pembolehubah dan skala pengukuran

7/23/2019 Pembolehubah Dan Skala Pengukuran

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PEMBOLEHUBAH,PEMBOLEHUBAH,

TAHAP PENGUKURAN & TAHAP PENGUKURAN &UJIAN STATISTIKALUJIAN STATISTIKAL



Section 2.1Section 2.1

Wht !e the T"#e$ o% t'



In E(e!" Stti$tic) St*+"In E(e!" Stti$tic) St*+"

Questions are posedCharacteristics are observed



-h!cte!i$tic$ !e-h!cte!i$tic$ !e VariablesVariables

A Variable is any characteristic

that is recorded for subjects inthe study



!ition in t!ition in t

The terminology variable

highlights the fact that datavalues vary .



E/0#)e St*+ent$ in Stti$tic$E/0#)e St*+ent$ in Stti$tic$

-)$$-)$$

Variables:

◦ Age

◦ GPA

◦ ajor

◦ !mo"ing !tatus◦ #



Data valuesData values !e c))e+!e c))e+

observationsobservations$ach observation can be:

◦ Quantitative

◦ Categorical



-teo!ic) !i)e-teo!ic) !i)e

$ach observation belongs to one of aset of categories

$%amples:

◦ Gender &ale or 'emale(

◦ )eligious A*liation &Catholic+ ,e-ish+

#(

◦ Place of residence &Apt+ Condo+ #(

◦ elief in /ife After 0eath &1es or 2o(



3*ntitti(e !i)e3*ntitti(e !i)e

3bservations ta"e numerical values

$%amples:◦ Age

◦ 2umber of siblings

◦ Annual 4ncome

◦ 2umber of years of educationcompleted



G!#h$ n+ N*0e!ic)G!#h$ n+ N*0e!ic)

S*00!ie$S*00!ie$0escribe the main features ofa variable

'or Quantitative variables:"ey features are center andspread

'or Categorical variables:"ey feature is the percentage in each of the categories



3*ntitti(e !i)e$3*ntitti(e !i)e$

Discrete Quantitative

Variables

and

Continuous Quantitative Variables



i$c!ete (!i)e$ !e (!i)e$ in 4hich the!e !e nointe!0e+ite ()*e$ #o$$i)e.e. The n*0e! o% #hone c))$ "o* !ecei(e #e! +". 5o*cnnot !ecei(e 6.7 #hone c))$.

-ontin*o*$ (!i)e$ !e e(e!"thin e)$e8 n" (!i)etht cn theo!etic))" h(e ()*e$ in et4een #oint$e.., et4een 197 n+ 19: )$. %o! in$tnce.

i$c!ete n+ -ontin*o*$ !i)e$



i$c!etei$c!ete

A 5uantitative variable is

discrete if its possible valuesform a set of separatenumbers such as 6+ 7+ 8+ 9+ #



E/0#)e$ o% +i$c!ete (!i)e$E/0#)e$ o% +i$c!ete (!i)e$

Number of pets in a household

Number of children in a family

Number of foreign languagesspo"en



-ontin*o*$-ontin*o*$

A 5uantitative variable is

continuous if its possiblevalues form an interval



E/0#)e$ o% -ontin*o*$ !i)e$E/0#)e$ o% -ontin*o*$ !i)e$

eight;eight

Age

Amount of time it ta"es tocomplete an assignment



I+enti%" the %o))o4in (!i)e $I+enti%" the %o))o4in (!i)e $

cteo!ic) o! ;*ntitti(ecteo!ic) o! ;*ntitti(e

Choice of diet

&vegetarian or non<vegetarian(:

a. Categorical

b. Quantitative



2umber of people you have "no-n -hohave been elected to political o*ce:

a. Categorical

b. Quantitative

Identify the following variable as categorical

or quantitative:



I+enti%" the %o))o4in (!i)e $I+enti%" the %o))o4in (!i)e $

+i$c!ete o! contin*o*$+i$c!ete o! contin*o*$

The number of people in line at a bo%o*ce to purchase theater tic"ets:

a. Continuous

b. 0iscrete



The -eight of a dog:

a. Continuous

b. 0iscrete

I+enti%" the %o))o4inI+enti%" the %o))o4in

(!i)e $ +i$c!ete o!(!i)e $ +i$c!ete o!

contin*o*$contin*o*$



E+*ction) Re$e!ch 2e-!e$4e))

M<)*0t A# "n <n +i<*0#*)'M<)*0t A# "n <n +i<*0#*)'

Jeni$2 t Pen*<*!n Jeni$2 t Pen*<*!n

In$t!*0en i)h $t* )t *<*! *nt*< 0en*<*!,0e0e!hti, t* 0en+o<*0ent$i<n +ti #e0o)eh*h <*ntitti%.

Jeni$2 In$t!*0en

◦ Pen*<*!n Penc#in=#e!%o!0nce >cth.U?in Penc#in@

◦ Pen*<*!n Si<#=Attit*+in) >$i<#=#e!$nte!h+# 0t#e)?!n $in$@

◦ Pen*<*!n Tin<h)<* >Pe0e!htintin<h)<*@

◦ Pen*<*!n <t >+o<*0en, !eco!+$@




Kitn nt. Pen*0#*)n +t +t +nKitn nt. Pen*0#*)n +t +t +n

#e0o)eh*h +n #e!$o)n <?in#e0o)eh*h +n #e!$o)n <?in

Aliran Aktiviti Contoh

Menen)#$ti Pe0o)eh*h

Men+en$i<n Pe0o)eh*h $ec!O#e!$i

Menen)#$ti +t>*<*!n, #e0e!htin,+o<*0en +n$o)n=ite0 +n $<)@

Men*0#*) t0en*n<n in$t!*0en" 0e0e!i<n $<o! +)0ent*< no0o!.

E<$iCKen+i!i *t<. Be)?! +!iR<n

Th# <e"<inn $e$eo!n

in+i(i+* "n 0e!e< +#t0e0e#e)?!i $e$*t* ?i< +i?!o)eh !<n

17 ite0 *t< self-ecacyattitudinal scale +!i Be!in>1DD@

S<o! *t< $eti# ite0 0e0#*n"i ?*)t +!i FC1F +n 1F i)hBe!<e"<inn Se#en*hn".




4nstrumen Apa"ah yang a"an anda4nstrumen Apa"ah yang a"an anda

Guna"an= endapat"an atau embinaGuna"an= endapat"an atau embina

4nstrumen4nstrumen

Liht +)0 #*)i$he+ ?o*!n) !tic)e$Penc!in ERI- $e!ch +n

0en*n<n te!0 in$t!*0ent$+n to#i< <?inERI- 4e $ite %o! E()*tion n+

A$$e$$0ent#t<n #n+*n <#+. U?in2 "n

+ +i#$!n.Bin $en+i!i in$t!*0en



OUR T5PES O ARIABLES

In+e#en+ent !i)e e#en+ent !i)e -ont!o))e+ !i)e E/t!neo*$ !i)e

ARIABLE

A (!i)e i$ n" %cto!, t!it, o! con+ition tht cne/i$t in +ie!ent 0o*nt$ o! t"#e$



In+e#en+ent !i)e

The (!i)e ein 0ni#*)te+ o! chne+

e#en+ent !i)e The o$e!(e+ !e$*)t o% the in+e#en+ent (!i)e ein

0ni#*)te+.

The e(ent $t*+ie+ n+ e/#ecte+ to chne 4hene(e! thein+e#en+ent (!i)e i$ )te!e+.

-ont!o))e+ !i)e The" !e the (!i)e$ tht !e <e#t con$tnt to #!e(ent

thei! in*ence on the eect o% the in+e#en+ent (!i)eon the +e#en+ent.

E/t!neo*$ !i)e !i)e tht 0iht ect the !e)tion$hi# et4een the

in+e#en+ent n+ +e#en+ent (!i)e$

ARIABLE



In+e#en+ent (!i)e$ n$4e! the ;*e$tion Wht

+o I chne'

e#en+ent (!i)e$ n$4e! the ;*e$tion Wht +oI o$e!(e'

-ont!o))e+ (!i)e$ n$4e! the ;*e$tion Wht +o I

<ee# the $0e'

E/t!neo*$ (!i)e$ n$4e! the ;*e$tion Wht*ninte!e$tin (!i)e$ 0iht 0e+ite the eect o%the I on the



Question IndependentVariable (What I

change)

DependentVariables

(What I

observe)

Controlled Variables(What I keep the same)

Doesfertilizermake aplant growbigger?

Amount offertilizer measuredin grams

•Growth of theplant measuredby its height•Growth of theplant measuredby the number of

leaves•See Measuringlant Growth formore ways tomeasure plantgrowth

•Same size pot for ea!h plant•Same type of plant in ea!hpot•Same type and amount ofsoil in ea!h pot•Same amount of water and

light•Make measurements ofgrowth for ea!h plant at thesame time"#he many variables above!an ea!h !hange how fast a

plant grows$ so to insure a fairtest of the fertilizer$ ea!h ofthem must be kept the samefor every pot%"



The )e(e) o% 0e$*!e0ent !e%e!$ to the !e)tion$hi#0on the ()*e$ tht !e $$ine+ to the tt!i*te$ %o! (!i)e.

The!e !e %o*! t"#e$ o% 0e$*!e0ent$ o!)e(e)$ o% 0e$*!e0ent o! 0e$*!e0ent $c)e$ *$e+ in$tti$tic$

No0in)

O!+in)

Inte!()

Rtio.

/$V$/! 3' $A!>)$$2T

No0in)

http://en.wikipedia.org/wiki/Level_of_measurement

http://en.wikipedia.org/wiki/Level_of_measurement



No0in)

(!i)e 0e$*!e+ on no0in) $c)e i$ (!i)e tht+oe$ not !e))" h(e n" e()*ti(e +i$tinction.

One ()*e i$ !e))" not n" !ete! thn nothe!.

The n*0e!ic) ()*e$ ?*$t n0e the tt!i*te *ni;*e)".

A oo+ e/0#)e o% no0in) (!i)e i$ $e/ >o! [email protected] In%o!0tion in +t $et on $e/ i$ *$*))" co+e+ $ F o!1, 1 in+ictin 0)e n+ F in+ictin %e0)e >o! the othe!4" !o*n+CCF %o! 0)e, 1 %o! %e0)e@.

C 1 in thi$ c$e i$ n !it!!" ()*e n+ it i$ not n"

!ete! o! ette! thn F. The!e i$ on)" no0in)+ie!ence et4een F n+ 1.

With no0in) (!i)e$, the!e i$ ;*)itti(e +ie!enceet4een ()*e$, not ;*ntitti(e one.



No0in) Sc)e

E/0#)e

Je!$e" n*0e!$ in $<et)) !e 0e$*!e$ t theno0in) )e(e).

A #)"e! 4ith n*0e! 7F i$ not 0o!e o% n"thin thn #)"e! 4ith n*0e! 19, n+ i$ ce!tin)" not t4ice

4hte(e! n*0e! 19 i$.

O!+in)



O!+in)

So0ethin 0e$*!e+ on n o!+in) $c)e +oe$ h(e ne()*ti(e connottion.

One ()*e i$ !ete! o! )!e! o! ette! thn the othe!.

E/0#)e P!o+*ct A i$ #!e%e!!e+ o(e! #!o+*ct B, n+the!e%o!e A !ecei(e$ ()*e o% 1 n+ B !ecei(e$ ()*eo% 2.

Anothe! e/0#)e Ac+e0ic 3*)iction 0iht e!tin on $c)e %!o0 1 to 1F, 4ith 1F !e#!e$entin thehihe$t c+e0ic ;*)iction.

With o!+in) $c)e$, 4e on)" <no4 tht 2 i$ ette! thn 1o! 1F i$ ette! thn D8 4e +o not <no4 " ho4 0*ch. It0" (!". The +i$tnce et4een 1 n+ 2 0"e $ho!te!thn et4een D n+ 1F.



A (!i)e 0e$*!e+ on n inte!() $c)e i(e$

in%o!0tion o*t 0o!e o! ette!ne$$ $ o!+in)$c)e$ +o, *t inte!() (!i)e$ h(e n e;*)+i$tnce et4een ech ()*e.

The +i$tnce et4een 1 n+ 2 i$ e;*) to the

+i$tnce et4een D n+ 1F.

Te0#e!t*!e *$in -e)$i*$ o! h!enheit i$ oo+e/0#)e, the!e i$ the e/ct $0e +ie!ence et4een1FF +e!ee$ n+ DF $ the!e i$ et4een :2 n+ 72.

Inte!()



So0ethin 0e$*!e+ on !tio $c)e h$ the $0e#!o#e!tie$ tht n inte!() $c)e h$ e/ce#t. With !tio $c)in, the!e i$ n $o)*te e!o #oint. Weiht i$ the e/0#)e, F )$. i$ 0enin%*) $ence

o% 4eiht.

Rtio



P!$ U<*!nt

Si%t

No0in) Pen<e)$n o?e< t* o!n +n $ein"

<e#+ <teo!i "n +i$<!it 0eni<*t $i%t<*)itti%.U<*!n #)in $$.-ontoh Pe0o)eh*h ?ntin +i<teo!i<e#+ )e)<i +n #e!e0#*n.

O!+in) Pen<e)$n o?e< t* o!n +n $ein"0eni<*t *!*tn <e*t0n t* !n<-ontoh Th# <e)*)*$n <+e0i<, #e!$e#$i.

Je+=Se)

>inte!()@

Me0#*n"i *!*tn t* !n< $e!t 4*?*+

#e!en nt! ?e+ tet#i ti+ 0*t)<<o$on-ontoh M!<h #e)?!, I3, $i<#, 0int.

Ni$h >!tio@ Me0#*n"i *!*tn t* !n< $e!t 4*?*+#e!en nt! ?e+ +n 0e0#*n"i 0*t)<

<o$on-ontoh Tin i, U0*!, Be!t



;hy is /evel of easurement 4mportant=

i!$t, <no4in the )e(e) o% 0e$*!e0ent he)#$ "o*+eci+e ho4 to inte!#!et the +t %!o0 tht (!i)e.

C When "o* <no4 tht 0e$*!e i$ no0in), then "o*<no4 tht the n*0e!ic) ()*e$ !e ?*$t $ho!t co+e$ %o!the )one! n0e$.

Secon+, <no4in the )e(e) o% 0e$*!e0ent he)#$ "o*+eci+e 4ht $tti$tic) n)"$i$ i$ ##!o#!ite on the()*e$ tht 4e!e $$ine+.

C I% 0e$*!e i$ no0in), then "o* <no4 tht "o* 4o*)+

ne(e! (e!e the +t ()*e$



P. U<*!n

t

Si%t T*?*n U?in 5

Se$*i

No0in) Pen<e)$n0eni<*t<teo!i

•Pe!<itn#e0o)eh*h

Khi K*$*

O!+in) Meni<*t*!*tn<e*t0nt* !n<

•Pe!<itn#e0o)eh*h

S#e!0n!hoMnnCWhitne"Wi)co/on

P.U<

Si%t T*?*n U?in 5 Se$*i



Jeda(interval)

Mempunyaiurutan atau rankserta wujudperbeaan antara jeda tetapi tiadamutlak kosong

• !erbeaan Min satu pembolehubahbersandar berdasarkan satupembolehubah tak bersandar ("kategori)

• !erbeaan Min satu pembolehubahbersandar berdasarkan satupembolehubah tak bersandar (# kategoriatau lebih)

• !erbeaan Min satu pembolehubahbersandar berdasarkan duapembolehubah tak bersandar

• !erbeaan Min bagi dua atau lebihpembolehubah bersandar berdasarkandua atau lebih pembolehubah takbersandar

• $orelasi antara pembolehubah• %umbangan pembolehubah tak

bersandar ke atas pembolehubahbersandar

&jian't

*+ %atu',ala

*+ -ua',ala

M*+

$orelasi !earson

.egrasi/erganda

isbah(ratio)

Mempunyaiurutan0 rank sertawujud perbeaanantara jeda danmutlak kosong

%ama seperti untuk skala Jeda %ama sepertiuntuk skala Jeda

U<*!nt

pembolehubah dan skala pengukuran

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