APPLI CATI ON OFSTATI STI CALCON ONCEPTSI N THE HE DETERMI MI NATI ON OFWEI GHTVARI ATI ON I N SAMPLES 1
K. MANGO GONON ON 1 I NSTI TUTEOF OFCHE HEMI MI STRY ,COL OLL EGEOF OFSCI ENCE UNI VERSI TYOFTHE HEPHI LI PPI NES,DI LI MAN,QUEZON CI TY1 101,PHI HI LI PPI NES DATESUBMI MI TTED:2FEBRUAR ARY20 16 DATEPERFORME MED: 28J ANUAR ARY2016
ANS NSWERSTOQU QUESTI ONS
1 .Gi v et hes i gni fic a nc eo fGr u bbst e s t . Dur i ng exper i ment s ,usi ng pr operl abor at ory met hods s houl d yi el d dat a val ues t hat ar e e x pe c t e dt obea c c ur a t ea ndpr e c i s e . Ho we we v e r ,i n da t as e t swi wi t hnume r o ust r i a l s ,g e t t i ngav al ue whi c hi squa nt i t a t i v e l ydi ffe r e n tf r om t her e s t , a n“ out l i e r ” ,i si ne vi t a bl e .Ani nc ons i s t e ntda t a po i nti st e r me da st hes u s pe c t e do ut l i e r .The s us p e c t e dout l i e rc a ns i gni fic a nt l yi nflue nc et he s t at i s t i c val ues , gi vi ng an i nacc ur at e r e pr e s e n t a t i ono ft hee nt i r es a mp mpl e[ 1 ] .Onema ma y o ptt or e j e c tt he o ut l i e rf r o m t he r e s toft he v a l ue sb yus i ngt heGr ub bst e s t .
2. Gi ve t he s i gni fica nc e of t he me an and s t a nda r dde vi a t i o n. The me a n,i sa s t a t i s t i c a lt o olt ha tg e t st he a v e r a g eofa l lt heva l ue si nt heda t as e t .T e r me me d a same me a s u r eo fc e nt r a lt e nde nc y ,o nec a nus ei t i nc o mp mpa r i s o nwi t hada t apo i ntt ono t et heda t a po i nt ’ s di s t a nc ef r o m t he c e n t e r .Ho w we e v e r ,i t l a c kst o qua nt i f yt hedi s t r i but i on o ft h e da t a val ues f r om t he mea n. Ac c or di ng t o St ee l e ( 2006) ,t hes t andar d devi at i on can be us ed t o de t e r mi mi net he“ s c a t t e r ”oft hev al ue sa r oundt he me an [ 4 ] .
Whe ng at he r i ngda t a ,t he s es a m mp pl es t a t i s t i c sa r e vi t al when eva l uat i ng t he ac c ur ac y and pr e c i s i o no ft hes e t .Whe nt heme me a ni sa n a l yz e d, Thef ormu mul aus ed byt heGr ubbst es tbasi cal l y i tg i v e sa mo c kb ul l ’ se y ev a l uei n ada t as e t . comp mpar es t he di s t ance oft he out l i ert ot he S i mpl yput ,a l lt heot he rv al ue sc i r c ul a t ea r ound s u ppo s e da l l o w wa a nc eofada t apo i nt ’ sde v i a t i o n t hec e nt r a lme a nv a l ue .Al t ho ug hi ti sag e ne r a l f r om t hemean.TheGr Gr ubbst es tal s ot akesi nt o c h ar a c t e r i s t i c( whi c hma yno tb ea c c ur a t ei ft he a c c o untt hec onfide nc el e v e lt ode c i det hel i mi t da t as e tha sout l i e r s ) ,i tc a ni mpl yt hea c c ur a c y oft he cal cul at ed g val ue i n a gi ven s etof of a par t i c ul ar dat a poi nt . The s t andar d t a bul a t e d ge ge x pe c t e dv al ue sf ort her e j e c t i o no f de vi a t i onqua nt i fie st hepr e c i s i onoft heda t a .I f t heo ut l i e r .Thei nc o ns i s t e ntda t apoi ntwo ul d t he mea n wasa moc k bul l ’ seye val ue,t he t henbeanal yzedt ofindouti fwhet heraner r or s t andar d devi at i on poi nt southow cl ose t he o fa n yt y pe( me t ho d,i ns t r ume nt a lo rope r a t i v e ) gat her edval uesar eaboutt hemean.Fr om t he wa spr o duc e d[ 1 ] .I tc a npo i nto utt hepo s s i b l e me a n,i tc a ni mpl yat he o r e t i c a lr a ng eo fwhe r e c o nt a m mi i na t i o nsore r r o r si ne x e c u t i o nf r o mt he t oe x pe c tt hev a l ue s .Thes t a nda r dde v i a t i o ni s e x pe r i me nta dmi ni s t r a t i o n,whi c hwi l lh e l pi n ani mpor t antwayt oknow i ft heme met hodus edi n t hee v a l ua t i o no ft heme me t ho do l o gy . t hee x pe r i me nti spr o net opr o duc eout l i e r s ,o r t og i v eme me a ni ng f ulda t ava l ue s . Pa g e1o f2
3. Gi ve t he s i gni fica nce of t he c onfidence i nt e r va l . Ac c or di ng t o Eas t on & Mc Col l( n. d. ) ,t he c o nfide nc ei nt e r v a li sc ons i de r e da sa ne s t i ma t e d r angei n whi ch t herei sadegre eofcer t ai nt y ( no t e db yt hec o nfide nc el e v e l )t ha ti tc ont a i nsa popul at i on par amet er[ 2] .Whi l et hecomput ed r ange of val ues onl yt ar gett he popul at i on par amet eri n an es t i mat e,i tcanpavewayf or how wel lt hepar amet erca nbeconcl udedf r om a s ampl e s t at i s t i c. Not e t hat t he c onfidence i nt e r v a lc o mput e dc a na l s oha v eal i mi t e ds c o pe . When a s pec i ficconfidenc ei nt er vali swi de, whi c h enc ompas s es a l ar ge por t i on of t he s a mpl e ,i tc a nde no t et ha tt he r ei sa nunc e r t a i nt y o nwhe r et hepi npo i ntt he“ c o r r e c t ”po pul a t i o n par amet er [ 3] .I ti st hen s ugges t ed t ot ake di ffer ents ampl es ,t odefineamorepr ec i s eand de fine di nt e r v a l .Thi sc a nt he npr o duc eac e r t a i n es t i mat ec an be ac c ur at ei n det er mi ni ng a de s i r e dpo pul a t i o npa r a me t e r . 4 .Ho w dot hes t a t i s t i c sc a l c ul a t e df r om da t as e t 1di ffe rf r o mt ho s eo bt a i ne df r o m da t as e t2 ? Thec o ndi t i onso ft het woda t as e t swe r et ha tt he numberofdat aval uesi n dat as et1i ssi x( 6) whi l eda t as e t2ha st e n( 1 0 ) .I nc o mpa r i s o n,da t a s e t1ha das ma l l e rs t a nda r dde v i a t i o nc o mpa r e d t odat aset2,wi t hamuchmorel i mi t edr angeof da t af o ra na l ys i sofv a l ue s .I nc o mpa r i ng t he
c o nfide nc ei nt e r v a l sofbo t hda t as e t s ,da t as e t2 ha sas ma l l e rc o nfide nc ei nt e r v a l ,a l t ho ughi tha s a hi gher val ue f or s t andar d devi at i on.Thi s me a nst ha ta l t ho ug ht hedi s p e r s i o no ft heda t a val uesi ndat as et1i smorecl umpedt oget her , t hee s t i ma t eoft her e a lpo pul a t i o npa r a me t e ri s s t i l lmo r eunc e r t a i ni ni t ,c o mpa r e dt oda t as e t2 . REFERENCES
[ 1 ]Al f a s s i ,Z.B. ,Boge r ,Z. ,& Rone n,Y.( 2 00 5. ) St a t i s t i c a lt r e a t me nt o fa na l yt i c a lda t a .Fl o r i da , US A:CRCPr e s sLLC. [ 2 ]Ea s t on,V.J .& Mc Col l ,J .H.( n. d. ) .St a t i s t i c s g l o s s a r y :Co nfide nc ei nt e r v a l s .Re t r i e v e dF e br u ar y 2 ,2 0 16f r o m ht t p: //www. s t a t s . gl a . a c . uk /s t e ps / g l o s s a r y /c o nfide nc e _ i nt e r v a l s . ht ml I nt e r p r e t i nga [ 3 ]Gr a phPa dS of t wa r e ,I nc .( 2 01 5 ) . c o n fid e nc ei nt e r v a lo fame a n .Re t r i e v e dF e br u ar y 2, 2016 f r om ht t p: //www. gr aphpad. c om/gui des / pr i s m/6 /s t a t i s t i c s /i nde x . ht m? s t a t _ mor e _ a bo ut _ c o nfide nc e _ i nt e r v a l . ht m [ 4 ]St e el e ,G.W.( 2 00 6) .St a t i s t i c alc ons i de r a t i ons i ns a mpl i nga ndt e s t i ng .Si g ni fic a nc eo fTe s t sa nd Pr o p e r t i e s o f Co n c r e t e a n d Co n c r e t e ma k i n g Ma t e r i a l s , ( 16 9) , 23 .
Pa g e2o f2
