pembolehubah dan skala pengukuran
TRANSCRIPT
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PEMBOLEHUBAH,PEMBOLEHUBAH,
TAHAP PENGUKURAN & TAHAP PENGUKURAN &UJIAN STATISTIKALUJIAN STATISTIKAL
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Section 2.1Section 2.1
Wht !e the T"#e$ o% t'
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In E(e!" Stti$tic) St*+"In E(e!" Stti$tic) St*+"
Questions are posedCharacteristics are observed
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-h!cte!i$tic$ !e-h!cte!i$tic$ !e VariablesVariables
A Variable is any characteristic
that is recorded for subjects inthe study
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!ition in t!ition in t
The terminology variable
highlights the fact that datavalues vary .
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E/0#)e St*+ent$ in Stti$tic$E/0#)e St*+ent$ in Stti$tic$
-)$$-)$$
Variables:
◦ Age
◦ GPA
◦ ajor
◦ !mo"ing !tatus◦ #
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Data valuesData values !e c))e+!e c))e+
observationsobservations$ach observation can be:
◦ Quantitative
◦ Categorical
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-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(
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3*ntitti(e !i)e3*ntitti(e !i)e
3bservations ta"e numerical values
$%amples:◦ Age
◦ 2umber of siblings
◦ Annual 4ncome
◦ 2umber of years of educationcompleted
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G!#h$ 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
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3*ntitti(e !i)e$3*ntitti(e !i)e$
Discrete Quantitative
Variables
and
Continuous Quantitative Variables
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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$
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i$c!etei$c!ete
A 5uantitative variable is
discrete if its possible valuesform a set of separatenumbers such as 6+ 7+ 8+ 9+ #
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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
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-ontin*o*$-ontin*o*$
A 5uantitative variable is
continuous if its possiblevalues form an interval
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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
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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
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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:
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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
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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*$
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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!+$@
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E+*ction) Re$e!ch 2e-!e$4e))
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".
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E+*ction) Re$e!ch 2e-!e$4e))
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$$0ent#t<n #n+*n <#+. U?in2 "n
+ +i#$!n.Bin $en+i!i in$t!*0en
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OUR T5PES O ARIABLES
In+e#en+ent !i)e e#en+ent !i)e -ont!o))e+ !i)e E/t!neo*$ !i)e
ARIABLE
A (!i)e i$ n" %cto!, t!it, o! con+ition tht cne/i$t in +ie!ent 0o*nt$ o! t"#e$
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In+e#en+ent !i)e
The (!i)e ein 0ni#*)te+ o! chne+
e#en+ent !i)e The o$e!(e+ !e$*)t o% the in+e#en+ent (!i)e ein
0ni#*)te+.
The e(ent $t*+ie+ n+ e/#ecte+ to chne 4hene(e! thein+e#en+ent (!i)e i$ )te!e+.
-ont!o))e+ !i)e The" !e the (!i)e$ tht !e <e#t con$tnt to #!e(ent
thei! in*ence on the eect o% the in+e#en+ent (!i)eon the +e#en+ent.
E/t!neo*$ !i)e !i)e tht 0iht ect the !e)tion$hi# et4een the
in+e#en+ent n+ +e#en+ent (!i)e$
ARIABLE
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In+e#en+ent (!i)e$ n$4e! the ;*e$tion Wht
+o I chne'
e#en+ent (!i)e$ n$4e! the ;*e$tion Wht +oI o$e!(e'
-ont!o))e+ (!i)e$ n$4e! the ;*e$tion Wht +o I
<ee# the $0e'
E/t!neo*$ (!i)e$ n$4e! the ;*e$tion Wht*ninte!e$tin (!i)e$ 0iht 0e+ite the eect o%the I on the
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Question IndependentVariable (What I
change)
DependentVariables
(What I
observe)
Controlled Variables(What I keep the same)
Doesfertilizermake aplant growbigger?
Amount offertilizer measuredin grams
•Growth of theplant measuredby its height•Growth of theplant measuredby the number of
leaves•See Measuringlant Growth formore ways tomeasure plantgrowth
•Same size pot for ea!h plant•Same type of plant in ea!hpot•Same type and amount ofsoil in ea!h pot•Same amount of water and
light•Make measurements ofgrowth for ea!h plant at thesame time"#he many variables above!an ea!h !hange how fast a
plant grows$ so to insure a fairtest of the fertilizer$ ea!h ofthem must be kept the samefor every pot%"
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The )e(e) o% 0e$*!e0ent !e%e!$ to the !e)tion$hi#0on the ()*e$ tht !e $$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!>)$$2T
No0in)
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No0in)
(!i)e 0e$*!e+ on no0in) $c)e i$ (!i)e tht+oe$ not !e))" h(e n" e()*ti(e +i$tinction.
One ()*e i$ !e))" not n" !ete! thn nothe!.
The n*0e!ic) ()*e$ ?*$t n0e the tt!i*te *ni;*e)".
A oo+ e/0#)e o% no0in) (!i)e i$ $e/ >o! [email protected] In%o!0tion in +t $et on $e/ i$ *$*))" co+e+ $ F o!1, 1 in+ictin 0)e n+ F in+ictin %e0)e >o! the othe!4" !o*n+CCF %o! 0)e, 1 %o! %e0)e@.
C 1 in thi$ c$e i$ n !it!!" ()*e n+ it i$ not n"
!ete! o! ette! thn F. The!e i$ on)" no0in)+ie!ence et4een F n+ 1.
With no0in) (!i)e$, the!e i$ ;*)itti(e +ie!enceet4een ()*e$, not ;*ntitti(e one.
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No0in) Sc)e
E/0#)e
Je!$e" n*0e!$ in $<et)) !e 0e$*!e$ t theno0in) )e(e).
A #)"e! 4ith n*0e! 7F i$ not 0o!e o% n"thin thn #)"e! 4ith n*0e! 19, n+ i$ ce!tin)" not t4ice
4hte(e! n*0e! 19 i$.
O!+in)
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O!+in)
So0ethin 0e$*!e+ on n o!+in) $c)e +oe$ h(e ne()*ti(e connottion.
One ()*e i$ !ete! o! )!e! o! ette! thn the othe!.
E/0#)e P!o+*ct A i$ #!e%e!!e+ o(e! #!o+*ct B, n+the!e%o!e A !ecei(e$ ()*e o% 1 n+ B !ecei(e$ ()*eo% 2.
Anothe! e/0#)e Ac+e0ic 3*)iction 0iht e!tin on $c)e %!o0 1 to 1F, 4ith 1F !e#!e$entin thehihe$t c+e0ic ;*)iction.
With o!+in) $c)e$, 4e on)" <no4 tht 2 i$ ette! thn 1o! 1F i$ ette! thn D8 4e +o not <no4 " ho4 0*ch. It0" (!". The +i$tnce et4een 1 n+ 2 0"e $ho!te!thn et4een D n+ 1F.
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A (!i)e 0e$*!e+ on n inte!() $c)e i(e$
in%o!0tion o*t 0o!e o! ette!ne$$ $ 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!()
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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
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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