nonequvlnt, slctn cn act alon nd/or cn ntrct w/othr fctrs 2 thrtn ntrnl vldty. Thr wud b an ntrctn btwn slctn nd hstry whn 1 grp is unintntnly xposd 2 an xtrnl evnt tht duz nt affct sbjcts n othr grps.
Statistics & Research
Threats to Internal Validity
Study tips
peop oftn hv trbldstngushng btwn maturtn nd hstry. Kp n mnd tht hstry cums frm w/ "out ther" nd ocurs @ arnd th sam tme tht th IV is admnstrd, whl matrtn rflcts chngs tht ocur w/ n sbjcts as th rslt of th pssg of tme. Als nte tht th name "slctn" is sumwht msledng: As a thrt 2 ntrnl vldty, slctn is relly an assgnmnt prblm.
Statistics & Research
Threats to External Validity
A rsrch srtdy hs xtrnl vldty whn its fndngs cb b gnrlzd 2 othr peop, sttngs, nd cndtns. Whn discsng xtrnl vldty, sum authrs dstngush btwn "popultn vldty" nd "ecolgicl vldty": pop vldty usd 2 dscrb th gnrlzblty of rsrch rslts 2 othr peop whl ecolgcl vldty rfrs 2 th gnrlzblty of rslts 2 othr sttngs. Ecolgicl vldty is a prblm n analog stdys, wch xamn th r/s btwn IVs nd DVs n a labtry or non-nturlstc sttng. Xtrnl vldty is alwys limtd by its ntrnl vldty: if u cnt cnclud tht ther is a causl r/s btwn varbls w/ n th cntxt of th stdy, u ctrnly cnt cnclud tht ther is a r/s 4 othr peop or othr crcmstncs. A hi dgre of ntrnl vldty duz nt hwvr guarnte xtrnl vldty. A r/s btwn varbls mit xst 4 th cndtns n wch th stdy ws cndctd or th prtculr peop hu prtcptd n th stdy, but it cnnt b gnrlzd 2 othr cndtns or othr peop.
Statistics & Research
Threats to External Validity
Xtrnl vldty als drctly affctd by svrl othr fctrs: Campbell & Stanley (1966) ID'd 4 fctrs tht cn thretn xtrnl vldty of mny dffrnt typs of rsrch stdys: Interaction between testing and tx, Interaction between Selection and tx, Reactivity (reactive arrangements) and Multiple tx interference (order effects and carryover effects).
Statistics & Research
Threats to External Validity
Interaction Between Testing and Treatment
Th admnstrtn of a pretst cn "snstz" sbjcts 2 th purps of th rsrch stdy nd thrby altr thr reactn 2 th IV. Whn a stdy's rslts hv bn cntmntd by sch pretst snstztn, thy cnt b gnrlzd 2 peop hu hv nt bn pretstd. Pretst snstztn cn be cntrld by nt admnstrng pretst or by usng th Solomon 4-grp dsgn, wch nabls nvstgtr 2 meas mpct of pretstng on bth th xtrnl nd ntrnl vldty of rsrch stdy. Whn usng ths dsgn, th pretst is tretd as an addtnl IV so tht ist effcts on th DV cn b ststcly anlzd.
Statistics & Research
Threats to External Validity Interaction Between Selection and Treatment
Sbjcts ncluded n a rsrch stdy cn hv chrctrstcs tht mk thm rspnd 2 th IV n a prtculr way. Whn ths ocurs, th rslys of th stdy cant b gnrlzd 2 peop hu dont hv thos chrctrstcs. An ntrctn btwn selctn nd tx is oftn a prblm whn sbjcts r vluntrs b/c vluntrs tnd 2 b mre mtvtd th nonvluntrs nd, cnsquntly mit b mre rspnsv 2 th IV. N ths situatn, th rslts apply 2 vluntrs bt cant b gnrlzd 2 othr peop. Th bst way 2 elmnt ths thrt is 2 nsur tht th smpl is rprsntv of th popultn of ntrst.
Statistics & Research
Threats to External Validity Reactivity (Reactive Arrangements)
Rsrch prtcpnts cn rspnd 2 an IV n a prtculr way smply b/c thy knw thr bhvr is bng obsrvd. Ths phnmon is kwn as rectvty. Whn a stdy hs bn cntmntd by rctvty, its rslts cant b gnrlzd 2 cndtns n wch rctvty is not oprtng.
Statistics & Research
Threats to External Validity Reactivity (Reactive Arrangements)
Svrl othr phnmnon r sumtms ncluded n ths ctgry of rctvty: th bhvr of rsrch sbjcts cn rflct evlutn apprhnsn, wch causes sbjcts 2 act n wys thy blev wil hlp thm avoid neg evlutns. Th bhvr of rsrch prtcpnts cn als b altrd by DEMAND CHARACTERISTICS, or cues n th xprmntl sttng tht nfrm sbjcts of th purps of th stdy or sggst wht bhvrs r xpctd of thm. Fnlly, a stdy's rslts cn b biased by xprmntr xpctncy: an xprmntr cn unintntnlly prvid sbjcrs w/cues (dmnd chrctrstcs) tht let thm knw wht bhvr is xpctd or cn act n wys th do nt affct sbjcts drctly but bias th rslts of the stdy. Als evdnc tht an xprmntr's cmputnl erprs r lkly 2 spprt th rsrch hypths nd tht xprmnts r mre lkly 2 rechk thr calcltns whn thy cnflct w/ th rsrch hypths thn whn thy spprt it. (note tht mny xprts cnsdr rectvty nd rltd phnmnon 2 act as drct threts 2 bth ntrnl nd xtrnl vldty.) Rctvty cn b cntrld by usng dcptn, unobtrsv (nonrctv) meas, or a sngl- or dubl-blnd tchnq.
Statistics & Research
Threats to External Validity Multiple Treatment Interference (Order effects and Carryover Effcts)
Whn a stdy nvolvs xposng ea sbjct 2 two or mre lvls of an IV (i.e., whn th stdy utlzs a w/ n-sbjct dsgn), th effcts of 1 lvl of th IV cn b affctd by prvius xposr 2 anthr lvl. Whn ths ocurs, th rslts cant b gnrlzd 2 situatns n wch peop wil b xposd 2 only 1 lvl of th IV. Multipl tx ntrfrnc cn b cntrld by usng COUNTERBALANCED DESIGN n wch dffrnt sbjcts (or grp of sbjcts) rcev th lvls of th IV n a dffrnt ordr. Th LATIN SQUARE DESIGN is 1 typ of contrblncd dsgn nd nvolvs admnstrng ea lvl of th IV so tht it appers th sam # of tms n ea postn (1st, 2nd, 3rd, etc).
Statistics & Research
Experimental Research Designs
Specific rsrch dsgns cn b dvded n2 two bsic typs: Group Design nd Single-Subject Designs
Statistics & Research
Experimental Research Designs
Group Designs
Between-Group Designs
Whn a btwn-grps (btwn sbjcts) desgn is usd, th effcts of dffrnt lvls of an IV r assesd by admnstrng ea lvl 2 a dffrnt grp of sbjcts nd thn cmprng th status or prfrmnc of th grps on th DV. Th simplst btwn-grp dsgn ncluds a sngl IV w/two lvls. Whn usng ths dsgn, th stdy ncluds 2 grps tht ea rcev a dffrnt lvl of th IV. Ths simpl 2-grp dsgn cn b xpnded n two wys. 1 way is 2 nclud mre thn two lvls of a sngl IV. Anthr way is 2 nclud two or mre IVs.
Statistics & Research
Experimental Research Designs
Group Designs
Between-Group Designs - factorial design
Whnvr a stdy ncluds two or mre IVs, it is clld a FACTORIAL DESIGN. Th mjr advntg of a fctrl dsgn is tht it prvids mre thoro nfo abt th r/s amng varbls by allwng an nvstgtr 2 anlyz th main effcts of ea IV as well as th ntrctn btwn IVs.
Statistics & Research
Experimental Research Designs
Group Designs
Between-Group Design - factorial design and Main & Interaction Effects
For th licensing exam, u shud b abl 2 dstngush btwn th main effect nd th intractn effcts. A MAIN EFFECT is th effct of 1 IV on th DV, dsrgrdng th effcts of INTERACTION rfrs 2 th effcts of two or mre IVs cnsdrd 2gthr. An INTERACTION ocurs whn effcts of an IV dffr at dffrnt lvls of anthr IV.
Statistics & Research
Experimental Research Designs
Group Designs
Between-Group Design - factorial design and Main & Interaction Effects
Study Tip
4 th exam, b sur u undrstnd wht main nd intractn effcts r on a cncptul lvl nd b abl 2 dtrmn, frm a tabl of data whthr it loks lk ther r main nd/or ntractn effcts. Keep n mnd tht THERE CAN"T B AN INTERACTION UNLESS THE STUDY HAS AT LEAST TWO IVs AND THAT, WHEN THERE IS AN INTERACTION, THE MAIN EFFECT MUST BE INTERPRETED IN LIGHT OF THE INTERACTION.
Statistics & Research
Experimental Research Designs
Group Designs
Within-Subjects Designs
Whn usng a within-subjects (repeated measures) dsgn, all lvls of th IV r admnstrd squntly 2 all sbjcts. Cnsquntly, cmprsns of dffrnt lvls of th IV r made within subjcts rthtr thn btwn grps of sbjcts. Lk btwn-grps dsgns, within-sbjcts dsgn cn nclud only 2 lvls of a sngl IV or cn b xpnded 2 ncluds 3 or mre lvls of a sngl IV or two or more IVs. Th sngl-grp tme-series dsgn is 1 typ of within-subjcts dsgn. Whn usng ths dsgn, th effcs of a tx r evaluatd by measrng th DV svrl tmes @ rglr ntrvls bth b4 nd aftr th tx is appld. Ths prcdr allws sbjcts 2 act as thr own no-tx cntrls. A shrt-cmg of the sngl-grp tme-series dsgn is tht its ntrnl vldty cn b thretnd by hx: it's pssbl tht an xtrnl evnt culd ocur @ abt th sam tme th IV is appld nd accnt 4 any obsrvd dffrnc n pre- nd posttst scors. Note, hwvr tht ths dsgn duz hlp cntrl maturtn snc maturtnl effcts tnd 2 ocur grduly ovr tme nd cn usuly b dtctd n th ovral pttrn of pre- nd postst scors.
Statistics & Research
Experimental Research Designs
Group Designs
Within-Subjects Designs
N anthr typ of within-sbjcts dsgn, 2 or mre lvls of an IV r appld squntly 2 ea sbjct nd th IV is measrd aftr ea lvl hs bn appld. A prblm w/th dsgn is tht it is suscptbl 2 crryovr effcts (mltpl tx ntrfrnc): countrbalncng cn b usd to cntrl crryovr effcts.
Statistics & Research
Experimental Research Designs
Group Designs
Within-Subjects Designs
A dsadvntg of th tme-series nd othr within-sbjcts dsgns is tht th anlys of th data cn b counfnded by AUTOCORRELATN. Sbjcts' prfrmnc on th poststs is lkly 2 crrlt w/thr prfrmnc on th pretsts. Autocrrltn cn nflat th valu of th nfrrntl stistc (e.g., the t or th F), thrby rsltng n an ncresd prblty of a TYP I error. 4 ths resn, a # of xprts rcmmnd tht spcl ststcl tchnqs b usd 2 anlyz data cllctd n a stdy usng ths typ of dsgn.
Statistics & Research
Experimental Research Designs
Group Designs
Mixed Designs
A mxd dsgn cmbns btwn-grps nd within-subjcts mthdolgs. Mxd dsgn r cmmn n rsrch tht nvolv measrng th DV ovr tme or acrss trials. N ths typ of stdy, tme or trials is an addtnl IV nd is cnsdrd a within sbjcts varibl b/c cmprsns on th DV wil nt b md within subjcts acrss tme or acrss trials.
Statistics & Research
Experimental Research Designs
Single-Subject Designs
Th sngl-sbjct dsgns wer derivd prmrly from th wrk of bhvrl psychlogsts, esp thos ngagd n appld bhvrl anlys, wch cmbns bhvrl prncpls with tchnqs of xprmntl psycholg 2 solv socly-rlvnt prblms. Whl th sngl-sbjct dsgns r oftn usd 2 nvstgt th effcts of an IV on th bhvr of 1 sbjct or smal # of sbjcts, thy cn als b usd w/grps of sbjcts. Two chrhctrstcs dstngsh th sngl-sbjct dsgns frm grp dsgns: 1) ea sngl-sbjct dsgn ncluds at least 1 basln (no tx) phz nd 1 tx phz. As a rslt, ea sbjct acts as own no tx cntrl; 2) th DV is measrd rptdly @ hghr ntrvls thruout th basln nd tx phzs. Rptd msmnt of th DV hlps cntrl any maturtnl effcts tht mit othrws thrtn ntrnl vldty by nblng an nvstgtr 2 dtct thos effcts n th pttrn of prfrmnc on th DV measr.
Statistics & Research
Experimental Research Designs
Group Designs
Within-Subjects Designs
AB Design
Th simplst sngl-sbjct dsgn is th AB DESIGN, wch ncluds a sngl basln (A) phz and a sngl tx (B) phz. As n all sngl-sbjct dsgns, th DV is measrd @ rgulr ntrvls durng bth phzs.
Experimental Research Designs
Group Designs
Within-Subjects Designs
Reversal Designs (ABA, ABAB, Etc)
Th AB dsgn cn b xpnded 2 nclud mre th 1 basln phz or mre th 1 basln nd mre thn 1 tx phz. B/c any xpnsn rqurs th wthdrwl of th tx durng th 2nd nd sbsqunt basln phzs, th xtnsns of th AB dsgn r clld REVERSAL (withdrawal) dsgns. An advntg of th rvrsl dsgn ovr th simpl AB dsgn is tht thy prvid addtnl cntrl ovr potntl thrts 2 ntrnl vldty. Whn ABAB dsgn usd, if status on th DV rtrns 2 initl basln (no tx) lvl durng th 2nd A phz nd thn 2 its prvius tx lvl durng th 2nd B phz, an nvstgtr cn b mre crtn tht any obsrvd chng n th DV is du 2 th IV rthr thn 2 a hstrcl evnt or othr xtrneus fctr. Th rvrsl dsgns r cnsdrd nappropriat whn wthdrwl of a tx durng th cors of th rsrch stdy wud b unethcl. N addtn, a rvrsl dsgn duz nt prvid cnclusv nfo if th effcts of an IV prsists rthr thn "rvrs" (rtrn 2 basln lvls) whn it is wthdrwn. Whn ths ocurs, an nvstgtr cant b crtn whthr an obsrvd effct on th DV is du 2 th IV or othr fctrs.
Experimental Research Designs
Group Designs
Within-Subjects Designs Multiple Baseline Design
If rvrsl dsgn is napprpriat 4 ethcl or prctcl resns, an nvstgtr mit use a MULTIPLE BASELINE DESIGN. Th mltipl bsln dsgn duz nt rquir wthdrwl of a tx durng th cors of th stdy bt nsted, nvolvs squntly applyng th tx ethr 2 dffrnt bhvrs of th sam sbjct (mltipl basln acrss bhvrs); 2 th sam sbjct n dffrnt sttngs (multipl basln acrss sbjcts). Onc th tx hs bn appld 2 a "basln" (bhvr, sttng, or sbjct), it is nt wthdrwn from tht basln durng th cors of th stdy. Squntly applyng an ntrvntn 2 dffrnt sttngs hlps dtrmn if an ntrvntn is rspnsbl 4 obrvd chngs n th trgt bhvr: if th bhvr chngs n a prtculr sttng only aftr th ntrvntn hs bn appld n that sttng, an nvstgtr cn b mre crtn that th chng is du 2 th ntrvntn rthr thn 2 hstry or othr fctrs. 2 b effctv, th sttng, bhvrs, or sbjcts chosn 4 nclusn n th stdy must b rltvly indpndnt. If thy r not, it may nt b pssbl 2 evluat th effcts of th IV w/ th multpl basln dsgn.
Statistics & Research Design
Statistics
Scales of Measurement
Th varius mthds of measrng varbls r ctgrzd n svrl ways. One mthd dstngushs btwn cntnuos nd dscret varibls. A CONTINUOUS varbl, at lst thertcly, cn tk on an nfint # of valus on th msmnt scal. A DISCRETE varbl cn asum only finit #s of valus. Anthr mthd dstngushs btwn 4 SCALES of MEASUREMENT: Nominal, Ordinal, Interval, and Ratio. Ea scal nvolvs dvdng a set of obsrvtns n2 mutuly xclusv nd xhaustv ctgres. Th 4 scals dffr n trms of th knd of nfo thy provd nd th mthmtcl oprtns thy prmt.
Statistics & Research Design
Statistics
Scales of Measurement
Nominal Scale
A nomnl scl of msmnt dvdes varbls n2 unordrd ctgres. Th sex, rlgn, plc of brth, or DSM dx of indv cnsdrd nomnl whn thy may be nmbrd but nmbrs usd act only as labls Prmry limtn of nomnl scl is tht th only mthmtcl oprtn th cn b prfrmd on th obtnd data is 2 count th frqncy (#) oc cses n ea catgry.
Statistics & Research Design
Statistics
Scales of Measurement
Ordinal Scale
an ordnl scl is mre mthmtcly cmplx thn a nomnl scl. Th ordnl scl dvdes obsrvtns n2 catgres and als provids nfo on th ordr of thos catgres. Whn usng an ordnl scl, it is pssbl 2 say tht 1 prsn hs mre or lss of th chrctrstc bng measrd thn anthr prsn. Ranks and Likert-scl scors r xmpls of ordnl scl scors. A limtn of ordnl scl scors is tht thy do nt lnd thmslvs 2 dtrmng just hw mch dffrnc ther is btwn scors.
Statistics & Research Design
Statistics
Scales of Measurement
Interval Scale
Th ntrvl scl hs th prprty of ordr as wel as th prprty of = ntrvls btwn sccssv points on th msmnt scl. Scors on stndrdzd IQ tsts r usuly cnsdrd 2 rprsnt an ntrvl scl nd as a rslt we cn say tht th ntrvl btwn th scors 90 nd 95 is = 2 th ntrvl btwn 100 -105 nd tht a scor of 95 is mdway btwn th scor of 90 - 100. th prprty of = ntrvls mks it pssbl 2 prfrm mthmtcl oprtns of addtn nd sbtrctn. It is lgitmt 2 add ntrvl scors n ordr 2 clcult a mean or std dvatn. Ntrvl (nd ordnl) scls sumtmes hv a zero point but its an rbtry not abslut zero. A scor of zero on a tst tht prvids ntrvl scors can't b ntrprtd as an abslut lck of absnc of th chrctrstc bng measrd by th tst.
Statistics & Research Design
Statistics
Scales of Measurement
Ratio Scale
Th ratio scl is th most mthmtcly cmplx of th 4 mesmnt scls. It hs th prprtes of ordr nd = ntrvls as wel as th prpty of an abslut zero point. Whn data r measrd on a ratio scl, a scor of 0 ndcts a cmplt absnc of th chrctrstc bng measrd. An abslut zero point mks it pssbl 2 multply and dvde ratio scors nd 2 dtrmn mre prcsly hw mch mre or lss of a chrctrstc 1 persn hs cmprd 2 anthr.
Statistics & Research Design
Statistics
Scales of Measurement
Study Tip
B carefl not 2 immedtly asum tht th wrd "frquncy" mplies a nomnl varbl. A varbl is measrd on a nomnl scl whn it is dvded n2 catgres nd th frquncy (#) of indvs n ea catgry wil b cmprd. Frquncy of aggrsv acts nd th # of hrs stdyed r ratios - not nomnl - data. Als kep n mnd tht whn pickng a dscrptv or nfrrntl tchnq, th same tchnqs r usd 4 ntrvl nd ratio data.
Statistics & Research Design
Statistics
Descriptive Statistics
Dscrptv ststcs r usd 2 dscrb or summrz a dstrbtn (set) of data. Dscrptv ststcs nclud tbls, frqncy dstrbtns, frqncy polgns, meas of cntrl tndncy, nd meas of variblty.
Statistics & Research Design
Statistics
Descriptive Statistics
Frequency Polygons
A set of data tht rprsnts an ordnl, ntrvl or ratio swcl cn b orgnzd n a frqncy polygn. Whn usng ths typ of ststc, th scors r rcrded on th hrzntl axis (abscissa), whl the frqnces r coded on th vertcl axis (ordinate). Frqncy polygns cn asum a varity of shaps. Whn a sffcntly lrg # of obsrvtns r mde, th data 4 mny varibls tk th shap of a NORMAL CURVE (or nrml dstrbtn). Th nrml curv is symmtrcl, bel shpd, nd dfnd by a spcfc mthmtcl frmula. Nrml curv vry mprtnt: whn scors on a varibl r nrmly dstrbted, crtn cnclusns cn b mde abt th NUMBER OF CASES THAT FALL BETWEEN SPECFIC POINTS IN TH DISTRIBUTION. Dstrbtns cn als dviat from th nrml curv. Th trm KURTOSIS rfrs 2 th rltv peakedness (hight or flatness) of a dstrbtn: whn a dstrbtn is mre "peaked" th th nrml dstrbtn, it is rfrd 2 as a LEPTOKURTIC; whn a dstrbtn is flttr, it is called PLATYKURTIC. (A nrml curv is MESOKURTIC.) Dstrbtns cn als b asymmtrcl rthr thn symmtrcl. N a SKEWED DISTRIBUTION, mre thn hlf of th obsrvtns fall on 1 side of th dstrbtn ns a rltvly few obsrvtns fall n th tail on th othr side of th dstrbtn. Skwd dstrbtns cn be ethr postv or negtv: N a pstvly skwd dstrbtn, most scors r n th ngtv (low scor) side of th dstrbtn nd th pstv tail is xtnded b/c of th prsnc of a few hi scors. N a ngtvly skwd dstrbtn, most scors r lctd n th pstv (hi scor) side of the dstrbtn nd th ngtv tail is xtnded du 2 th prsnc of a few low scors. (Diffnce btwn pstv nd ngtv skwd dstrbtns - it's "th tail that tels th tale."
Statistics & Research Design
Statistics
Descriptive Statistics
Measures of Central Tendency
Altho frqncy polgns nd othr dscrptv tchnqs prvid mprtnt nfo abt a dstrbtn, an nvstgtr usuly wnts 2 dscrb th data cllctd w/a sngl #. 2 b usfl, ths # shud cnvy a maxm amt of nfo, summrz th ntir set of obsrvtns, nd b a "typcl" meas of all th obsrvtn. MEASURES OF CENTRAL TENDENCY r th dscrptv tchnqs tht addrss thes gols; nd th mode, the median, nd th mean r th most cmmnly-usd meas of cntrl tndncy.
Statistics & Research Design
Descriptive Statistics
Measures of Central Tendency
Mode
Th MODE (Mo) is th scor or ctgry tht ocurs most frqntly n a set of data. A dstrbtn cn b mutlimodal.
; tht is, it cn hv 2 or mre scorsw or ctgrys tht ocur =ly oftn nd mre oftn th any othr scor or ctgry. A dstrbtn w/two modes is clld BIMODAL. Whn all scors ocur =ly oftn, th dstrbtn duz not hv a uniq mode. Th prmry advntg of th mode is tht it is ez 2 ID. A dsadvntg is tht it is vry suscptbl 2 samplng flctatns. Th means tht if a lrg # of sampls r rndmly selctd from th popltn, th mode cn b xpctd 2 vary cnsdrbly from smpl 2 smpl nd any 1 smpl mit nt prvid an accurt est of th popltn mode. Anthr dsadvntg is tht th mode is not usfl for oth ststcl purposes ns servs only as a dscrptv tchnq.
Statistics & Research Design
Descriptive Statistics
Measures of Central Tendency
Median
Th Median (Md) is th scor tht divids a dstrbtn n hlf whn th data hv bn orfrd frm hi 2 low. Whn a dstrbtn has an odd # of obsrvtns, th Md is = 2 th mddl obsrvtn. If a dstrbtn hs an evn # of obsrvtns, thMD is th valu tht lies midway btwn th two mddl scors. I advntg of th Md is tht if 1 scor n a dstrbtn of 10 scors is xtrmly hi or low, th valu of th Md in not affctd. B/c th Md is nsnstv 2 outliers, th Md is a usfl meas of cntrl tndncy whn dstrbtn cntains 1 or few xtrm scors. A dsadvntg is tht, lke the Md, its use n othr quntatv prcdrs is limtd, nd it srvs prmrly as a dscrptv ststc.
Statistics & Research Design
Descriptive Statistics
Measures of Central Tendency
Arithmetc Mean
Th MEAN (M) is th arthmtc avg. 1 advntg of th M - of the 3 meas of cntrl tndncy, it is th lst suscptbl 2 samplng flctuatns. Cnsqntly, th M of a sampl tht hs bn rndmly selctd from th popultn usuly prvid an unbiasd est of th popltn M. Anthr advntg is tht it cn b usd n a # of ststcl prcdrs. A potntl dsadvntg is tht it is affctd by th mgntud of evry scor n th dstrbtn. As a rsly, whn dstrbtn is skwd or cntaind 1 or few outliers, th M cn b a msleadng meas of cntrl tndncy.
Statistics & Research Design
Descriptive Statistics
Coosing a Measures of Central Tendency
Th 1st cnsdrtn is th data's scal of msmnt: Nominal = Mo; Ordinal = Mo or Md; Interval = Mo, Md or M; Ratio = Mo, Md, or M. Nrmly, th meas of cntrl tndncy usd lnds itslf 2 th grtst # of mthmtcl oprtns. Whn th data reprsnt a ordnl scl, th Md is usuly th prfrd meas of cntrl tndncy; whn th data rprsnt an ntrvl or ratio scl, th M is prfrd. Evn tho a varibl hs bn measrd on an ntrvl or ratio scl, th Md is oftn usd whn th dstrbtn is vry skwd or whn ther is mssng data, (esp at th hi or lo end of th dstrbtn) b/c it is mre rsprntv of th dstrbtn of scors. Th r/s btwn th 3 meas of cntrl tndncy n skwd dstrbtns: n a pstvly skwd dstrbtn, th M is grtr th th Md wch, n trn, is grtr th th Mo. N a ngtvly skwd dstrbtn, th r/s btwn th 3 meas is rvrsd: the Mo is grtr thn th Md, wch is grtr thn th M.
Statistics & Research Design
Descriptive Statistics
Measures of Central Tendency
Study Tip
4 th exam, u don't need 2 knw hw 2 dtrmn th Mo or th Md or calculat th M. Hwevr, mk sur tht u knw th r/s btwn th 3 meas of cntrl tndncy n skwd dstrbtns.
Statistics & Research Design
Descriptive Statistics
Measures of Variabilty
A meas of cntrl tndncy oftn provids an ncmplt dscrptn of a dstrbtn of data, nd invstgtr als wnts 2 calcult a meas of variblty. Meas of variblty ndcat th amt of hetrognty or dsprsn w/n a set of scors nd nclud th rng, th varinc, nd the std dev.
Statistics & Research Design
Descriptive Statistics
Measures of Variabilty
Range
Range is calcultd simply by sbtrctng th lwst scor n th dstrbtn frm th hghst scor. B/c th rng is bsed only on th two most xtrm scors, it cn b msleadng whn a dstrbtn cntains an atypcly hi nd/or lo scor.
Statistics & Research Design
Descriptive Statistics
Measures of Variabilty
Variance (Mean Square)
Th varinc is a mre thoro meas of variblty thn th rng b/c its calcultn ncluds all of th scrs n th dstrbtn rthr thn just th hghst nd lwst scors. FORMULA: The numerator of th varinc is clld th sum of squares, wch is shrt 4 th "sum of the squared deviation scores." Th sum of squars is calcultd by sbtrctng th mean from ea scor 2 obtain dviatn scors, squarng ea dvatn scor, nd thn summng th squared dvatn scors. Note tht th size of th Sum of Squars is affctd not only by th amt of varbilty n th dstrbtn but als by th # of scors: th mre scors n a dstrbtn, th lrgr th sum of squars. Cnsqntly, 2 b usfl as a meas of variblty, th sum of squars is dvided by N-1 (or as dscussd next, by N). Th rslt is th varinc (mean squar), or th "mean of th squard dviatn scors." Th varinc provids a meas of th avrg amt of th variblty n th dstrbtn by ndcatng th dgre 2 wch th scors r dsprsd around th dstrbtn's mean. Note tht the denominator 4 th varinc is N whn th varinc 4 th popultn is bng calcultd. Hwvr, whn a sampl varinc is bng calcultd (esp whn it's gong 2 b usd as an est of th popultn) th denmntr is N-1. Ths is b/c a sampl varinc tnds 2 undrstmt th popultn varinc, nd sbtrctng 1 from N helps reduc ths bias.
Statistics & Research Design
Descriptive Statistics
Measures of Variabilty
Standard Deviation
B/c clcultn of th varinc requirs squarng ea dvatn scor, th varinc rprsnts a unit of msmnt tht dffrs from th orgnl unit of msmnt. 4 ths rsn, th varinc is dffclt 2 ntrprt, nd th STANDARD DEVIATION is mre oftn usd as a meas of variblty. TH STD DEV IS CLCULTD BY TKNG TH SQUAR ROOT OF TH VARINC, wch cnvrts it 2 th sam unit of msmnt as th orgnl scors. Standard Deviation Formula: Std.Dev = the square root of the sum of squares divided by N-1. Th std dev cn b ntrprtd drctly as a meas of variblty: th lrgr th std dev, th grtr th dsprsn of scors arond th dstrbtn's M. Ths mthd of ntrprtn is usfl whn cmprng th variblty of two or mre dstrbtns.
Statistics & Research Design
Descriptive Statistics
Measures of Variabilty
Standard Deviation
Std dev cn als b ntrprtd n trms of th nrml dstrbtn. Whnvr th shp of a dstrbtn of scors apprchs nrml, it is pssbl 2 drw crtn cnclusns abt th # of cses tht fal w/n limts tht r dfnd by th std dev: Whn th dstrbtn is nrml, 68.26% of th scors fal btwn th scors tht r plus nd minus one std dev from th M; 95.44% of th scors fal btwn th scors tht r plus nd minus two std devs from th M; nd 99.72% of th scors fal btwn th scors tht r plus nd minus three std devs from th M. E.g., if a tst hs a M of 50 nd a std dev of 5 nd scors on th tst r nrmly dstrbtd, it is pssbl 2 cnclud tht abt 68% of th peop hv scors btwn 45 nd 55.
Statistics & Research Design
Descriptive Statistics
Measures of Variabilty
Standard Deviation
A # of othr cnclusns cn b drwn whn a dstrbtn is nrml nd its M nd std dev r unknwn. E.g., if a tst hs a M of 50 nd std dev of 5 nd scors on th tst r nrmly dstrbtd, it's pssbl 2 cnclud tht abt 84% of th peop hv scors below 55. Ths ws dtrmnd by addng 50% (th # hu obtain scors blw th M) to 34% (th # hu obtaind scors btwn th M nd one std dev abv th M). It is als pssbl 2 cnclud tht if th purpos of th tst is 2 selct indvs whos scors r n th top 16%, th cutof scor s/b set @ 55. (snc 84% fal blw th scor tht is one std dev abv th M, th remning 16% fal abv tht scor.)
Statistics & Research Design
Descrptive Statistics
Measures of Variability
Study Tip
Th trm "variblty" is an mprtnt one n ststcs. Rsrchrs cndct studies 2 dtrmn th causes of variblty n a DV - i.e., thy attmpt 2 dtrmn if dffrncs on th DV r du 2 effcts of th IV or 2 error. U DON'T need 2 knw th formula 4 th varinc, but u shud undrstnd wht it is measrng. Als rembr tht th std dev is th square root of th varinc nd b sur 2 rembr memrz th "areas under th norml curv."
Statistics & Research Design
Descrptive Statistics
Effects of Mathmatical Operations On Measures of Central Tendency & Varibilty
N sum situatns, it may b ncssry 2 ad or sbtrct a cnstnt to or from ea scor n a dstrbtn or multply or dvid ea scor by a cnstnt. 2 cnvrt a dstrbtn of heights xprssd n inchs 2 feet, e.g., ea prsn's height must b dvided by 12. Whn a cnstnt is aded or sbtrctd 2 evry scor n a dstrbtn, th measrs of cntrl tndncy chng but th measrs of variblty do not. adng a cnstnt of 5 to ea scor n a dstrbtn wil ncres th dstrbtn's M but not its std dev. N cntrst, whn ea scor n a dstrbtn is multpld or dvided by a cnstnt, th measrs of cntrl tndncy nd variblty r all affctd. MULTPLYNG EA SCOR N A DSTRBTN BY 5 WIL NCRES BOTH TH "M" ND TH "STD DEV."
Statistics & Research Overview of Inferential Statistics
Whl dscrptv ststcs r usd 2 smmrz data, nfrntl ststcs r usd 2 mk infrncs abt a popultn bsed on data cllctd from a sampl drwn from tht popultn nd 2 do so w/ a pre-dfnd dgre of cnfdnc.
Statistics & Research
Overview of Inferential Statistics The Logic of Statistcal Inference
Th tchnqs of ststcl nfrnc allw invstgtr 2 mk nfrncs abt th r/s btwn varibls n popultn bsed on r/s obsrvd n a smpl.
Statistics & Research Overview of Inferential Statistics - Population of Parameters and Sample Statistics
2 undrstnd nfrntl ststcs, it is ncssry 2 frst dstngush btwn smpl valus nd popultn valus. Whn cndctng a rsrch stdy, an nvstgrt duz nt hv accss 2 ntir popultn of ntrst but, nsted estmts pop valus bsed on obtnd smpl valus. Thus, an nvstgtr uses a smpl ststc 2 est a pop parmtr.
Statistics & Research Overview of Inferential Statistics - Symbols for Sample and Population Values
Value for Mean = population parameter u(mu) & sample statistic X (with a line over the X) or M. Value for Standard Deviation = population parameter o(sigma) and sample statistic S or SD. Value for Variance = population parameter O2 (sigma squared) or sample statistic S-squared or V.
Statistics & Research Overview of Inferential Statistics - Symbols for Sample and Population Values
Study tip
Symbols sometimes appear on th licensing exam, nd u dont wnt 2 get a qustn wrng b/c u dont knw wht the symbl means. B sur u cn trnslt all of th symbl usd 4 both ststcs & tst cnstrctn.
Statistics & Research
Overview of Inferential Statistics - Characteristics of Sampling Distributions
Du 2 effcts of rndm (chnc) fctrs, it is unlkly tht any smpl wil prfctly rprsnt th pop frm wch it ws drwn. Cnsqntly, an ntir pop prmtr from a smpl ststc is alwys sbjct 2 som nacurcy. B/c of th effcts of smplng eror, smpl ststcs dviat from pop prmtrs nd from ststcs obtnd frm othr smpls drwn from sam pop. Thy r/s btwn smpl ststcs nd pop prmtrs cn b dscrbd n trms of Sampling Distribution - frqncy dstrbtn of th means or othr smpl valus of a vry lrg # of = szd smpls tht hv bn rndmly slctd from th popultn. KEEP N Mind tht a smplng dstrbtn is NOT a dstrbtn of ndvdul scors but a dstrbtn of smpl ststcs. Smplng dstrbtn mprtnt n nfrntl ststcs b/c it allws rsrchr 2 dtrmn th prblty tht a smpl hvng a prtculr mean or othr valu cud hv bn drwn frm a pop w/ a knwn prmtr.
Statistics & Research Overview of Inferential Statistics - Sampling Distribution of the Mean & Central Limit Theorem
Th smplng dstrbtn of mean is bell shpd (nrml) nd its mean is = 2 th popltn. Rsrchrs do nt actuly cnstrct a smplng dstrbtn of th mean by obtng a lrg # of smpls nd clcultng ea smpl's mean. Nsted, thy dpnd on a prblty thery 2 tel thm wht a smplng dstrbtn wud lok lik. Th smplng dstrbtn dfind by prblty thery is clld a theortcl smplng dstrbtn, nd it is bsed on th asmptn tht an nfinte # of =szd smpls hv bn rndmly drwn frm th sam pop. Th chrctrstcs of a smplng dstrbtn of mean r spcfd by th Central Limit Theorem wch mks crtn prdctns: 1) rgrdls of th shp of th dstrbtn of ndvdl scors n th pop, as th smpl sz ncreses, th smplng dstrbtn of th mean apprchs a nrml dstrbtn; 2) th mean of th smplng dstrbtn is = 2 th pop mean; and 3) the std dev of th smpln dstrbtn is = 2 th pop std dev dvided by th squar root of th smpl sz.
Statistics & Research
Overview of Inferential Statistics - Standard Error of the Mean
The std dev of a smplng dstrbtn of th mean is knwn as th Standard ERROR of the Mean wch provids an est of th xtnt 2 wch th mean of any one smpl rndmly drwn frm th pop cn b xpxctd 2 vary frm th pop mean as th rslt of smplng error. Lik othr SDs, th std error of th mean is a msmnt of variblty, but it is a meas of varblty tht is du 2 th effcts of rndm error. Th frmula 4 th std eror of th mean ndcts tht th sz of th std eror of th mean is affctd by th popultn std dev nd th smpl sz (N): TH LRGR TH POP SD ND TH SMLLR TH SMPL SZ, TH LRGR TH STD EROR ND VICE VERSA.
Statistics & Research
Overview of Inferential Statistics - Sampling Distrbutions
A smplng dstrbtn cn b drivd 4 any smpl ststc. A smplng dstrbtn cn b obtned 4 std dev, proprtns, crreltn coeffcnts, th dffrncs btwn means, nd so on. N EA CSE, TH BSIC CHRCTRSTCS OF TH SMPLNG DSTRBTN R SIMLR 2 THOS OF TH SMPLNG DSTRBTN OF TH M. Th smplng dstrbtn is th fndtn of nfrntl ststcs. It is th smplng dstrbtn tht nabls rsrchrs 2 mk nfrncs abt th r/s btwn varibls n th pop bsed on obtnd smpl data.
Statistics & Research
Overview of Inferential Statistics - Study Tip
4 th eppp, u'll wnt 2 knw th 3 prdctns of th Cntrl Limt Theorm. U shud als memrz th frmla 4 th std eror of th mean snc th eppp may nclud a qustn rquirng u 2 clcult th std eror.
Statistics & Research
Overview of Inferential Statistics - The Logic of Hypothesis Testing
An nvstgtr usuly cndcts a rsrch stdy 2 tst th hypthsis tht an IV hs an effct on th DV. Th truth of th hypthses cud b tstd n svrl ways. 1 way wud b 2 use an nfrntl ststcl tst 2 cmpr th M scor of grp recvng IV 2 a knwn pop M. Altrntvly, an nfrntl ststcl tst cud b usd 2 cmpr th dffrnc btwn Ms obtnd by 2 grps hu hv nd hv not rcvd th IV. N ethr cse, th ststcl tst wud cmpr th obtnd smpl valu 2 th appopriat smplng dstrbtn, nd th rslts of th tst wud ndicat whthr an obsrvd effct was du 2 smplng eror or th effct of th IV. Tstng a rsrch hypthsis abt effcts of IV on DV nvolvs fllwng steps: 1) trnslt vrbl rsrch hypthsis abt r/s btwn IV & DV n2 two cmptng ststcl hypthses: null & altrntv hypthses; 2) Cndct stdy nd anlyz th obtnd data w/ an nfrntl ststcl tst; and 3) dcid, on th bsis of th rslts of ststcl tst, whthr 2 retain or rjct ststcl hypths.
Statistics & Research
Overview of Inferential Statistics - Defining th Statistical Hypotheses
An nvstgtr tsts a vrbl rsrch hypthsis by smultnsly tstng 2 cmptng ststcl hypothses. Th 1st, th null hypths statd n a way th mplys tht th IV duz nt hv an effct on the DV. Th 2nd , th altrntv hypthsis states tht th IV effcts the DV. Altrntv hypths H1, usuly rflct th vrbl rsrch hypths and it is th null hypths (Ho) tht is ether rjctd or rtaind. Dcsn to rjct or rtain is scndry.
Statistics & Research
Overview of Inferential Statistics - Nondirectional & Directional Alternative Hypotheses
A nondrctnl hypths ("two tailed") altrntv hypths sates tht th null hypths is false. It duz nt prdct whthr pop prmtr estmtd by th obtnd smpl ststc wil b grtr thn or lss thn th prmtr prdctd by th null hypthsis. A drctnl ("one tailed") altrntv hypthsis states that th null hypths is false and als prdcts whthr th pop prmtr estmd by th obtnd smpl ststc wil b grtr thn or lss thn th prmtr spcfd n th null hypthsis. Usuly, nondrctnl altrntv hypthsis usd unlss ther r xprmntl or thertcl grnds 4 chuzng a drctnl one.
Statistics & Research
Overview of Inferential Statistics - Study Tip
U're not lkly 2 ncntr qstns on th null nd altrntv hypthses or drctnl nd drctnl hypths on th eppp. Ths nfo ncluded 2 fcltat undrstndng of dcsn erors nd pwr, wch r lkly 2 b addrssd.
Statistics & Research
Overview of Inferential Statistics - Analyzing the Data and Making a Decision
Aftr statng the null nd altrntv hypthses nd cllctng th smpl data, nvstgtr anlyzs th data usng an nfrntl ststcl tst such as th t-test or ANOVA. Th choic of a ststcl tst is bsed on svrl fctrs ncludng scal of msmnt of th data 2 b anlyzd. Th nfrntl ststcl tst ylds a t, an F, or othr valu tht ndicats wher th obtnd smpl ststc falls n th approprit smplng dstrbtn. i.e., th tst ndicats whthr th ststc is n th rjctn regn or th rtntn regn of smplng dstrbtn.
Statistics & Research
Overview of Inferential Statistics - Analyzing the Data and Making a Decision
Th REJECTION REGION or "rgn of unlkly valus" lies n one or both tails of th smpling dstrbtn nd cntains th smpl valus tht r not lkly 2 ocur simply as th rslt of smplng eror. Th RENTENTION REGION or "rgn of lkly valus" lies n th cntrl prtn of th smplng dstrbtn nd cnsists of th valus tht r lkly 2 ocur as a cnsqnc of smplng eror only. Whn th rslts of th ststcl tst ndicat tht th obtnd smpl ststc is n th rjctn regn of th smplng dstrbtn, th null hypthsis is rjctd nd th altrntv hypthsis is rtaind. Th nvstgrt cncluds tht th smpl ststc is nt lkly 2 hv bn obtaind by chnc alon nd tht th IV hs had an effct on th DV. Cnvrsly, if th ststcl tst ndicats tht th smpl ststc lies n th rtntn regn of th smplng dstrbtn, th null hypthsis is rtaind, nd th altrntv hypthsis is rjctd.
Statistics & Research
Overview of Inferential Statistics - Analyzing the Data and Making a Decision - Alpha
Th sz of th rjctn regn dfnd by ALPHA, or th lvl of sgnfcnc. If alpha is .05, then 5% of th smplng dstrbtn rprsnts th rjctn regn nd th rmaing 95% rprsnts th rtntn regn. Th rjctn regn alwys lies n 1 or bth tails of th smplng dstrbtn; i.e., n tht prtn of th smpln dstrbtn tht cntains th valus tht r lst lkly 2 ocur as th rslt of smpln eror only. Th valu of alpha is set by an xprmntr prior 2 cllctng nd/or anlzng th data. N othr wrds, it is th xprmntr hu dcids wht proprtn of th smplng dstrbtn wil rprsnt th regn of unlkly valus. Alpha usuly set at .05 or .01 nd whn rslts of an nfrntl ststcl tst ndicat tht th obtnd smpl ststc lies n th rjctn regn of th smplng dstrbtn, th stdy's rslts said 2 b ststcly sgnfcnt.
Statistics & Research
Overview of Inferential Statistics - Analyzing the Data and Making a Decision - One- v. Two-Tailed Tests
Sum nfrntl ststcl tsts cn b cndctd as ethr a 1- or 2-taild tst. Whn a 2-taild tst is usd, th rjctn regn is =ly dvided btwn th 2 tails of th smpl dstrbtn. If th alpha is set @ .05, 2.5% of th rjctn regn lies n th pstv tail of th smplng dstrbtn nd 2.5% of th rjctn regn lies n th ngtv tail. W/ a 1-taild tst, th ntir rjctn regn is plcd n only 1 of th tails. It is th altrntv hypthsis tht dtrmns whthr a 1- or a 2-taild tst s/b cndctd. A 2-tails tst is usd whn th altrntv hypthsis is nondrctnl, whl a 1-taild tst is usd whn th altrntv hypthsis is drctnl. If a drctnl altrntv hypthsis prdcts tht th smpl ststc wil b grtr thn th valu spcfd n th hull hypthsis, th ntir rjctn regn lies n th pstv tail of th smpl dstrbtn. If a drctnl altrntv hypthsis prdcts tht th smplng ststc wil b lss thn th valu spcfd n th null hypthsis, th rjctn regn is loctd n th ngtv tail.
Statistics & Research
Overview of Inferential Statistics - Decision Outcomes
Rgrdls of whthr xprmntr dcids 2 rtain or rjct th null hypthsis, ther r 2 pssbl outcms of th dscsn: th dcsn cn b ethr crrct or n eror, nd xprmntr cn nvr b ntirly crtn wch typ of dcsn hs bn mad. Th pssbl outcms of a dcsn abt th null hypthsis cn be: th dcsn is CORRECT when retaining a TRUE null hyothesis & a TYPE II ERROR if retaining a False null hyothesis; it is a TYPE II ERROR whn rejecting a TRUE null hypothesis & CORRECT if rejecting a FALSE null hypothesis.
Statistics & Research
Overview of Inferential Statistics - Decision Outcomes - Study Tip
EPPP lkly 2 nclud 1 or two qustns rltd 2 th nfo cntaind n th dcsn outcm tbl. U mit wnt 2 memrz th tbl nd b abl 2 rcnstrct it whn u r tkng th xam. Hvng th tbl n frnt of u whn answrng a qustn abt thes trms nd cncpts wil hlp u clrfy th qustn nd ID th crrct rspns.
Statistics & Research
Overview of Inferential Statistics - Decision Errors
TYPE I
Two knds of dcn erors: TYPE I & TYPE II. TYPE I ERROR ocurs whn an nvstgtr rjcts a tru nul hypthsis. Th prblty of mkng a typ I eror is = 2 alpha. As th valu of alpha ncreses, th prblty of rjctng a tru nul hypthsis ncreses. B/c xprmntr sets valu of alpha, xprmntr hs cntrl ovr prblty of mkng typ I eror. Typ 1 eror als ncrsd whn smpl sz is smll or whn obsrvtns r dpndnt.
Statistics & Research
Overview of Inferential Statistics - Decision Errors
TYPE II
typ 2 eror ocurs whn nvstgtr rtains false nul hypthsis. Prblty of mkng typ 2 erors = 2 beta nd is mre lkly whn valu of alpha is lo, whn smple sz is smll, nd whn IV is not admnstrd n suffcnt ntnsty. Nvers r/s btwn typ 1 & typ 2 erors: as prblty of mkng 1 ncreses, prblty of mkng typ 2 dcreses nd vice versa. Slctn of a lvl of sgnfcnc dpnds on sriunss of mkng thes 2 erors.
Statistics & Research
Overview of Inferential Statistics - Correct Decision
Nvstgtr cn mk a crrct dcsn by rtaing th nul hypthsis whn it is tru or by rjctng nul hypthsis whn it is false. Whn a ststcl tst nabls xprmntr 2 rjct false hypthsis, tst said 2 hv Statistical Power. Pwr Mxmzd whn: 1) ncresng alpha - nul hypthsis (tru or fals) mre lkly 2 b rjctd whn alpha is .05 thn .01; 2) ncresng smpl sz - crrct dcsn mre lkly whn smpl sz is 50 rthr thn 25; 3) ncresng effct sz - mxmzng effct of IV ncreses lklihd tht effcts wil b dtctd. Effcts of th IV r mxmzd by admnstrng th IV 4 lng enuf period of tm or n suffcnt ntnsty; 4) mnmzng eror - whn ptntl srces of systmtc nd rndm eror r cntrlld, it is ezr 2 dctct th effcts of th IV. 1 wy 2 rduc eror is 2 mk sur DV meas is rlibl. Anthr wy is 2 rduc wthn-grp varblty by cntrllng xtrnus varibls or by usng a wthn-sbjcts dsgn; 5) usng 1-taild tst whn apprpriat - 1-taild tst mre pwrfl thn 2-taild tst as lng as it is apprpiatly usd; 6) usng a paramtrc tst - parmtrc ststcl tsts, such as th t-test or ANOVA r mre pwrfl thn nonparmtrc tsts.
Statistics & Research
Overview of Inferential Statistics - Decision Errors
Power v Confidence
Pwr nt ths sam as cnfdnc. Pwr rfrs 2 ablty 2 rjct a false null hypthsis nd is affctd by th sz of alpha: pwr ncreses as alpha ncreses nd vice versa. Ststcl pwr is smthng a rsrchr is cncrnd abt b4 a dcsn abt th nul hypthsis is mad. Confidence rfrs 2 th crtnty a rsrchr hs abt th dcsn th rsrchr hs alrdy mad abt th nul hypthsis. An xprmntr hs mre cnfdnc tht his dcsn 2 rjct th nul hypthsis ws crrct whn alpha is smll (e.g., .01 rthr thn .05)
Statistics & Research
Inferential Statistical Tests
Scal of msmnt of th data 2 b anlyzd is 1 fctr to b cndsdrd whn slctng an nfrntl ststcl tst. Whn stdy has an IV nd DV, it is th msmnt scal of the DV tht is of ntrst snc it is th data on th DV tht wil b anlyzd w/th ststcl tst. Th dsgn of stdy shud als b cnsdrd. Chrctrstcs of th rsrch dsgn dtrmn wch ststcl tst 2 use nclud th # of IV or if ther is only 1 IV, th # of lvls; whthr th grps r ndpdnt or crrltd; whthr ther r xtranus varibls tht ned 2 b cntrlld; nd th # of DVs.
Statistics & Research
Inferential Statistical Tests
Study Tip
Grp sumtms intrchngd w/smpl; "dpndnt," "rltd," nd "crrltd" usuly mean th sam thng. Th t-tst 4 crrltd smpls is sumtms clld th t-tst 4 rltd (or dpndnt) smpls, nd th word "smpls" is relly rfrrng 2 grps.
Statistics & Research
Inferential Statistical Tests
Nonparametric Tests
Infrntl ststcl tsts usd 4 Nominal data nclud sngl-smpl chi-square (1-variable) and multi-smpl chi-square (2+ variables). 4 Ordinal data, th Mann Whitney U tst (2 ndpndnt grps) Wilcoxon matched-pairs tst (2 corrltd grps) and th Kruskal-Wallis tst (2+ ndpndnt grps)
Statistics & Research
Inferential Statistical Tests
Parametric Tests
Th nfrntl ststcl tsts usd 4 Intrvl nd Ratio data nclud: t-tst 4 sngl smpl (smpl vs popultn); t-tst 4 crrltd smpls (2 crrltd grps) t-tst 4 ndpndnt smpls (2 ndpndnt grps); one-way ANOVA (1 IV, 2+ ndpndnt grps); factorial ANOVA (2+ IVs); repeated measures ANOVA (2+ correlated grps); randomzd block ANOVA (extraneous variable); trend analysis (quantitatv IV); and MANOVA (2+ DVs).
Statistics & Research
Inferential Statistical Tests
Parametric & Nonparametric Tests
Use of bth typs of nfrntl ststcl tsts r bsed on th asumptn tht th smpl hs bn rndmly slctd frm th popultn. Thes tsts asum tht obsrvtns r ndpndnt. Ths means tht a sbjct's prfrmnc n th stdy or prfrmnc on th DV s not affctd by or rltd 2 th prtcptn or prfrmnc of any othr sbjct (except 2 th xtnt tht prfrmnc is du 2 effcts of th IV).
Statistics & Research
Inferential Statistical Tests
Parametric Tests
Nclud th t-tst nd ANOVA and r usd 2 elvuat hypthses abt popultn means, variances, or othr parameters. Ths tsts r apprpriat only whn th varibl of ntrst hs bn measrd on an ntrvl or ratio scal nd whn crtn asumptns abt th popultn dstrbtn(s) r met. Frst asmptn is tht th valu of ntrst is nrmly dstrbtd n th popultn. Scnd asumptn is tht, whn a stdy ncluds ,re thn 1 grp, ther is HOMOSCEDASTICITY; i.e., th varincs of th popultn tht th dffrnt grps rprsnt r =. Violtn of thes asumptns - esp th asumptn of homscdstcty - cn ncres th prblty of mkng TYP I or TYP II error. Parmtrc tsts r rltvly robust w/rgrd 2 violtn of thr asumptns, meang tht sum dvatn frm th nrml curv or frm homoscdcty wil nt necssrly nvldat tst's rslts. Th mst effctv way 2 mxmz th robstnss is 2 hv an = # of sbjcts n ea grp. Robstnss als ncresd by hvng lrg smpl sz nd sttng alpha @ a lwr lvl (01 rthr th .05). Parmtrc tsts r nt rbst w/rgrd 2 th asumptn of ndpndnc of obsrvtns. Evn smll amt of dpndnc amng obsrvtns cn ncres prblty of mkng Typ I error abv th prblty ndicatd by alpha.
Statistics & Research
Inferential Statistical Tests
Nonparametric Tests
Nonparmtrc tsts r usd 2 anlyz data cllctd on varibls tht hv bn measrd on a nominl or ordinal scal. Thes tsts do nt mk sam asumptns abt th shp of th popultn dstrbtn(s) nd r rfrd 2 as dstrbtn-free tsts. Ths tsts r usd 2 evluat hypthses abt th shp of a dstrbtn rthr thn th dstrbtn M, S, or othr parmtr. A shrtcmng of th nonparmtrc tsts is tht, b/c thy nvolv usng lss prcis (nomnl or ordnl) data, thy r lss pwrfl. Rsrch is lss lkly 2 rjct a false nul hypthsis w/ a nonparmtrc tst th w/a parmtrc one. Thus, parmtrc tsts alwys prfrd whnvr thy cn b lgtmtly usd.
Statistics & Research
Inferential Statistical Tests
Study Tip
Rembr, whn pckng nfrntl ststcl tst, 1st thng u wnt 2 cnsdr is scal of msmnt of th data 2 b analyzd. Th wil hlp u dstngush btwn th tst 4 nmnl, ordnl, nd ntrvl/ratio data. Nxt cnsdrtn is th natur of th rsrch dsgn.
Statistics & Research
Inferential Statistical Tests
Critical Values & Degrees of Freedom
Th rslts of an nfrntl ststcl tst yld a ststc (t, F, etc) tht allws nvstgtr 2 dtrmn whthr th obtnd smpl valu is n th rjctn or rtntn regn of th smplng dstrbtn. Ths is don by cmprng th tst ststc 2 a critcl valu, wch is th # tht crrspnds 2 th boundry th dvids th smplng dstrbtn n2 rjctn nd rtntn regns. Crtcl valus r usuly ncluded n th appndcs of th ststcs txtbks. 4 most ststcl tsts, whn th tst ststc =s or xceds th crtcl valu, ths meantht th obtnd smpl lis n th rjctn regn; whn th ststc is lss thn th crtcl valu, th smpl valu is n th rtntn regn. Mgntud of crtcl valu dtrmnd by 2 fctrs: alpha nd th dgres of frdm. Alpha dtrms wht proprtn of th smplng dstrbtn rprsnts th rjctn regn, nd th dgres of frdm (df) dtrmn th dstrbtn's exct shp. Dgres of frdm r the #s of valus or ctgres n a dstrbtn tht r "free 2 vary" gvn tht crtn valus or ctgres r knwn 2 b fxd. Th mthd 2 clcult dgres of frdm dpnds on th ststcl tst. 4 th t-tst 4 a sngl smpl, th smplng dstrbtn is bsed on th smpl sz, nd th dgres of frdm r drivd frm th totl # of sbjcts (N-1). Whn usng a sngl smpl chi-squr tsts, a dffrnt knd of smplng dstrbtn is usd. It is bsed on th # of ctgres (lvls) of th varibls, nd th dgres of frdm r drivd frm th totl # of catgres (C-1)
Statistics & Research
Inferential Statistical Tests
Study Tip
4 th EPPP, u dont ned 2 knw wht crtcl valus r or undrstnd wht dgres of frdm r, bt u shud b able 2 clcult th dgres of frdm frm th chi-squr tsts nd th t-tsts.
Statistics & Research Design
Inferential Statistical Tests
Tests For Nominal Data
Chi-square
Th Chi-square is usd 2 analyz th frquncy of obsrvtns n ea ctgry (lvl) of a nmnl varibl (or othr varibl tht is bng tx'd as a nmnl varibl). Th Chi-sqr tst wud b apprpriat 4 cmprng th # of peop hu prfr one of 4 poltcl cndidts or cmprng th # of mngrl nd non-mngrl mplyes hu say tht ethr psychlgcl, sfty, socl, slf-estm, or slf-actulztn neds r most mprtnt. Chi-sqr tst usd 2 dtrmn if dstrbtn of obsrvd (smpl) frquncys is =vlnt 2 th dstrbtn of xpctd frqncys. Th xpctd frqncys r prdctd by th nul hypthsis nd rflct no dffrnc btwn ctgres. Use of th chi-sqr tst reqirs th data 2 b rprtd n ntrms of frqncys nd als tht th xpctd frqncy 4 any 1 ctgry b no lss thn 6 nd tht obsrvtns b ndpndnt (i.e., ea sbjct cn apper n only 1 ctgry).
Statistics & Research Design
Inferential Statistical Tests
Tests For Nominal Data
Chi-square - Study Tip 2
2 forms of chi-sqr tsts - th sngl-smpl nd th multi-smpl. 2 hlp rmbr whn ea tst is usd, it is bttr 2 thnk of thm as th "sngl-varibl" nd th "multipl-varibl" chi-sqr tsts. Th formr usd whn stdy ncluds only 1 varibl; th lttr whn th stdy ncluds 2 or mre varibls. (Whn countng th # of varibls 4 th chi-sqr tst, u don't dstngsh btwn IV nd DV.) Als, note tht u don't hv 2 knw how th xpctd frqncys r dtrmnd 4 th ch-sqr tst.
Statistics & Research Design
Inferential Statistical Tests
Tests For Nominal Data
Single-Sample Chi-square Test
Th sngl-smpl ch-sqr tst (aka th "goodness of fit) usd whn a dscrptv study ncluds only 1 varibl nd th data 2 b analyzd r th # of obsrvtns n ea ctgry of tht varbl. SUMMARY: Sngl-Smpl Chi-sqr Tst. USE: One Varibl; Nominl (frqncy) data. STATISTIC: X(squared). df: (C-1), where C=number of "columns" (lvls of th varibl). (e.g., nvstgtr ntrstd n fndng out if th 120 pts n th stdy dffr w/rgrd 2 fmly bckgrnd. hw mny hv 1) one biolgcl prnt w/ schzo; 2) both prnts w/ schizo; or 3) no prnts w/schizo. B/c stdy is dscptv nd ncluds only 1 nomnl varibl, th apprpriat tst is th sngl-smpl ch-sqr tst nd th df 4 ths stdy r: (C-1)= (3-1)=2
Statistics & Research Design
Inferential Statistical Tests
Tests For Nominal Data
Multi-Sample Chi-square Test
Th multi-smpl chi-sqr tst ("chi-sqr tst 4 cntngcy tbls") is usd whn dscrptv or xprmntl stdy ncluds two or mre varibls nd th data 2 b anlyzd r th # of obsrvtns n ea ctgry. SUMMARY: Multi-Smpl Ch-sqr Tst. USE: Two or mre varibls; nomnl (frqncy) data. STATISTC: x(squared). df: (C-1)(R-1), where C=number of "columns" nd R=number of "rows." (e.g., rsrchr wnts 2 dtrmn if pt's spcfc dx (1-catatonic, 2-paranoid, 3-disorganized, 4-undifferentiated, 5-residual) rlts 2 fmly bckgrnd nd dtrmns ea pt's DSM dx nd fmly hx. Th xpnded stdy cn b cnsdrd ethr dscrptv stdy w/two varibls or an xprmntl stdy w/one IV nd 1 DV (fmly bckgrnd is IV nd dx is DV). B/c stdy ncluds mre thn one varibl nd th anlysis wil nvolv cmprng frqncys n ea ctgry, th apprpriat tst is th multi-smpl ch-sqr tst, nd th df r = to: (C-1)(R-1)=(3-1)(5-1)=2(4)=8
Statistics & Research Design
Inferential Statistical Tests
Tests For Nominal Data
Single- & Multi-Sample Chi-square Test (Study Tip)
N th tbl usd 2 dpict a stdy n wch th data 2 b anlyzd r nominl (i.e., n wch th data wil b anlyzd usng a chi-squr tst), th IV nd th DV r bth lstd outsid th tbl nd th #s plcd nsid th cells (ctgrys) r th obsrvd frqncys. A simlr tbl cn b usd 2 dpict a stdy n wch th data rprsnt an ntrvl or ratio scal nd a t-tst or ANOVA wil b employd, but n tht cse only th IVs r lstd outsid th tbl nd th #s n th cells r th grp means on th dpndnt varibl. Altho ths nfo wil nt b askd abt on th exam, bng abl 2 dpict a stdy n trms of a tbl cn hlp 2 cncptulz a rsrch stdy dscrbd n an exam qustn.
Statistics & Research Design
Inferential Statistical Tests
Tests For Ordinal Data
Ststcl tsts 4 ordnl data nclud th sign tst, th median tst, th Kolmongorov tst, th Mann-Whitney U tst, th Wilcoxon matched-pairs tst, nd th Kruskal-Wallis tst. Th last 3 tsts r usd 2 anlyz rank-ordrd data.
Statistics & Research Design
Inferential Statistical Tests
Tests For Ordinal Data
Mann-Whitney U Test
ths tst apprpiat whn stdy ncluds 2 ndpndnt grps nd th data on th DV r rprtd n trms of ranks. SUMMARY: Mann-Whitney U Tst. USE: One IV; two independent groups; One DV; rank ordered data.STATISTIC: U. (e.g., rsrchr dcids 2 assess th effcts of drug on cgntv fnctng by cmprng IQ scrs of pts hu rc'd modrt dos of th drug 2 pts hu rc'd placbo. IQ scres r very skwed. B/c scres violat asmptn of nrmlty 4 parmtrc tsts, th rsrch cnvrts IQ scres 2 rank nd uses th Mann-Whitny U tst 2 anlyz th data.
Statistics & Research Design
Inferential Statistical Tests
Tests For Ordinal Data - Wilcoxon Matched-Pairs Signed-Ranks Test
Ths tst usd whn stdy ncluds 2 crrltd (matchd) grps nd th dffrncs btwn th DV scrs of sbjcts hu hv bn matchd n pairs r cnvrtd 2 ranks. SUMMARY: Wilcoxon Matched-Pairs Signed-Ranks Test. USE: One IV; two crrltd grps; One DV; rank-ordrd data; STATISTIC: T. (e.g., rsrchr assgns pts 2 grps by matchng thm on bsis of thr scres on a meas of premrbid adjmnt nd rndmly assgng membrs of ea matcd pair 2 ethr th drug grp or placebo grp. B/c stdy nvolvs crrltd grps nd th IQ scres r nt nrmly dstrbtd, rsrchr clcults dffrnc scres 4 ea pair of matcd pts, cnvrts dffrnc scres 2 ranks, nd uses th Wilcoxon tst 2 anlyz th data.
Statistics & Research Design
Inferential Statistical Tests
Tests For Ordinal Data Kruskal-Wallis Test
Ths tst is simlr 2 th Mann-Whitney U Test bt cn b usd whn stdy ncluds 2 or mre ndpndnt grps nd th dta 2 b anlyzd r ranks. SUMMARY: Kruskal-Wallis Test. USE: One IV, two or mre ndpndnt grps; One DV; rank-ordered dta. STATISTIC: H. (e.g., rsrch xpnds stdy by ncludng 3 grps: 1 tht recvs hi dos of drug, 1 tht recvs lo dos of drugs, and 1 that recvs placebo. If IQ scres violat one or bth asmptns 4 a parmtrc tst, th rsrch cn cnvrt th IQ 2 ranks nd use th Kruskal-Wallis tst 2 anlyz th data.
Statistics & Research Design
Inferential Statistical Tests
Tests For Ordinal Data
Study Tip
Th main thng u wnt 2 rembr abt th tsts 4 ordnl dta is tht thy can b dscrbd as "nonparmtrc altrntvs" 2 spcfc parmtrc tsts. Mann-Whitney is th nonparmtrc altrntv 2 th t-tst 4 ndpndnt smpls; th Wilcoxon is th nonparmtrc altrntv 2 th t-tst 4 crrltd smpls; nd th Kruskal-Wallis is th nonparmtrc altrntv 2 th one-way ANOVA.
Statistics & Research Design
Inferential Statistical Tests
Tests For Interval and Ratio Data
Th STUDENT'S t-test nd th anlysis of varinc r th most cmmnly-usd nfrntl ststcl tsts 4 varibls measrd on an ntrvl or ratio scal.
Statistics & Research Design
Inferential Statistical Tests
Tests For Interval and Ratio Data - Student's t-test
Usd 2 evaluat hypthsis abt dffrncs btwn 2 means. Ther r 3 forms of th t-tst 4 sngl-smpl, t-tst 4 ndpndnt smpls, nd t-tsts 4 crrltd smpls, Th slctn of a t-tst is dtrmnd by how th 2 means are obtnd. NOTE: a t-tst cn b usd 2 anlyz data cllctd frm a stdy nvolvng mre th 2 means, but it wud b ncssry 2 cndct mre thn 1 tst. ths is prblmtc snc th lrgrth # of ststcl cmprsns mad n 1 stdy, th mre lkly tht a Typ ! error wil be mad. TH GRTR th # of XPRMNTS, TH GRTR th XPRMNTWSE ERROR RATE. 4 ths resn, th ANOVA is prfrd whn mre thn 2 means r 2 b cmprd (i.e., whn th IV hs mre thn 2 lvls).
Statistics & Research Design
Inferential Statistical Tests
Tests For Interval and Ratio Data - Student's t-test for a Single Sample
Th t-tst for a sngl smpl is usd whn a stdy ncluds only 1 grp nd th grp (smpl) mean wil b cmprd 2 a knwn popultn mean. (n ths situatn, th popultn is actng as a n0-tx cntrl grp.) SUMMARY: Student's t-Test for a Sngl Smpl. USE: 1 IV; sngl grp; 1 DV; ntrvl or ratio dta. STATISTIC: t. df: (N-1), where N=# of sbjcts. (e.g., hypthsis is slf-cntrl prcdur ncreses acadmc achvmnt by trng a rndm smpl of 20 6th grdrs hu hv rcv'd a dx of ADHD n th prcdur nd, fllwng trng admnstrng th tst of acdmc achvmnt. Rsrch then uses t-tst 4 sngl smpl 2 cmpr mean achvmnt tst scres obtnd by chldrn n th smpl 2 th mean scre 4 popultn of 6th grdrs w/ADHD. Th df 4 ths stdy r = 2: (N-1)=(20-1)=19.
Statistics & Research Design
Inferential Statistical Tests
Tests For Interval and Ratio Data - Student's t-test for a Independent Samples
Th t-tst for ndpndnt (unrltd)smpls is th apprpriat ststcl tst whn a stdy ncluds 2 ndpndnt grps nd th means of th 2 grps wil b cmprd. SUMMARY: Student's t-Test for INDEPENDENT Samples. USE: 1 IV; 2 ndpndnt grps; 1 DV; ntrvl or ratio dta. STATISTC: t. df: (N-2), where N=total # of sbjcts. (e.g., rsrchr obts smpl of 20 chldrn w/ADHD nd rndmly assgns 10 to xprmntl (slf-cntrl) grp nd 10 to cntrl (no tx) grp. Aftr trng xprmntl grp, rsrch admnstrs th acdmc achvmnt tst 2 all chldrn nd uses th t-tst 4 ndpndnt smpls 2 cmpr th means of th2 grps. Th df r = 2: (N-2)=(20-2)=18.
Statistics & Research Design
Inferential Statistical Tests
Tests For Interval and Ratio Data - Student's t-test for Correlated Sample
Th t-tst 4 crrltd (rltd) smpls is usd whn th 2 means 2 b cmprd hv cum frm crrltd grps. It is th apprpriat tst 4 a stdy usng a w/in-sbjct dsgn n wch a sngl grp of sbjcts hv bn matchd on an xtranus varibl nd mbrs of ea match pair hv bn assgnd 2 a dffrnt grp or whn subjcts cum 2 th stdy alrdy matchd n pairs (e.g., twins). SUMMARY: Student's t-Test 4 Crrltd Smpls. USE: 1 IV; 2 crrltd grps; 1DV; ntrvl or ratio dta. STATISTIC: t. df: (N-1), where N=# of pairs of scores. (e.g., rsrch dcids 2 use a sngl-grp pretest/posttest rsrch dsgn and slcts 20 sbjcts hu rec'd a dx of ADHD nd admnstrs th acdmc achvmnt tst. Then, trans sbjcts n th slf-cntrl grp nd aftr a period of tme, readmnstrs th achvmnt tst. B/c th ststcl tst anlysis wil nvolv cmprng mean scors obtnd by th same grp of sbjcts b4 nd aftr bng trand n th slf-cntrl prcdur, th rsrchr wil use the t-tst 4 crrltd smpls. Th df r: (N-1)=(20-1)=19.
Statistics & Research design
Inferential Statistical Tests
Student's t-Test for Correlated Samples
Study Tip
Rembr tht th t-tst is usd 2 cmpr only two means at a tme nd tht th choic of a t-test dpnds on how th two means wer obtnd (smpl nd popultn, ndpndnt grps, or crrltd grps). A stdy ncludng mre thn 1two means (e.g., mre thn two lvls of th IV) wud requir cndctng multipl t-tsts, wch wud ncres th prblty of mkng a Type I eror.
Statistics & Research Design
Inferential Statistical Tests
Analysis of Variance
Th ANOVA is usd 2 cmpr two or mre means. An advntg of th ANOVA is tht it simultnusly mks all cmprns of th grp means whl holdng th prblty of mkng a Typ I eror at th lvl of sgnfcnc set by th nvstgtr. An ANOVA hlps cntrl th xprmntrwse eror rate. Ther r svrl vrsns of th ANOVA. Prbly th most cmmnly usd r th one-way ANOVA nd th Factorial ANOVA, wch r apprpriat whn a stdy ncluds, rspctvly, one IV or mre thn one IV. Th othr ANOVAs r usd whn a stdy mploys a mre cmplx rsrch dsgn.
Statistics & Research Design
Inferential Statistical Tests
Analysis of Variance
One-Way ANOVA
A one-way ANOVA is usd whn a stdy ncluds one IV nd two or mre ndpndnt grps nd one DV tht is measrd on an ntrvl lvl or ratio scal. (whn a stdy ncluds only two unrltd grps nd nvolvs cmprng only two means, th t-tst 4 ndpndnt smpls nd th one-way ANOVA r essntly ntrchngbl, but th cnvntn is 2 use th t-tst whn th analysis ntails two means nd th ANOVA whn it nvolvs three or mre means.
Statistics & Research Design
Statistic & Research Design
Inferential Statistical Tests
Analysis of Variance
The Logic of the One-Way ANOVA
Lk th t-tst, th analysis of variance cmprs means, but it duz so n a mre cmplx way by analyzng variblty around means. Th ANOVA nabls a rsrchr 2 evaluat th rltv cntrbtns of dffrnt fctrs 2 th totl amt of variblty obsrvd n a set of scors. Ths is don by "partitiong th sum of squares." Th one-way ANOVA dvids th totl sum of squars (SST) n2 a "btwn grp sum of squars" (SSB) nd a "within grp sum of squars (SSW) so tht: SST = SSB + SSW. Th sums of squars r cnvrtd 2 mean squars (varincs) by dvidng ea sum of squars by th apprpriat df (4 th ANOVA, th df r usd not only 2 ID th crtcl valu but als 2 calcult th F-ratio): MST = SST/df; MSB = SSB/df; MSW = SSW/df. MSW (mean square within) nd MSB (mean square btwn) r then usd 2 calcult th F-RATIO, wch is th tst ststc prducd by th ANOVA. MSW is a poold meas of variblty WITHIN ea of th tx grps. MSW reprsnts a meas of variblty for sbjcts hu hv bn tx'd alik nd prvids an est of variblty tht is du to eror only. MSB is a meas of variblty BTWN tx grps nd srvs as an est of variblty du 2 both eror nd th effcts of th IV. Th F-ratio is calcultd by dvidng MSB/MSW: F = MSB/MSW = (tx + error)/error.
Statistics & Research Design
Inferential Statistical Tests
Analysis of Variance
The Logic of the One-Way ANOVA
Wh th nul hypthsis is tru (whn th IV hs not had an effct on th DV), MSB nd MSW r th same nd th F-ratio is = to 1. Whn th nul hypthsis is false (whn th IV has had an effct on th DV), MSB is lrgr thn MSW nd th F-ratio is grtr thn 1. Th lrgr th valu of F, th mre lkly tht it wil b ststcly sgnfcnt. If a stdy ncluds mre thn two grps, a ststcly sgnfcnt F ndicats tht ther is sum dffrnc btwn grps but duz not ndicat wch of th grps dffr. Cnsqntly, whn a one-way ANOVA ylds a sgnfcnt F, a post-hoc tst is usuly cndctd n ordr 2 ID wch grp means r sgnfcntly dffrnt. E.G., a rsrch mit use th Scheffe S tst 2 mk all pairwse nd cmplx cmprsns (Grp1 v Grp2, Grp1 v GRP2 nd 3, etc) or th Tukey tst 2 mk pairwse cmprsns whn grps r of = sz. Whn a one-way ANOVA ylds an nsgnfcnt F, no frthr anlys of dta is requird, nd th nul hypthsis is retaind.
Statistics & Research Design
Inferential Statistical Tests
Analysis of Variance
The Logic of the One-Way ANOVA
SUMMARY: One-Way Analysis of Variance. USE: One IV; two or mre ndpndnt grps; One DV; ntrvl or ratio dta. Statistic: F. df: (C-1), (N-C), where C= # of lvlv of th IV nd th N= # of sbjcts. e.g., rsrchr cmprs th effcts of three lvls of drugs on WAIS-III scors by obtng a smpl of 75 pts nd rndmly assgng thm 2 ethr hi dos, lo dos, or placebo grp. Aftr sbjcts hv tkn th drug or placebo 4 three mnths, rsrch admnstrs th WAIS-III 2 all sbjcts nd uses a one-way ANOVA 2 cmpr th mean IQ scors of th three grps. Two dffrnt df r calcultd 4 th ANOVA, one 4 th numrtr nd one 4 th dnomntr. 4 ths stdy, th numrtr df r = to: (C-1)=(3-1)=2; th dnomntr df r = to: (N-C)=(75-3)=72
Statistics & Research Design
Inferential Statistical Tests
Analysis of Variance
The Logic of the One-Way ANOVA - Study Tip
Th ANOVA summary tbl prvids svrl pcs of nfo. It ncluds th nfo usd 2 clculat th F-ratio nd it ndicats whthr or not th F-ratio is sgnfcnt. 4 th exm, u shud knw wht th numrtr nd th dnmtr of th F-ratio rprsnt. Hwvr, it is nt lkly tht u wil ncntr a qustn rquirng u 2 knw wht th df r 4 th ANOVA or how 2 clcult MSB, MSW, or n F-ratio.
Statistics & Research Design
Inferential Statistical Tests
Analysis of Variance
The Factorial ANOVA
th fctrl ANOVA is an xtnsn of th one-wy ANOVA tht is mplyd whn a stdy ncluds 2 or mre IVs. (Whn a stdy hs 2 IVs, th fctrl ANOVA is als clld a two-wy ANOVA; whn it hs three IVs, it is clld a three-wy ANOVA; etc)
Statistics & Research Design
Inferential Statistical Tests
Analysis of Variance
The Logic of the Factorial ANOVA
Th lgc undrlyng th fctrl ANOVA is bscly th sam as tht 4 th one-wy ANOVA. Th dffrnc is tht th variblty btwn grps is "partitioned" evn frthr so F-ratios r obtnd 4 th main effcts of ea IV nd 4 thr ntrctns. E.G., n a 2-wy ANOVA, three separt F-ratios r clcultd, one 4 ea main effct nd one 4 th ntrctn: i.e., F(A), F(B), nd F(AxB). Whn any of th F-ratios r ststcly sgnfcnt, only th frst stp of th anlsis hs bn cmpltd. B/c th stdy nvolvs mre th 2 grps, frthr post-hoc anlyses r ncssry. If all of th F-ratios r sgnfcnt, no frthtr anlysis r requird, nd th nul hypthsis is retand.
Statistics & Research Design
Inferential Statistical Tests
Analysis of Variance
The Logic of the Factorial ANOVA
SUMMARY: Factorial Analysis of Variance. USE: two or mre IVs; ndpndnt grps; one DV; ntrvl or ratio dta. STATISTIC: F. e.g., rsrch wnts 2 cmpr th effcts of varuis cmbntns of three lvls of drgs nd 4 lvls of thrpy on cgntv ablty. He obtns a smpl of 120 pts nd rndmly asgns thm 2 1 of th tx grps. Aftr 3 mos, WAIS-III admnstrd 2 all pts. B/c stdy hs two IVs (drgs nd thrpy) nd one DV tht is measrd on an ntrvl scal, rsrchr uses a 2-wy (fctrl) ANOVA 2 anlyz th dta cllctd. Rslts of stdy allw rsrch 2 dtrmn if ther r main effcts of drgs, main effcts of thrpy, nd/or an ntrctn btwn drgs nd thrpy.
Statistics & Research Design
Inferential Statistical Tests
Analysis of Variance
The Logic of the Factorial ANOVA - Study Tip
Rembr tht th one-wy ANOVA is usd whn a stdy ncluds 1 IV, whl th fctrl ANOVA is usd whn stdy mplys a fctrl dsgn (i.e., whn it ncluds TWO OR MORE IVs).
Statistics & Research Design
Inferential Statistical Tests
Other Forms of th Analysis of Variance
Svrl othr vrsns of th ANOVA r avalbl 4 use w/mre cmplx dsgns: Rndmzd Blck Fctrl ANOVA, Analysis of Covariance (ANCOVA), Repeated Meas ANOVA, Mixed (Split Plot) ANOVA, Trend Analysis, Multivariate Analysis of Variance (MANOVA).
Statistics & Research Design
Inferential Statistical Tests
Analysis of Variance
Randomized Block Factorial ANOVA
Ths knd of ANOVA is mplyd whn "blockng" hs bn usd 2 cntrl an xtranus varibl. Th rndmzd blk fctrl ANOVA nvolvs tretng th xtranus varibl as an IV so tht its main nd ntrctn effcts cn b ststcly anlyzd. Tretng th xtranus varibl as an IV hlps rduc within grp variblty, thrby ncresng th pwr of th ststcl anlysis.
Statistics & Research Design
Inferential Statistical Tests
Analysis of Variance
Analysis of Covariance ANCOVA
Th ANCOVA cmbns th alysis of varinc w/rgrssn anlysis nd allws rsrchr 2 cntrl an xtranus varibl by ststcly rmvng th prtn of variblty n th DV tht is due 2 th xtranus varibl. By rmvng th effcts of an xtranus varibl, th ANCOVA reduces within-grp variblty, rsltng n a mre pwrfl tst. Cndctng an ANCOVA requirs usng sbjcts' scors on th xtranus varibl (th covariate) 2 adjst thr scors on th DV.
Statistics & Research Design
Inferential Statistical Tests
Analysis of Variance
Repeated Measures ANOVA
Th rptd meas ANOVA is apprpriat 4 stdys usng with-in sbjcts dsgn n wch th dffrnt lvls of th IV or cmbntn of lvls of 2 or mre IVs r seqntly admnstrd 2 ea sbjct.
Statistics & Research Design
Inferential Statistical Tests
Analysis of Variance
Mixed (Split-Plot) ANOVA
Th mxd (splt-plt) ANOVA is th apprpriat tst4 styds usng a mxd dsgn n wch at lst one IV is a btwn-grps varibl nd one is a with-in grps varibl.
Statistics & Research Design
Inferential Statistical Tests
Analysis of Variance
Trend Analysis
Trnd Anlysis is usd whn a stdy nvolvs one or mre quntatv IVs, nd th rsrchr wnts 2 evluat th shp or form of th r/s btwn th IVs nd th DVs. Th rslts of a trnd anlysis ndicat whthr or not thr is a ststcly sgnfcnt linear or non linear (quadratic, cubic, quartic) trend. (e.g. measuring the effects of varius drug doses).
Statistics & Research Design
Inferential Statistical Tests
Analysis of Variance
Multivariate Analysis of Variance (MANOVA)
Th MANOVA cn b usd whn a study ncluds one or mre IVs nd two or mre DVs tht r ea measrd on an ntrvl or ratio scal. Th MANOVA allws rsrchrs 2 simultanusly asses th effcts of th IV(s) on all of th DVs and thrby hlps cntrl th xprmntwse error rate. Whn th IV hs only small effct on th DV, separt analyses mit not dtect thos effcts. Th MANOVA hlps ncres ststcl pwr n ths situatn by simultanusly assesng th effcts of th IV on all of th DVs.
Statistics & Research Design
Correlation And Prediction
Crrltnl tchnqs r usd 2 dscrb thn dgre of assctn btwn two or mre varibls - th dgre 2 wch two or mre varibls covary - and mak prdctns abt one varibl or a set of varibls bsed on status or prfrmnc on anthr varibl or set of varibls. Whn crrltnl tchnqs r usd 4 th purps of prdctn, th X (ndpndnt) varibl is oftn rfrd 2 as th prdctr, whl th Y (dpndnt) varibl is clld th criterion. technqs usd 2 asses dgre of crrltn nd 2 fciltat prdctn r bivariate nd multivariate
Statistics & Research Design
Correlation And Prediction
Bivariate Techniques
Bivriat crrltnl tchnqs r usd 2 dscrb or smmrz th dgre of assctn btwn two varibls nd nclud scattergrams nd crrltnl coeffcnts.
Statistics & Research Design
Correlation And Prediction
Bivariate Techniques
Scattergram
Th dgre of assctn 4 two varibls cn b dpictd n a scttrgrm (aka a scttr diagrm or scttrplot). N a scttrgrm, th X (prdctr) varibl is plcd on th hrzntl axis, whl th Y (criterion) varibl is lctd on th vrtcl axis. Whn th dta points r wdly scttrd, ths means tht th varibls hv a weak r/s. Cnvrsly, whn ther is a nrrw scttr of dta points (i.e., whn th dta points assum th shp of an elips), ths ndicats a strng r/s.
Statistics & Research Design
Correlation And Prediction
Bivariate Techniques
Correlation Coefficient
A correlation coefficient smmrzs th dgre of assctn btwn varibls w/ a sngl #. Ther r svrl crrltn coeffcnts, nd th slctn of a cofficnt is bsed on th scal of msmnt of th varibls bng measrd. Th PEARSON R (Pearson prduct moment crrltn coffcnt) is th coffcnt most cmmnly usd w/ntrvl nd ratio dta.
Statistics & Research Design
Correlation And Prediction
Bivariate Techniques
Correlation Coefficients
Pearson Product Moment (r)
Variable 1 = ntrvl or ratio (e.g., product Knowledge tst scors). Variable 2 = ntrvl or ratio (e.g., Yearly sales n $).
Statistics & Research Design
Correlation And Prediction
Bivariate Techniques
Correlation Coefficients
Spearman Rank-Order (rho)
Variable 1 = Rank-ordered (e.g., rank in hi schol clss). Variable 2 = Rank-ordered (e.g., Rank in trms of SAT scors).
Statistics & Research Design
Correlation And Prediction
Bivariate Techniques
Correlation Coefficients
Phi
Variable 1 = true dichotomy (e.g., Sex - male/female). variable 2 = true dichotomy (e.g., Reading preference - fiction/nonfiction).
Statistics & Research Design
Correlation And Prediction
Bivariate Techniques
Correlation Coefficients
Tetrachoric
Variable 1 = Artificial dichotomy (e.g., Company climate favorable/unfavorable). Variable 2 = Artificial dichotomy (e.g., Sales success successful/unsuccessful).
Statistics & Research Design
Correlation And Prediction
Bivariate Techniques
Correlation Coefficients
Contingency
Variable 1 = Nominal (e.g., DSM dx). Variable 2 = Nominal (e.g., past hospitalization yes/no).
Statistics & Research Design
Correlation And Prediction
Bivariate Techniques
Correlation Coefficients
POINT BISERIAL
Variable 1 = True dichotomy (e.g., sex male/female). Variable 2 = Interval or ratio (e.g., IQ scors).
Statistics & Research Design
Correlation And Prediction
Bivariate Techniques
Correlation Coefficients
Biserial
Variable 1 = Artificial dichotomy (e.g., company climate favorabl/unfavorable). Variable 2 = Interval or ratio (e.g., yearly sales in $).
Statistics & Research Design
Correlation And Prediction
Bivariate Techniques
Correlation Coefficients
Eta (used to assess nonlinear relationships)
Variable 1 = Interval or ratio (e.g., level of anxiety - GSR). Variable 2 = Interval or ratio (e.g., performance on memorization task).
Statistics & Research Design
Correlation And Prediction
Bivariate Techniques
Correlation Coefficients
Th Pearson r nd crrltn coeffcnts derivd from it range in valu from -1.0 to +1.0. Th mgntud of th coffcnt ndicats th r/s's strngth. Th clsr th coffcnt is to -1.0 or +1.0, th strngr th r/s. Th sign of th crrltn coffcnt ndicats th r/s's dirctn. Whn ther is a pstv (dirct) crrltn btwn X nd Y, th valus of Y ncres as th valu of X ncres. Cnvrsly, whn ther is a ngtv (invrs) crrltn, th valus of Y dcres as th valus of X ncres.
Statistics & Research Design
Correlation And Prediction
Bivariate Techniques
Correlation Coefficients
Assumptions
Use of th Pearson r nd most othr coeffcnts rquir tht three asumptns b met. Violtn of one or mre of thes asumptn cn prduc an inaccurt or msldng crrltn coeffcnt.
Statistics & Research Design
Correlation And Prediction
Bivariate Techniques
Correlation Coefficients
Assumptions - Linearity
Th frst asumptn is tht ther is a linear r/s btwn th varibls. I.e., n a scttrgrm, th r/s btwn X nd Y cn b smmrzd by a strght lin. If th r/s is nonlinear, th Pearson r wil undrest th dgre of assctn.
Statistics & Research Design
Correlation And Prediction
Bivariate Techniques
Correlation Coefficients
Assumptions - Unrestricted Range
Use of th Pearson r is also bsed on th asumptn tht ther is an unrstrctd rng of scors on bth varibls. Ths means tht th dta hv bn cllctd from peop hu r heterognus w/rgrd to th chrctrstcs measrd by X nd Y. If ther is a rstrctn n rng (if peop r homogenus), th Pearson r is lkly 2 b an undrestmt.
Statistics & Research Design
Correlation And Prediction
Bivariate Techniques
Correlation Coefficients
Assumptions - Homscedasticity
Th thrd asumptn is tht th rng of Y scors is abt the same 4 all valus of X - i.e, tht ther is homoscedstcty. E.g., if th rng of Y scors is 10 at lo valus of X, th rng shud als b abt 10 at modrte nd hi valus of X. Th dffrnc btwn homoscdstcty nd heteroscdastcty duz nt ncssrly rslt n a cffcnt tht is too lo or too hi but producs a cffcnt tht duz nt rprsnt th full rng of scors.
Statistics & Research Design
Correlation And Prediction
Bivariate Techniques
Correlation Coefficients
Study Tip
U shud knw hw to trnslt "scttrplt lnguag if u run acrss it. (e.g., u mit find a qustn tht asks wht it means whn the rng of Y scors at evry valu of X is = to th totl rng of Y scors. Ths stmt is vry simlr 2 th frst sntnce n th abv dscrptn of homoscdstcty, but it is nt idntcl to tht sntnc. Bth dscrib homoscdstcty but ths stmt rfrs 2 a prtculr knd of homoscdstcty tht ocurs whn ther is vry wide scttr of dta points n th scttrplt or whn all of th dta points fall on a hrzntl lin. Th answr 2 ths qustn is tht it means tht ther is a 0 (or near 0) crrltn coffcnt.
Statistics & Research Design
Correlation And Prediction
Bivariate Techniques
Correlation Coefficients
Interpretation of a Correlation Coefficient - Degree of Association
A crrltn coffcnt cn b ntrprtd dirctly n trms of dgre of assctn. Th clsr th coffcnt is to ether -1.0 or +1.0, th strngr th assctn btwn varibls; th clsr it is to 0, th weakr th assctn. Note tht th crrltn coffcnt is smtmes erroneusly ntrprtd n trms of causlty. Hwvr, it is th rsrch mthd tht prmts causl nfrnces, not th way n wch th dta r anlyzd or dscrbd. If a tru xprmntl mthd is usd, a rsrchr cn nfr a caus-effct r/s whn th crrltn coffcnt is suffcntly lrg. Hwvr, a lrg coffcnt alon duz not mean tht variblty n one varibl causes varbilty n th othr varibl.
Statistics & Research Design
Correlation And Prediction
Bivariate Techniques
Correlation Coefficients
Coefficient of Determination
Whnvr a crrltn coffcnt rprsnts th dgre of assctn btwn two dfrnt varibl, it cn b squrd 2 obtn a coffcnt of dtrmntn, wch provids a measr of SHARED VARIABILITY. I.e., th squrd crrltn coffcnt ndicats th proprtn of variblty n Y tht is xpland by, or accntd 4 by, variblty in X. E.g., if th crrltn coffcnt 4 sales succss nd prdct knwldg is .60, then 36% (.60 squrd=.36) of variblty n sales succss is accntd 4 by prduct knwldg. Th rmaing 64% is unxplaind variblty, wch mit b du 2 such fctrs as attitud twrd th cmpny, mtvtn to sell, prvius sales xprnc, nd sales teritory.
Statistics & Research Design
Correlation And Prediction
Bivariate Techniques
Correlation Coefficients
Coefficient of Determination
Keep n mind tht a crrltn coffcnt shud b squrd to obtn a measr of shrd varbilty only whn it ndicats th dgre of asscitn btwn two dffrnt varibls. Whn a crrltn coffcnt is a relablty coffcnt, wch is th crrltn of a meas itslf, th coffcnt is NEVER squrd. Nsted, it is ntrprtd dirctly as a meas of "tru scor variblty." Th sbscpt of a crrltn coffcnt ndicats whthr it is a coffcnt 4 two dffrnt varibls or a sngl varibl. If th sbscrpt cntains two dffrnt lttrs or #s (e.g., "xy"), it rprsnts th crltn btwn two dffrnt varibls. Whn th sbscrpt cntans th same lttrs or #s (e.g., "xx"), it is a reliablity coffcnt.
Statistics & Research Design
Correlation And Prediction
Bivariate Techniques
Correlation Coefficients
Hypothesis Testing
Crrltn coffcnts cn b tstd 2 dtrmn if thy r ststcly sgnfcnt by cmprng th obtnd cffcnt 2 th appropriat crtcl valu. Th mgntud of th crtcl valu is dtrmnd by th lvl of sgnfcnc (alpha) nd th smpl sz. Th smllr th smpl, th lrgr th crrltn coffcnt must b to b ststcly sgnfcnt. Eg., whn th lvl of sgnfcnc is .05, nd th # of obsrvtns is 10, th crrltn coffcnt must b at lst .63 to b ststcly sgnfcnt. N cntrst, whn th # of obsrvtns is 50, a crrltn of only .28 is sgnfcnt.
Statistics & Research Design
Correlation And Prediction
Bivariate Techniques
Correlation Coefficients
Regression Analysis
Nvstgtrs r oftn ntrstd n crrltn b/c thr gol is 2 use a prdctor 2 prdct or estmt prfrmnc on a criterion. Regression Analysis is th tchnq tht allws such prdctns 2 b mad. An asumptn undrlyng rgrssn anlysis is tht ther is a linear r/s btwn X nd Y, nd, ther4, tht thr r/s cn b dscrbd by a strght lin. Whn ther is a linear r/s btwn varibls, thr r/s cn b dscrbd by a rgrssn lin (line of best fit). Th tchnq usd to locat th rgrssn lin in a scttrplt rfrd 2 as th lest squrs criterion. It locats th rgrssn lin so tht th amt of error n prdctn is mnmzd. Th rgrrsn lin or its formula (th rgrssn equation) is then usd 2 mk prdctns abt Y bsed on nfo on X. Th dgre of prdctv accurcy whn usng a rgrssn equatn is dirctly rltd 2 th mgntud of th crrltn coffcnt. Unlss th coffcnt is = to +1.0 or -1.0, ther wil b som error n prdctn. Cnsqntly, th std error of estimt is usd 2 cnstrct a cnfdnc ntrvl around a prdctd Y scor so tht th scor is not "ovrntrprtd."
Statistics & Research Design
Correlation And Prediction
Multivariate Techniques: Correltion and Prediction
Multivrite tchnqs r usd 2 asses th dgre of assctn amng 3 or mre varibls nd 2 mak prdctns tht nvolv, at a mnimum, 2 prdctrs nd 1 critrn. Th choic of multivrit tchnq is bsed on svrl fctrs ncludng th scal of msrmnt of th prdctr nd critrn varibls nd th # of critria.
Statistics & Research Design
Correlation And Prediction
Multivariate Techniques: Correltion and Prediction
Multiple Regression
Multpl rgrssn is th apprpriat multivrit tchnq whn 2 or mre cntnus or dscret prdctrs wil b usd 2 prdct status on a sngl cntnus critrn. The use of mltpl rgrssn is bsed on asumptn tht th r/s btwn varibls is lnear (altho adaptns of multpl rgrssn 4 nonlinear r/s r avlbl).
Statistics & Research Design
Correlation And Prediction
Multivariate Techniques: Correltion and Prediction
Multiple Regression
Th outpt of a multpl rgrssn anlys is a multpl crrltn cffcnt nd a multpl rgrssn equtn. Th multpl crrltn coffcnt (R) ndicats th dgre of assctn btwn critrn nd a linear cmbntn of th prdctrs. Lik th crrltn 4 two varibls, R cn b squrd 2 obtn a meas of shrd variblty. Th multpl rgrssn equtn is an xtnsn of th rgrssn equtn nd prmts prdctn of a prsn's scor on th critrn bsed on a linear cmbntn of prsn's scors on th 2 or mre prdctrs. Multipl Rgrssn Equtn is Y=b1x1 + b2x2 + ... + bkxk + a where Y= predicted scor on Y; X= scor in X; b= rgrssn cffcnt; a= y ntrcpt. Th sz of th rgrssn coffcnt (b) for ea prdctr is dtrmnd by cmbntn of th mgntud of th crrltn btwn th prdctr nd th critrn nd th mgntud of th crrltn btwn th prctr nd evry othr prdctr. Th optml situatn (nd th situtn tht ylds th lrgst nd most ezly ntrprtbl rgrssn cffcnts) is for ea prdctr 2 hv a hi crrltn w/ th critrn nd lo crrltns w/ th othr prdctrs. Hi crrltns btwn prdctrs is rfrd 2 as multicollnearity nd is cnsdrd an undsrbl cndtn 4 at least 2 resns. 1st, th prsnc of multicllnrty means tht th prdctrs r prvdng rdundnt nfo. 2nd, whn prdctrs r hily crrltd, th mgntud of a rgrssn cffcnt is not proprtnl to th crrltn btwn prdctr nd critrn, wch maks it dffclt to ntrcpt th rgrssn cffcnt.
Statistics & Research Design
Correlation And Prediction
Multivariate Techniques: Correltion and Prediction Types of Multple Regression
Th most bsic form of mutipl rgrssn is clld simultneus (smpl) rgrssn nd ntails anlzng th effcts of all of th prdctrs on th critrn at onc. Anthr form is stpws rgrssn, wch cn b ethr "frwrd" or "bckwrd." N frwrd (stp-up) rgrssn, one prdctr is aded n ea sbsqnt anlys; n bckwrd (stp-dwn) rgrssn, th anlys bgns w/all prdcts nd one prdctr is elmintd n ea sbsqnt anlys. Th gol of stpws rgrssn is 2 xplain th grtst amt of variblty n th critrn usng th fwst # of prdctrs. Whn usng ths mthd, th dcsn 2 ad or sbtrct a prdctr is bsed on th rsltng chng n th sz of R-squrd.
Statistics & Research Design
Correlation And Prediction
Multivariate Techniques: Correltion and Prediction Multiple Rgrssn v. ANOVA
Mltpl rgrssn is ncresngly bng usd n plc of ANOVA. Mltpl rgrssn is prtculry usfl whn grps r uneql n sz snc ths cndtn cn rduc bth th pwr nd th rbstnss of th anova. It is usfl whn th IVs r measrs on a cntnus scal b/c, n ths cse, th anova requrs th cntnus dta 2 b cnvrtd to ctgres, wch als reducs pwr. Anthr advntg of multpl rgrssn ovr th anova is tht it prmts a rsrchr 2 ad or sbtrct IVs (prdctrs) 2 th anlys to dtrmn wch sbset of varibls bst xplans variblty n th DV (critrn).
Statistics & Research Design
Correlation And Prediction
Multivariate Techniques: Correltion and Prediction Cross-Validation
Whnvr a mltipl crrltn cffcnt nd mltpl rgrssn equtn r crss-vldtd (tried out) on a smpl, th sz of th crrltn cffcnt tnds 2 "shrnk" nd th prdctv accrcy of th rgrssn equtn dcreses. SHRINKAGE ocurs b/c th rgrssn weights, wch r usd n th clcutns of R as wel as n th rgrssn equtn, wer drivd from th orgnl smpl nd do nt "fit" th new smpl as wel snc th sam chnc fctrs oprtng n th orgnl smpl r not prsnt n th sbsqnt smpls. Shrinkage is th grtst whn th orgnl was smll nd th # of prdctrs is lrg.
Statistics & Research Design
Correlation And Prediction
Multivariate Techniques: Correltion and Prediction Canonical Correlation
Canonicl Crrltn is an xtnsn of mltpl rgrssn tht is usd whn 2 or mre cntnus prdctrs r to b usd 2 prdct status on 2 or mre cntnus critria. Canonicl crrltn wud b th aproprit tchnq if rsrch wnts to use measrs of ntrprsnl assrtvnss, atitud twrd cmpny, nd prevus xprinc to prdct status on svrl dffrnt measrs of jb prfrmnc such as yrly sals, # of new cstmrs, nd lvls of cstmr stsfctn. Canonicl crrltn cn als b mplyd 2 ID th # nd natur of th undrlyng dmnsns tht accnt 4 th crrltn btwn two sets of varibls.
Statistics & Research Design
Correlation And Prediction
Multivariate Techniques: Correltion and Prediction Discriminant Function Analysis
Dscrmnt fnctn anlys is th aproprit tchnq whn two or mre cntinus prdctrs wil b usd 2 prdct or est a prsn's status on a sngl dscret (nominal) critrn. dscrmnt anlys cud b usd if svrl measrs r to b usd 2 prdct whthr sals applcnts wil blong 2 th "scssfl salsprsn" or "unscssful salsprsn" grp aftr prsn is hired. Th accurcy of a dscrmnt anlys is oftn measrd by dtrmng th hit rate, wch is th proportn of cses tht r crrctly clssfd.
Statistics & Research Design
Correlation And Prediction
Multivariate Techniques: Correltion and Prediction
Logistic Regresion
Logstc rgrssn is simlr 2 dscrmnt anlys nd is usd to prdct status on a sngl dscret critrn usng two or mre cntinus or dscret prdctrs. N cntrst 2 dscrmnt anlys, wch rquirs th r/s btwn varible 2 b linear, lgstc rgrssn asums tht th r/s r nonlinear. Lgstc rgrsn wud b aproprit if ntrprsnl assrtvnss hs a curvilinear r/s w/sals succss; i.e., if mdrte lvls of assrtvnss r chrctrstc of succssfl salspeop, whl lo nd hi lvls of assrtvnss r chrctrstc of unsccssfl salspeop. As n mltpl rgrssn, lgstc rgrssn cn nvolv assng th effcts of all prdctrs simultanusly or cn ntail adng or sbtrctng one prdctr at a time.
Statistics & Research Design
Correlation And Prediction
Multivariate Techniques: Causal Modeling
Svrl mltivrit tchnq hv bn dvlpd spcfcly 2 tst a predfnd causl modl or thry. lik othr crrltn tchnqs, thes tchnqs cnnt pruv causlty bt, n cntrst 2 thos tchnqs, thy cn prvid nvstgtrs w/som evdnc tht thr causl thry or modl is crrct or ncrrct. Thes tchnqs r clld causl (structual equation) modlng tchnqs, nd thy nclud path analysis nd LISREL.
Statistics & Research Design
Correlation And Prediction
Multivariate Techniques: Path Analysis
Pth Anlys cn b cnsdrd an xtnsn of mltpl rgrssn. It nvolvs trnsltng a thry abt causl r/s amng a set of varibls n2 a path diagrm, cllctng dta on th varibls, nd usng th dta 2 deriv path cffcnts (rgrssn cffcnts), wch ndicat th drctn nd strnght of th r/s btwn pairs of vribls. If th pttrn of cffcnts is cnsistnt w/wht is prdctd by th thry, th anlys prvids spprt 4 th thry. One rstrctn whn usng th pth anlys is tht all pths must b recursiv, tht is, thy must nvol only a one-way causal flow.
Statistics & Research Design
Correlation And Prediction
Multivariate Techniques: LISREL
LISREL (linear structual relations analysis) is mre cmplx thn pth anlys nd cn b usd whn a causl modl ncluds recursiv (one-way) nd nonrecursv (two-way) paths. Lik pth anlys, LISREL xamns th r/s btwn obsrvbl (measurd) varibls, but it als taks n2 accnt th latent traits thos varibls r blevd 2 measr nd th effcts of msmnt error.