2. INTRODUCING VARIABLES AND UNDERSTANDING THEIR LEVELS OF MEASUREMENT

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1 2. INRODUCING VARIABLES AND UNDERSANDING HEIR LEVELS OF MEASUREMEN Dr om Clark & Dr Liam Fostr Dpartmnt of Sociological Studis Univrsity of Shffild

2 CONENS 2. Introducing and undrstanding variabls Rcording data numrically Rcoding variabls pag 2 pag 8 hinking critically about variabls pag 10 minal lvls of masurmnt Idntifying lvls of masurmnt Lablling variabls Ordinal lvls of masurmnt Intrval (and ratio) lvls of masurmnt pag 2 pag 4 pag 7 Lvls of masurmnt flow diagram Why do I hav to b abl to idntify lvls of masurmnt? pag 9 pag 10 pag 10 Rsarch qustions, hypothss, and variabls Rounding up pag 11 pag 14 pag 15 *Within qualitativ worlds, thr ar diffrnt ways of rcording data about our social livs. W may us visual matrial in th form of picturs, oral tstimony in th form of intrviws, or thick dscription in our thnographis. All of ths forms hlp us to rsarch social action and all hav particular advantags and disadvantags Rcording data numrically Equally, not all quantitativ data is th sam and hr ar diffrnt ways in which w can rcord quantitativ matrial in ordr to xplor our social worlds and answr our rsarch qustions. W may wish to simply count somthing; w might want to think of masuring an attitud on som sort of scal; or w might vn attmpt to spcify whr somthing lis with rspct to an stablishd format lik, for instanc, th amount of mony somon arns in an hour. Any attmpt to masur somthing quantitativly can b similar, or diffrnt, to anothr attmpt to captur data. Indd, all typs of quantitativ data can b dividd into particular lvls of masurmnt and ths lvls hav diffrnt tchniqus of analysis associatd with thm. How you summaris data is ntirly dpndnt on th lvl of data that you hav. his is, ssntially, why it is so important to b abl to rcognis th lvl at which data is bing masurd. his workbook will introduc you th diffrnt ways in which w can rcord quantitativ matrial. By th nd of th workbook you should b abl to: Idntify diffrnt lvls of masurmnt B abl to construct variabls at an appropriat lvl hink critically in rlation to variabl masurmnt Undrstand th rol of a variabl with rspct to your rsarch aims and objctivs, and your hypothss 2.2. Undrstanding quantitativ variabls: Idntifying lvls of masurmnt Look at ths xampls: 2.1. Do you smok cigartts? Ys 2.2. Do you considr yourslf to b a: non-smokr mdium smokr Each of ths closd qustions rprsnts somthing - a variabl - w might b intrstd in. In this cas it is smoking bhaviour. Howvr, whilst all of ths variabls ar concrnd with smoking, thy ar rcording th information in subtly diffrnt ways. hs diffrnt ways of rcording quantitativ data ar mor commonly known as lvls of masurmnt. hr ar thr main lvls of masurmnt: nominal, ordinal, and intrval. W shall dal with ach in turn minal lvls of masurmnt Look again at th first qustion. light-smokr havy smokr 2.3. How many cigartts hav you smokd in th last svn days? (writ hr) 2.1. Do you smok cigartts? Ys 1. 2.

3 Hr, th qustion constructs a catgory btwn cigartt smokrs on on hand, and non-cigartt smokrs on th othr. It assums that all popl can b dividd into two sparat groups. In this particular cas, you ar ithr a cigartt smokr or you ar not. hr is no middl ground you ar ithr on or th othr. Whn you ar daling with variabls that masur catgoris such as ths, you ar daling with a variabl that is oprating at a nominal lvl of masurmnt. minal simply mans nam. It is, howvr, worth noting that nominal variabls ar also somtims calld catgorical variabls bcaus thy masur distinct catgoris. Confusingly prhaps, whilst all nominal variabls ar catgorical, not all catgorical variabls ar nominal as catgorical can also b applid to ordinal variabls too but w ll dal with thos in a minut. Although this particular smoking variabl is a binary catgory you ar ithr a smokr or you ar not not all nominal variabls ar binary. Ethnicity, marital status, nationality, gographical location, and occupation ar all commonly usd forms of nominal data. Class is also somtims tratd as a nominal variabl. Hr is an xampl of a variabl that is masurd at th nominal lvl: thnicity. It was includd in th 2011 cnsus (ONS, 2012): 2.4. What is your thnic group? Choos on sction from A to E, thn tick on box to bst dscrib your thnic group or background A. Whit English / Wlsh / Scottish / rthrn Irish / British Irish Gypsy or Irish ravllr Any othr background, writ in: B. Mixd / Multipl thnic groups Whit and Black Caribban Whit and Black African Whit and Asian Any othr Mixd / multipl thnic background, writ in: C. Asian / Asian British Indian Pakistani Bangladshi Chins Any othr background, writ in: D. Black / African / Caribban / Black British African Caribban Any othr Black / African / Caribban background, writ in: E. Othr thnic group Arab Any othr thnic group, writ in: tic th instruction at th start: Choos on sction from A to E, thn tick on box to bst dscrib your thnic group or background. You ar ithr in group A, B, C, D, or E thr is no sliding scal btwn Whit, Mixd, Asian, Black, or Othr. Onc you hav dcidd which catgory you ar in, you now hav to tick which sub-st of that catgory you blong to. Again thr is no sliding scal btwn th catgoris and thy ar mutually xclusiv thy don t bld into ach othr. Lt us suppos that I m intrstd in xploring th rlationship btwn marital status and monysaving bhaviour. I would first nd to construct a nominal variabl that masurs marital status. Rmmbr, vryon who answrs a qustion that is masurd at th nominal lvl has to b abl answr it th rang of answrs nds to covr vry possibility. ry to construct a variabl at th nominal lvl for marital status mak sur that th rang of your answrs covrs vry possibility. his is how marital status was masurd in th British Social Attituds Survy in 2007: 2.5. Can I just chck, which of ths applis to you at prsnt? Plas choos th first on th list that applis: Marrid In a civil partnrship Living with a partnr Sparatd (aftr bing marrid) Divorcd Widowd Singl (nvr marrid) (Don t know) (t answrd) his qustion is actually dsignd to b rad aloud by th intrviwr. What is important to rcognis, howvr, is that all possibilitis ar covrd: vrybody who rsponds to th qustionnair will fall into on of ths catgoris. w w nd to dsign a variabl that will allow us to assss mony-saving bhaviour: w dcid to masur this at th nominal lvl. Construct a variabl at th nominal lvl for mony-saving bhaviour. It might look somthing lik this: 2.6. Do you sav mony on a rgular basis? Of cours, w could masur mony-saving bhaviour in a slightly diffrnt mannr. W might just ask how much popl sav on a wkly basis. Howvr, such a masurmnt would not b at th nominal lvl. W now hav all our variabls that will nabl us to answr our rsarch qustion. Ys Howvr, bfor w clbrat our nwly discovrd knowldg by actually conducting a survy with ths variabls, in which ordr do you think ths variabls should b prsntd within a survy? Wll, th answr dos dpnd on a fw things. If w ar only intrstd in masuring ths variabls and our projct is vry small, thn w don t rally hav to worry about it as thr ar only two qustions. Howvr, if this is just on rsarch qustion of many concrning financial habits thn it is oftn good practic to put th marital status variabl with othr so-calld dmographic variabls such as gndr, social class, thnicity, rligious prsuasion tc, tc. Dmography ssntially mans th masurmnt of popl. Dmographic variabls ar usually takn to b quit gnral variabls that dscrib th various catgoris that a prson has and many ar nominal in natur 1. It is oftn usful to plac such variabls toward th start of a qustionnair as thy ar asy to answr and oftn allow th rspondnt to gt th fl of th qustions. Mor substantiv variabls, that is variabls that covr mor spcific or spcialist topics such as th saving status on that w constructd abov, tnd to com latr in th qustionnair as thy can rquir a littl mor thought and can somtims rquir som rapport with th rspondnt. his rapport is oftn dvlopd by placing th asy qustions first Ordinal lvls of masurmnt Look again at th 2.2. from our smoking xampl: 2.2. Do you considr yourslf to b a: n-smokr Mdium smokr Light-smokr Havy smokr Lik 1, this qustion is still concrnd with smoking but it is a littl mor rfind as it suggsts thr is som sort of ordr to th answr. It is still possibl to divid popl into non-smokrs and smokrs, but th qustion gts a littl mor spcific about how thy prciv what typ of smokr (or not) thy actually ar. Unlik 2.1, thr is som middl ground. h world is no longr bing rducd to smokrs and non-smokrs, and instad thr is som room for shading btwn thos catgoris. Aftr all, som popl might considr thmslvs to smok only in spcific circumstancs,whilst othrs might considr thmslvs to b chain smokrs. 1 It s worth noting that ag, common to dmographic masurmnts, is an outlir in this rspct and is not a nominal variabl

4 Howvr, whilst thr is a scal hr, it is non spcific and thr is a lot of room for intrprtation: th catgoris ar not nat and wll boundd. What havy smoking mans for on prson, may b light smoking for anothr. In this sns, th distancs btwn th points on th scal ar not qual or wll dfind. Ordinal variabls can also b usd to group togthr counts of things. For instanc th following scal, also a smoking variabl, is also constructd on an ordinal scal:.2.2a. How many cigartts do you smok a day? tic how th rang btwn ach point is not qual. h first point covrs 18 possibilitis, but th scond only 12, th third just 10 and th final point is unlimitd. Can you think of any particular rason why th answrs ar groupd in this mannr? Without any clar rational for constructing th rang of answrs lik this, data in this format probably would not b usful th catgoris ar rlativly maninglss as thy ar built upon nothing but guss work. A much bttr way of constructing this particular qustion would b to find som prcdnc within th litratur. How might you do this? A good option is to map our rangs onto ons that ar standard within variabls of this typ. On potntial option is to us currnt undrstandings of havy smoking. Whilst thr is no univrsally accptd dfinition for havy smoking, thr is som accptanc within th mdical litratur that mor than 10 pr day is havy. Som studis hav masurd 1-9 cigartts pr day as modrat smoking, and lss than that as light. Using this rational, a bttr qustion might b:.2.2b. How many cigartts do you smok a day? I nvr smok Lss than on pr day h possibl rang of rspons now corrsponds with mor standardisd dfinitions of non-smokr, light smokr, modrat smokr, and havy smokr. Howvr, th valus btwn th scals ar still unqual. Hnc, this is still an ordinal variabl, but now it has a firmr mthodological justification. his is not to say that ordinal scals hav to hav som thortical basis. Indd, othr variabls that mploy an ordinal scal will simply group counts qually as it is an asy way to summaris widranging data. Many ag variabls, for instanc, will appar in formats lik blow:.2.7. Plas stat your ag: Ordinal scals ar not, howvr, only suitabl for prcptions of bhaviour, aggrgatd counts or othr forms of ordrd data. Indd, on of th most popular uss of th ordinal scal is to mploy it to masur attituds. A popular vrsion of this sub-typ of ordinal scal is calld a Likrt scal. Namd aftr th psychologist who invntd it, Rnsis Likrt, a Likrt scal is a sris of rating scals on which rspondnts spcify thir blifs, attituds, or flings about a particular topic or issu. ypically, Likrt scals nabl th rspondnt to numrically xprss th strngth of fling with rspct to a spcific statmnt or qustion topic. Multipl masurmnts mad on scals ar usually bipolar in dsign in that thy ar constructd around two polar opposits with a numbr of points inbtwn. Howvr, th numbr of points on a Likrt itm dos vary and 3 point, 5 point, 7 point, and vn 10 point scals ar popular. Indd, vn numbrd scals ar possibl if th rsarchr wants to forc a choic in situations whr a nutral option is undsirabl. chnically, Likrt scals ar usd to summaris a rang of rsponss across a sris of variabls so that an undrlying attitud can b assssd. Howvr, sinc its introduction th maning has loosnd and it is now oftn usd to rfr to a sris of singl unconnctd itms. Whn usd in this singular format, th qustion is oftn bttr rfrrd to as Likrt itm or a Likrt-typ variabl. Look at ths xampls of Likrt itms takn from th last wav of th British Houshold Survy 2 - again, it is a qustion that is rad aloud by an intrviwr: 2.8. Plas look at th card and tll m how much you agr or disagr with th following statmnts? A. It taks too much tim and ffort to do things that ar nvironmntally frindly: Nithr agr Strongly agr Agr nor disagr Disagr Strongly disagr B. Scintists will find a solution to global warming without popl having to mak big changs to thir lifstyl: Nithr agr Strongly agr Agr nor disagr Disagr Strongly disagr C. h nvironmnt is a low priority for m compard with a lot of othr things in my lif: Nithr agr Strongly agr Agr nor disagr Disagr Strongly disagr D. I am nvironmntally frindly in most things that I do: Nithr agr Strongly agr Agr nor disagr Disagr Strongly disagr In ach of ths variabls, attitud toward an aspct of nvironmntal frindlinss is bing masurd on a fiv point Likrt scal. Howvr, ach itm is masuring a slightly diffrnt aspct of nvironmntal frindlinss. h first is masuring th prcivd cost of ngaging in nvironmntally frindly bhaviour; th scond xplors th prcivd locus of control with rspct to th solutions for nvironmntal problms; th third asssss th priority of nvironmntally frindly bhaviour against gnralisd goals; and, th final masur is xamining th prcption of slf with rspct to bing nvironmntally frindly. h itms could b usd as singl masurs, or takn collctivly to masur gnral attitud to nvironmntal frindlinss. Howvr, if you wr to tak ths variabls as bing indicativ of an undrlying attitud towards nvironmntal frindlinss, you also nd to not that th wight of th statmnt is not th sam for all four qustions: it s not quit as asy as adding up th rlativ answrs and dividing by th numbr of obsrvations to gt th avrag. In th first thr variabls, th mphasis is on agring with statmnts that ar broadly ngativ towards nvironmntally frindly bhaviour. In th fourth, agrmnt is broadly positiv. Indd, it is important to rcognis th dirction of masurmnt: agrmnt dos not always man th sam thing. If you wr to us ths variabls collctivly as a Likrt scal, it is also important to rcognis that th diffrnc btwn ach point is opn to intrprtation: what is th distanc btwn Strongly Agr and Agr? h answr will largly dpnd on individual prcption and th points on th scal ar not clar and continuous. As a rsult, thy should b takn to b qual in natur: this is xactly why a Likrt scal is ordinal in dsign. 2 S

5 It is worth noting, howvr, that thr is som discussion amongst statisticians and social rsarchrs concrning whthr Likrt scals should b tratd at th ordinal or intrval lvl. It is actually common practic, particularly in aras of psychomtrics, to trat Likrt-basd attitud masurs at th intrval lvl particularly whn multipl itms ar usd in conjunction with on anothr. his is an important issu to rcognis bcaus th appropriat dscriptiv and infrntial tchniqus usd to analys quantitativ data diffr btwn ordinal and intrval variabls. If th wrong statistical tchniqu is usd, th rsarchr incrass th chanc of coming to th wrong conclusion about th significanc (or othrwis) of thir findings. So, until you ar abl to clarly justify why you want to us a Likrt scal at th intrval lvl, it is bst to rr on th sid of caution and trat ths masurs at th ordinal lvl. Look at th xampls from th British Houshold Survy abov. Lt us suppos that I want to masur th xtnt to which rspondnts think that popl who havn t paid any taxs should not rciv any bnfits construct an ordinal variabl that would allow you to do this. his is how it was masurd in th British Social Attituds Survy in 2007 (BSA, 2008): h govrnmnt raiss mony through taxation to pay for social bnfits lik th stat pnsion, unmploymnt bnfits and sicknss bnfits. How much do you agr or disagr with ach of th statmnts blow about social bnfits lik ths?.2.9. Popl who havn t paid taxs should not b ntitld to any bnfits: A. Agr Strongly B. Agr C. Nithr agr nor disagr D. Disagr E. Disagr strongly F. Can t choos As you can s, somtims Likrt-typ ordinal scals mploy th us of short vigntts, prompts, or cus to contxtualis th issu at hand. his mthod is particularly appropriat to mploy whr thr might b som misundrstanding about what is bing askd of th rspondnt. Likrt scals also nd not b numbrd within a survy or qustionnair. In th st of qustions at 8, for xampl, numbrs ar includd; in 9, thy ar not. Howvr, it should always b possibl to put th points on a numrical scal if you so wish latr on. In th cas of this particular variabl, it would b rlativly asy to altr th lttrs so thy rflctd a numrical scal of 1 to 5. h final catgory Can t Choos would not b on th scal, and would instad srv as a count of thos popl who wr unabl to offr an answr Intrval (and ratio) lvls of masurmnt Lt us go back to th third qustion it is yt mor spcific than th first two smoking variabl w saw How many cigartts hav you smokd in th last svn days? (writ hr) his is an xampl of an intrval variabl. An intrval variabl is similar to an ordinal variabl, xcpt that th intrvals btwn th valus of th intrval variabl ar qually spacd and th gaps btwn ach point ar clar, consistnt, and continuous. In th abov xampl, th diffrnc btwn on cigartt and two cigartts is th sam as it is btwn fiv and six th gap btwn ach masur is always th sam. o rpat, whr thr is no room for individual intrprtation btwn ach point on a scal, and th distanc btwn points ar qual, thn it is likly that you ar daling with an intrval masur. Lt us suppos that I m intrstd in th amount of hours young popl work. Construct a variabl at th intrval lvl that will hlp you to do this. his is how it was don in th British Houshold Panl Survy for Young Popl (Wav 17) How many hours paid work did you do last wk? If you hav mor than on job plas writ in th total hours you workd at all of thm. Writ in hours: Howvr, not all intrval variabls ar th sam. A ratio variabl has all th proprtis of an intrval variabl, but also has a clar dfinition of 0. Ag, for instanc, has a logical 0 point and is a ratio variabl. Indd, lik th xampl abov, most intrval lvl variabls within social statistics ar actually also ratio variabls. In fact, I can t actually think of on that you ar likly to com across in social rsarch that isn t, but many txtbooks will still mntion it. Howvr, tmpratur is a good xampl of an intrval variabl that isn t a ratio variabl th 0 on th Clsius tmpratur scal is arbitrary. Although it is basd on th frzing point of watr, th 0 point could just as asily b basd on th frzing point of alcohol. In any cas, you ar unlikly to us this in social rsarch. Strictly spaking, intrval masurs ar not that common in social rsarch as thr ar not many social phnomna that tak intrval form. Itms lik incom ar usually th xcption rathr than th rul. Whr thy ar usd, thy tnd to b constructd from multipl masurs, as is th cas with psychomtric intllignc tsts. As prviously statd, som rsarchrs do occasionally us ordinal lvl data as if it wr intrval lvl data, but this should only b don with xtrm caution Rcoding variabls Although variabls masurd at th intrval lvl ar oftn considrd th bst form of data - mainly bcaus thy ar th most rfind - somtims w may want to rcod intrval data into ordinal data, or vn nominal data. Can you think of a rason why would w want to rcod a variabl? into ordinal or vn catgorical ons. For instanc, although Ag in yars is a ratio variabl, it is oftn rcodd into an ordinal variabl with six catgoris as follows: 0-15 = = = = = 5 ovr 75 = 6 hr ar many ways of rcording th ag variabl and intrval lvl data can vn b rcodd into a nominal lvl data. For instanc, if you wr intrstd in diffrncs in attitud towards ngaging with nvironmntally frindly bhaviour (s 8) btwn thos of working ag and thos of rtirmnt ag it would b a rlativly straight-forward job to aggrgat all thos btwn 16 and 64, and thos who wr 65+. Rcoding variabls oftn hlps you to s pattrns and trnds in your data mor asily bcaus you ar intrprting a smallr numbr of catgoris. In som cass, particularly whr you ar trying to mploy infrntial statistics, you may vn find yourslf having to rcod a variabl bcaus th data fails to satisfy an assumption of th tchniqus you ar attmpting to mploy. Howvr, do this with car. Rcodd data is lss and lss rfind and you invitably los th snsitivity of your data to idntify smallr diffrncs and similaritis. It s oftn asir to s pattrns in our data whn w us lumpir catgoris - hnc somtims it is a good ida to rcod intrval/ratio lvl variabls 7. 8.

6 2.3. Idntifying lvls of masurmnt You should now b abl to idntify th lvls of masurmnt for any particular variabl. ry to idntify th lvl of masurmnt for ach of ths variabls takn from th British Social Attituds Slf Compltion ustionnair How many journys of lss than two mils do you mak by car in a typical wk? Plas writ in: How much do you agr or disagr with ach of ths statmnts? A. A lot of fals bnfit claims ar a rsult of confusion rathr than dishonsty: Nithr agr Strongly agr Agr nor disagr Disagr Strongly disagr is an intrval variabl 2.12A. and 2.12B. ar ordinal variabls 2.13 is a nominal variabl 2.14A and 2.14B ar ordinal variabls 2.15 is an ordinal variabl Lvls of masurmnt flow diagram If you ar still having troubl undrstanding which lvl of masurmnt is which, th following flow chart should hlp you to idntify what particular lvls of masurmnt your variabls ar. Dos th answr rquir you to tick a box? (or us a ky) Ys Why do I hav to b abl to idntify lvls of masurmnt? You nd to b abl to tll th diffrnc btwn a scrwdrivr, a hammr and a spannr if you ar to fix a brokn pip or build a wall. Diffrnt tools always do diffrnt jobs. h sam is tru with statistics; you nd to b abl to idntify and us th right lvl of masurmnt bcaus th appropriat dscriptiv and infrntial statistical mthods that you will us to analys your data will diffr for nominal, ordinal and intrval variabls. If you us th wrong tool to fix your pip, th chancs ar that you won t b abl to fix your pip and you will com to th conclusion that you nd a nw on. But this would b th wrong conclusion to mak. Equally, if you us th wrong statistical tchniqu th liklihood is that you will com to th wrong conclusion about your findings. Your ability to invstigat your hypothsis, and subsquntly achiv your rsarch aim, will b svrly limitd. B. h rason that som popl on bnfit chat th systm is that thy don t gt nough to liv on: Nithr agr Strongly agr Agr nor disagr Disagr Strongly disagr Which is it mor important for th Govrnmnt to do? PLEASE SELEC ONE ANSWER ONLY o gt popl to claim bnfits to which thy ar ntitld OR o stop popl claiming bnfits to which thy ar not ntitld OR Can t choos 2.14a. Considr this situation: a prson in work taks on an xtra wknd job and is paid in cash. H dos not dclar it for tax and so is 500 in pockt. Do you fl this is right or wrong? A. t wrong B. A bit wrong C. Wrong D. Sriously wrong E. Can t choos 2.14b. Considr this situation: and how likly do you think it is that you would do this if you found yourslf in this situation? A. Vry likly B. Fairly likly C. t vry likly D. t at all likly E. Can t choos Is thr a scal of thr or mor possibl answrs? Ys minal: if th catgoris ar xclusiv, that is thr ar no maningful midpoints, thn th masurmnt is nominal. Ordinal: if you can maningfully rank catgoris in a linar fashion thn th masurmnt is ordinal. Intrval: dos th masurmnt also hav a univrsal zro point? (for xampl, stopwatch masurmnts do, tmpratur dos not). Ys Ratio: if th zro point is fixd and rlativly prmannt, thn th intrval masurmnt can also b considrd to a ratio masurmnt (if not, it is just an intrval variabl). For instanc, it would not mak sns to calculat an avrag thnicity. his is bcaus thr is no intrinsic ordring of th lvls of th catgoris thr is no mid-point. W could say which particular thnic group is most or last common, for xampl, or w could work out th proportion of popl in ach particular group, but w could not talk about a maningful avrag. W ll dal with ths statistical tchniqus in mor dtail latr, but for now w will concntrat on anothr rason that it is important to idntify and undrstand lvls of masurmnt. W nd to b abl to think critically about what a variabl is actually masuring w nd to hav an ida of how to assss its rliability and its validity hinking critically about variabls Validity and rliability Broadly spaking, th validity of a variabl rfrs to th ability of th variabl to masur what it suggsts it is masuring. On th othr hand, th rliability of a variabl rfrs to its stability and its consistncy. hinking critically about th rliability and validity of a variabl is crucial in assssing how good our answr to our rsarch qustion is, and whthr w hav actually achivd our rsarch aims. hink about it: if a variabl is not masuring th thing it

7 is supposd to thn it is not a good masur of that thing. Similarly, if our masurmnt of that thing varis wildly ach tim you masur it, thn w will struggl to say anything maningful about it bcaus by th tim w hav masurd it, th answr will hav changd. hrfor validity and rliability ar crucial to undrstanding th usfulnss of a variabl. Of cours, w can t xhaust th rang of potntial problms with all variabls hr - thr ar simply too many variabls to do this - but w will dmonstrat how you can think critically about th validity and rliability of variabls, and why it is important to do so Lablling variabls On way of thinking critically about th validity of a variabl is to b vry spcific about what a variabl is doing whn w labl it. h mor spcific w ar about what a variabl is actually doing, th lss likly w ar to go byond what that variabl is actually tlling us. Lt s go back to th original smoking xampls Do you smok cigartts? Ys 2.2. Do you considr yourslf to b a: n-smokr Mdium smokr Light-smokr Havy smokr 2.3. How many cigartts hav you smokd in th last svn days? (writ hr) h tmptation might b to labl ths variabls: smoking status; lvl of smoking; amount of smoking. Howvr, ths labls ar not ncssarily valid. h first thing to not is that thy ar all slf-rportd masurs. hat is, thy dal with prcivd smoking bhaviour not th actual bhaviour. Prcivd smoking bhaviour is not always a rliabl prdictor of actual smoking bhaviour. Indd, thr is a good dal of vidnc to suggst that risky bhaviours ar commonly undr-rportd in survy qustions of this typ. hrfor, for us to b abl to say that rportd masurs accuratly rflct th actual numbr of cigartt smokd, thr assumptions would nd to b mt. Firstly, that popl can rcognis and intrprt thir bhaviour maningfully and consistntly; scondly, that thos intrprtations can b maningfully and consistntly mappd on to th masurs w hav built; and thirdly, that rspondnts will choos to rprsnt thir intrprtations as accuratly as is possibl. Can w say this with confidnc? It s actually fairly asy to qustion all ths assumptions. For th first assumption - do popl rcognis and intrprt thir bhaviour maningfully and consistntly - how many popl do you know who smok whn thy drink alcohol and still considr thmslvs to b non-smokrs? What about popl who only smok cannabis? What about popl who sm to b in a constant cycl of trying to giv up and giving up - how long dos it tak bfor you can actually class yourslf as actually givn up? For th scond assumption - can th intrprtations b mappd maningfully and consistntly on to th masurs w hav built - what actually constituts a mdium smokr? If w askd th qustion again two wks latr, would thy rspond th sam? For that mattr what counts as a cigartt? For th final assumption - do rspondnts choos to rprsnt thir intrprtations as accuratly as is possibl - ar popl rally going to admit to thir smoking lvls or ar thy likly to undr-stimat it? Bsids, don t smoking lvls vary from wk to wk? his final difficulty is basically a problm of rliability - can w rally infr accurat lvls of smoking from on masur at on particular point in tim? his might sm to b a littl pdantic, and prcivd lvls of bhaviour can somtims b good prdictors of actual bhaviours, howvr, masurs that dal with social bhaviour ar oftn much mor pron to problms of rliability and validity than thir natural countrparts - a rd blood cll dos not ract to th fact that it is bing countd but a prson might. hink about th diffrnc btwn ths two statmnts: 57% of Univrsity of Shffild studnts smok lss than 10 cigartts a wk. 57% of Univrsity of Shffild studnts in th prsnt sampl rportd that thy smokd lss than 10 cigartts a wk. h diffrnc is subtl, but th inclusion of rportd and th prsnt sampl in th scond cas is important. Accurat naming of variabls can hlp you to avoid making spurious statmnts of fact with imprssiv numbrs to match this is all too asily don whn rporting statistical data. Whnvr you s statmnts such as ths two xampls, you nd to b asking th qustions: how is that variabl bing masurd? and dos that variabl allow us to com to that conclusion scurly? As a rsult of all of this, it is probably bttr to nam our thr variabls: slf-rportd smoking status; prcivd lvl of smoking; stimatd lvl of cigartts smokd pr wk. Howvr, it is not just th lablling of variabls that you nd to b awar of whn working with variabls. Having a critical undrstanding of any potntial problms of masuring that variabl is also crucial. Lt s look again at th thnicity qustion that has bn proposd for th 2011 cnsus on th nxt pag. Lt us rturn to th validity assumptions w suggstd abov: Is our sampl likly to rcognis and intrprt thir bhaviour maningfully and consistntly? Can thos intrprtations b maningfully and consistntly mappd on to th masurs w hav built? Will th rspondnts choos to rprsnt thir intrprtations as accuratly possibl? ak ach assumption and think about it in rlation to th thnicity qustion that was askd in th UK Cnsus of 2011: Can you idntify any problms? 2.4. What is your thnic group? Choos on sction from A to E, thn tick on box to bst dscrib your thnic group or background A. Whit English / Wlsh / Scottish / rthrn Irish / British Irish Gypsy or Irish ravllr Any othr background, writ in: B. Mixd / Multipl thnic groups Whit and Black Caribban Whit and Black African Whit and Asian Any othr Mixd / multipl thnic background, writ in: C. Asian / Asian British Indian Pakistani Bangladshi Chins Any othr background, writ in: D. Black / African / Caribban / Black British African Caribban Any othr Black / African / Caribban background, writ in: E. Othr thnic group Arab Any othr thnic group, writ in: Ethnicity is not a fixd or natural catgory: it is a social on that nds to b undrstood in rlation to its contxt - it is crtainly not as rigid as this qustion might suggst. In answr to th first qustion, th catgoris prsum that thnicity is largly rlatd to a stabl and linar lin of ancstral origin. hat is crtainly part of th answr, but thnicity is much richr - and mor complicatd - than this. Look again at catgory C Asian / British Asian. Hr w hav a tick box for th catgory Indian. As you may know, India is a hug country, with many distinct rgions that hav vry distinct traditions. Similarly, immigration from India to Britain has bn on-going sinc at last th 18th cntury and has historically bn comprisd of a divrs rang of popl including princs, srvants, studnts, samn, doctors, and prformrs. Whilst som ar rlativly rcnt arrivals, som hav livd in th UK for ovr four gnrations. Furthr still, whilst rcnt immigration has bn comprisd of conomic migrants who cam to work in th burgoning manufacturing trad, many ar actually profssionally qualifid political immigrants

8 who cam via East Africa in th 1960 s and 1970 s. Howvr, this thnicity qustion ignors all of th potntial diffrnc within groups and largly lumps vryon togthr in a sris of homognous groups. Indd, it is not hard to qustion how this masur can adquatly rprsnt all th potntial diffrnc in an incrasingly globalisd world. In answr to our scond and third assumptions, w could also qustion whthr popl will accuratly rprsnt this information. Many xcludd groups - which includs som thnic groups - hav a particularly high rat of non-rspons in th cnsus. In fact, a pilot thnicity qustion that was administrd in th 1979 cnsus mt with such hostility, th qustion was rmovd from th 1981 cnsus. Although th qustion mt much lss rsistanc in 1991, som popl still rfusd to answr it, or simply couldn t. hink about th various mixd thnicitis w can crat. Imagin somon born in Britain from a first gnration Indian mothr (by way of Uganda) and a scond gnration fathr of mixd Whit and Black Caribban hritag - whr would thy fit? Of cours, not all data is of th slf-rportd typ, and this is not to say slf-rportd masurs ar uslss far from it but any variabl is a pragmatic solution to difficult problms of masurmnt. W hav to masur social phnomna somhow, and whilst ths masurmnts might not b prfct thy ar oftn th bst w can manag givn th circumstancs. h qustion for thnicity was, in part, dsignd to valuat th 1978 Rac Rlations Act and it dos allow us to s gnral pattrns of inquality across th country. It is a problmatic variabl, but it is also a potntially usful on if w rcognis its limitations. W ar not trying to put you off using variabls lik ths in your rsarch, but you nd to b awar of any potntial issus/ limitations with variabls you choos and th possibl impact that this could hav on your rsarch Rsarch qustions, hypothss, and variabls: Working xampls Variabls and rsarch qustions and hypothss ar a lot lik th cogs in a machin. h cogs allow th machin to work and th machin givs th cogs purpos - but without ach othr thy ar quit limitd. Similarly, variabls ar not too much us without a hypothsis and a hypothsis is not much us without a rsarch qustion. hrfor w nd to mak thm work in tandm with ach othr. Suppos that I m intrstd in th rlationship btwn gndr and body imag - this is my rsarch aim. Mor spcifically, I want to discovr whthr womn ar mor likly to b dissatisfid with thir body imag than mn - this is my rsarch qustion. In ordr to invstigat this, and subsquntly achiv my rsarch aim, I m making th assumption that gndr is rlatd to body imag - or not: this is, ffctivly, my hypothsis. So now I nd to construct two variabls to hlp to assss it. Firstly, I nd to build a variabl that will masur th gndr of th rspondnt. Scondly, I nd to construct a variabl that will allow m to masur how satisfid th rspondnt is with thir body. Idntify th lvl of masurmnt rquird for ths variabls and attmpt to construct thm. As gndr is a catgorical variabl, I can us a nominal lvl of masurmnt. So: Plas stat your gndr: Mal Fmal Having lookd at som similar studis in th litratur, I find that thr is mthodological prcdnc for a masur of body imag satisfaction that uss a fiv point Likrt scal. Hnc I am masuring my body satisfaction variabl at th ordinal lvl. So: Look again at th procss w hav workd through in this xampl. I bgin with th original ida my rsarch aim; from that ida I thn dvlop a hypothsis; using this hypothsis I can thn idntify th variabls that I nd to masur; from ths variabls I can thn idntify th lvl of masurmnt that ar rquird by ths variabls; finally, I construct a qustion with rspctiv answrs Rounding up his workbook has introducd you to th diffrnt ways in which w can rcord quantitativ matrial, and how you can us variabls to hlp you to answr your rsarch qustions and hypothss. You should now b abl to: Idntify diffrnt lvls of masurmnt B abl to construct variabls at lvl appropriat to your rsarch aims Undrstand issus of rliability and validity and think critically about thm in rlation to variabl masurmnt Undrstand th rol of a variabl to answr your rsarch qustions and hypothsis By now, you should b abl to gnrat a rsarch projct, writ a rational and accompanying aims, qustions and hypothss, and dsign som survy qustions that ar appropriat to your study. Howvr, you r not quit rady to go yt. Bfor you bgin collcting data, you nd to b abl to hav a good undrstanding of analysis and how you will mak sns of your data. Indd, th prsntation of th rsarch procss looks to b a linar on. Bfor you carry out any data collction, you nd to undrstand how you will analys your data. h nxt book in this sris will introduc you to som of th main issus of analysis that you will nd to answr your rsarch qustions. Indd, a failur to rcognis th problms of any variabl can rsult in you going byond what is actually bing suggstd by th data that you gt from your variabls. Hnc w nd to think critically about any variabl that w choos to us. o paraphras Dming (1986), a famous statistician: th bttr w undrstand th limitations of an infrnc th mor usful bcoms th infrnc. his starts with a clar undrstanding of what your variabls ar actually masuring and th dvil is oftn in th dtail How satisfid ar you with th way you look: A. Vry dissatisfid B. Dissatisfid C. Nithr satisfid or dissatisfid D. Satisfid E. Vry satisfid

9 his workbook by om Clark and Liam Fostr is licnsd undr a Crativ Commons Attribution n Commrcial - SharAlik 4.0 Intrnational Licns. Contains public sctor information licnsd undr th Opn Govrnmnt Licnc v2.0. Crown Copyright.