Handout KOM 204 Kuliah 2

KULIAH II

STATISTIK

 TABEL DATA YANG BERTUJUAN UNTUK SIMPLIFIKASI
DATA.

 ANALISIS STATISTIK BERURUSAN DENGAN DATA
MENTAH.
 BAGAIMANA MELAKUKAN STRUKTURISASI SEHINGGA
DATA TERSEBUT DAPAT DIKOMUNIKASI SECARA
EFEKTIF.
 TABEL DAN DIAGRAM HARUS JELAS DAN AKURAT DAN
BERKOMUNIKASI SECARA CEPAT.

STATISTIK DESKRIPTIF
 D e s c r i p t i v e s t a t i s t i c s a re , b y a n d l a rg e , re l a t i v e l y s i m p l e v i s u a l a n d
numerical techniques
 f o r d e s c r i b i n g t h e m a j o r f e a t u re s o f o n e ’ s d a t a . Re s e a rc h e r s m a y p ro d u c e
descriptive
 s t a t i s t i c s i n o rd e r t o c o m m u n i c a t e t h e m a j o r c h a r a c t e r i s t i c s o f t h e d a t a t o

others,
 b u t i n t h e fi r s t i n s t a n c e t h e y a re u s e d b y re s e a rc h e r s t h e m s e l v e s i n o r d e r
to understand
 t h e d i s t r i b u t i o n o f p a r t i c i p a n t s ’ re s p o n s e s i n t h e re s e a rc h . N e v e r re g a rd
descriptive
 s t a t i s t i c a l a n a l y s i s a s a n u n n e c e s s a r y o r t r i v i a l s t a g e i n re s e a rc h . I t i s
p ro b a b l y m o re
 i n f o rm a t i v e t h a n a n y o t h e r a s p e c t o f d a t a a n a l y s i s . B ox 2 . 2 ex p l a i n s t h e
c r u c i a l ro l e o f
 d e s c r i p t i v e s t a t i s t i c s i n re s e a rc h f u r t h e r.
 T h e d i s t i n c t i o n b e t w e e n n o m i n a l ( c a t e g o r y ) d a t a a n d n u m e r i c a l s c o re s
discussed in the
 p re v i o u s c h a p t e r i s i m p o r t a n t i n t e rm s o f t h e a p p ro p r i a t e t a b l e s a n d
diagrams to use.

 2.2 Choosing tables and diagrams
 So long as you are able to decide whether your data
are either numerical scores or
 nominal (category) data, there are few other choices
to be made since the available tables

 and diagrams are essentially dependent upon this
distinction. Figure 2.1 gives some of
 the key steps when considering tables and diagrams.

 ■ Tables and diagrams for nominal (category) data
 One of the main characteristics of tables and
diagrams for nominal (category) data is
 that they have to show the frequencies of cases in
each category used. While there may
 be as many categories as you wish, it is not the
function of statistical analysis to communicate
 all of the data’s detail; the task is to identify the
major trends. For example,
 imagine you are researching the public’s attitudes
towards private health care. If you ask
 participants in your research their occupations then
you might fi nd that they mention

 t e n s i f n o t h u n d re d s o f d i ff e r e n t j o b t i t l e s – n e w s a g e n t s , h o m e m a ke r s , c o m p a n y
e xe c u t i v e s

 a n d s o f o r t h . S i m p l y c o u n t i n g t h e f re q u e n c i e s w i t h w h i c h d i ff e re n t j o b t i t l e s a re
 m e n t i o n e d re s u l t s i n a v a s t n u m b e r o f c a t e g o r i e s . Yo u n e e d t o t h i n k o f re l e v a n t a n d
 m e a n i n g f u l w a y s o f re d u c i n g t h i s v a s t n u m b e r i n t o a s m a l l e r n u m b e r o f m u c h b ro a d e r
 c a t e g o r i e s t h a t m i g h t r e v e a l i m p o r t a n t t r e n d s . Fo r e x a m p l e , s i n c e t h e re s e a rc h i s
about
a health issue you mi ght wi sh to form a categ ory made up of those invol ved in health
work – some mi ght be dentis ts , some nur ses, s ome doctors, some paramedi cs and so
 f o r t h . I n s t e a d o f ke e p i n g t h e s e a s d i ff e r e n t c a t e g o r i e s , t h e y m i g h t b e c o m b i n e d i n t o a
 c a t e g o r y ‘ h e a l t h w o r ke r ’ . T h e re a r e n o h a r d - a n d - f a s t r u l e s a b o u t c o m b i n i n g t o f o r m
broader categ ori es. The following mi ght be useful rule s of thumb:
 1 . Ke e p y o u r n u m b e r o f c a t e g o r i e s l o w , e s p e c i a l l y w h e n y o u h a v e o n l y s m a l l n u m b e r s
 o f p a r t i c i p a n t s i n y o u r r e s e a rc h .
 2 . Tr y t o m a ke y o u r ‘ c o m b i n e d ’ c a t e g o r i e s m e a n i n g f u l a n d s e n s i b l e i n t h e l i g h t o f t h e
 p u r p o s e s o f y o u r r e s e a rc h . I t w o u l d b e n o n s e n s e , f o r e x a m p l e , t o c a t e g o r i s e j o b s b y
the l etter of the alp habet with whi ch they s tart – nurs es, nuns, nurser y teachers and
national football ers. All of these have jobs beg inning with the same l etter, but it i s
 v e r y d i ffi c u l t t o s e e a n y o t h e r c o m m o n t h re a d w h i c h a l l o w s t h e m t o b e c o m b i n e d
 m e a n i n g f u l l y.

 Slices for a pie diagram

 There is n othin g diffi cult in constructing a pie diagram. Our
recommendation is that you turn each of your freq uencies
 in to a percentage frequency. Since there are 360 d egrees in a
circle, if you mu ltiply each percentage frequency by 3.6
 you will obtain the angle (in degrees) of the slice of the pie
w hich you need to mark out. In order to create the diagram,
 you will requ ire a protractor to measu re the angles. H ow ever,
compu ter graph packages are standard at any u niversity
 or college and do an impressive job.
 In Table 2.1, 25.00% of cases were stu dents. In ord er to turn
this into the correct angle for the slice of th e pie, you
 simp ly n eed to multiply 25.00 by 3.6 to give an an gle of 90
degrees.
 FIGURE 2.2 A s imple pie diagram

 One advan tage of u sing compute rs is that the y e nable
expe rime n tation w ith diff e re nt
 sche mes of cate gorising data in orde r to de cide w hic h is be st for
you r p urpose s. In this
 cas e, you would use in itially narrow c ate gor ie s for coding your

data. The n you can te ll
 th e compu te r which of the s e to combine into broad er cate g orie s.
 Some times it is pre fe rable to tu rn fre qu en cy tab le s into
diagr ams. Good d iagrams
 are q uic kly unde rs tood and add var ie ty to the p re se ntation. The
main type s of diagr am
 for nominal (c ate gory) data are pie diagrams and bar charts . A
pie diagram is a very
 familiar form of pre se n tation – it simply expres se s e ach cate gory
as a s lice of a pie which
 re pre se nts all case s (s e e Figu re 2.2).

Notice that the number of slices is small – a multitude of slices can be
confusing. Each
 s l i c e i s c l e a r l y m a r ke d w i t h i t s c a t e g o r y n a m e , a n d t h e p e rc e n t a g e
f re q u e n c y i n e a c h
category also appears.
 C H A P T E R 2 D E S C R I B I N G VA R I A B L E S 1 7
 l e g e n d o r ke y t o i d e n t i fy t h e c o m p o n e n t s t o h e l p c o p e w i t h t h e o v e rc ro w d i n g
 p ro b l e m . I n o t h e r w o rd s , t o o m a n y c a t e g o r i e s h a v e re s u l t e d i n a d i a g r a m

which is
 f a r f ro m e a s y t o re a d – a c a rd i n a l s i n i n a n y s t a t i s t i c a l d i a g r a m .
 A s i m p l e f re q u e n c y t a b l e m i g h t b e m o re e ff e c t i v e i n t h i s c a s e .
 A n o t h e r v e r y f a m i l i a r f o rm o f s t a t i s t i c a l d i a g r a m f o r n o m i n a l ( c a t e g o r y ) d a t a
is
 t h e b a r c h a r t . A g a i n t h e s e c h a r t s a re v e r y c o m m o n i n t h e m e d i a . B a s i c a l l y
t h e y a re
 d i a g r a m s i n w h i c h b a r s re p re s e n t t h e s i z e o f e a c h c a t e g o r y. A n ex a m p l e i s
shown in
 Fi g u re 2 . 4 .

 T h e re l a tiv e len g t h s ( o r h e i g h t s ) o f t h e b a r s q u i ck l y re v e a l t h e m a i n
t re n d s in t h e d a t a .
 Wit h a b a r c h a r t , t h ere i s v e r y l i t t l e t o re m e m b e r o t h e r t h a n t h a t t h e
b a r s h a ve a s t a n d a rd
 s p a c e s e p a r a t in g t h em . T h e s p a c e s in d i c a t e t h a t t h e c a t e g o r i e s a re
n o t i n a n u m er ic a l
 o rd e r ; t h ey a re f req u e n ci e s o f ca t e g o r i e s , no t s c o re s .
 I t is h a rd t o g o w ro n g w i t h a b a r ch a r t ( t h a t i s n o t a ch a l l e n g e ! ) s o
lo n g a s y o u

 re m e m b er t h e f o llo w in g :
 1 . T h e h eig h ts o f t h e b a r s re p re s e n t f re q u e n ci e s ( n u m b e r o f c a s e s ) i n
a ca t e g o r y.
 2 . E a ch b a r s h o u ld b e cl e a r ly l a b e l l e d a s t o t h e c a t e g o r y i t re p re s e n t s .
 3 . To o m a n y b a r s m a ke b a r ch a r t s h a rd t o f o l lo w.
 F I G U R E 2 . 3 A p o o r p ie d i a g r a m
 F I G U R E 2 . 4 B a r ch a r t s h o w i n g o c cu p a t i o n a l ca t e g o r i e s i n Ta b l e 2 . 1
 1 8 PA RT 1 D E S C R I PT I V E S TAT I S T I C S

 4 . Av o i d h a v i n g m a n y e m p t y o r n e a r- e m p t y c a t e g o r i e s w h i c h r e p r e s e n t v e r y f e w c a s e s .
Gener al ly, the inform ati on about s ubs tantial c a tegor ie s is the m os t im port ant . (Sm al l
 c a t e g o r i e s c a n b e c o m b i n e d t o g e t h e r a s a n ‘ o t h e r ’ c a t e g o r y. )
5 . N e ve rt he l e s s, i f i m po rta nt c ate gor i e s h ave ve r y fe w e ntr i e s th e n th i s n e e d s re c ord i ng .
So , f or exam p l e , a re se arc h e r wh o i s p ar ti c u l ar l y i n te re st e d i n op p or tun i t i e s for
 w o m e n s u r v e y s p e o p l e i n t o p m a n a g e m e n t a n d fi n d s v e r y f e w w o m e n e m p l o y e d i n
suc h jobs. It i s im por tant to dra w atte nt ion to thi s in the ba r c har t of m ales and
fe m al e s i n top m a na ge m e n t. On c e ag ai n , th e re are no h ard - an d- fas t r ul e s to gu i d e
 y o u – c o m m o n s e n s e w i l l t a ke y o u a l o n g w a y.
 6 . M a ke s u re t h a t t h e v e r t i c a l a x i s ( t h e h e i g h t s o f t h e b a r s ) i s c l e a r l y m a r ke d a s b e i n g
fre qu e n c i e s or pe rc e nta ge fre qu e n c i e s.

7 . The bar s s ho ul d be of e qual wi dth.
 I n n e w s p a p e r s a n d o n t e l e v i s i o n y o u a r e l i ke l y t o c o m e a c r o s s a v a r i a n t o f t h e b a r
c ha rt c al l e d t he p i c t ogr am . In thi s, th e b ars of the bar c h art a re re p l a c e d by var yi ng si ze d
dr awi n g s of s o m e th i ng e ye -c atc h i n g to d o wi t h you r c a te g or i e s . T hu s , p i c t ure s of m e n
 o r w o m e n o f v a r y i n g h e i g h t s , f o r e x a m p l e , r e p l a c e t h e b a r s . Pi c t o g r a m s a r e r a r e l y u s e d
i n p rof e s si o na l pre se nt ati o ns . T he m ai n re as on i s th at p i c tu re s of thi ng s g e t wi d e r as we l l
as ta l l e r as th e y i n c re as e i n s i ze . T hi s c a n m i s re p re s e n t th e re l ati ve si z e s of t he
categories,
gi ve n th at re ad e r s f org e t th at i t i s on l y th e h e i g h t of th e p i c tu re th at c oun ts .

 ■ Ta b l e s a n d d i a g r a m s f o r n u m e r i c a l s c o r e d a t a
O ne cr ucia l co ns idera tio n w hen deciding w ha t ta bles a nd diagrams to use f or sc ore
data
 i s t h e n u m b e r o f s e p a r a t e s c o re s r e c o r d e d f o r t h e v a r i a b l e i n q u e s t i o n . T h i s c a n
vary
 m a r ke d l y. S o , f o r e x a m p l e , a g e i n t h e g e n e r a l p o p u l a t i o n c a n r a n g e f r o m n e w l y b o r n
 t o o v e r 1 0 0 y e a r s o f a g e . I f w e m e r e l y re c o r d e d a g e s t o t h e n e a r e s t w h o l e y e a r
then a
 t a b l e o r d i a g r a m m a y h a v e e n t r i e s f o r 1 0 0 d i ff e r e n t a g e s . S u c h a t a b l e o r d i a g r a m
would

loo k horrendo us . If w e reco rded a ge to the nea res t month, then w e could multiply
this
number of ages by 12! Such s cores can be grouped into bands or r anges o f s cores
to
 a l l o w e ff e c t i v e t a b u l a t i o n ( Ta b l e 2 . 2 ) .
Many psychological variables have a much smaller range of numerical values. So,
f or exa mple, it is f airly co mmo n to use ques tio ns which pre-spec ify just a few
respons e
 a l t e r n a t i v e s . T h e s o - c a l l e d L i ke r t - t y p e q u e s t i o n n a i r e i t e m i s a g o o d c a s e i n p o i n t .
 Ty p i c a l l y t h i s l o o k s s o m e t h i n g l i ke t h i s :
Statistics is my favourite university subject:

 A h i s t o g r a m m i g h t b e t h e b e s t f o r m o f s t a t i s t i c a l d i a g r a m t o re p r e s e n t t h e s e d a t a . A t
 fi r s t s i g h t , h i s t o g r a m s l o o k v e r y m u c h l i ke b a r c h a r t s b u t w i t h o u t g a p s b e t w e e n t h e
bars.
Th is i s becau se the hi sto gram do es not represe nt dis tin ct un rela ted cate go ries but
d i ff e r e n t
 p o i n t s o n a n u m e r i c a l m e a s u re m e n t s c a l e . S o a h i s t o g r a m o f t h e a b o v e d a t a m i g h t
 l o o k l i ke Fi g u r e 2 . 5 .
 B u t w h a t i f y o u r d a t a h a v e n u m e r o u s d i ff e re n t p o s s i b l e v a l u e s o f t h e v a r i a b l e i n

question?
 O n e c o m m o n d i ffi c u l t y f o r m o s t p s y c h o l o g i c a l r e s e a rc h i s t h a t t h e n u m b e r o f
 r e s p o n d e n t s t e n d s t o b e s m a l l . T h e l a r g e n u m b e r o f p o s s i b l e d i ff e r e n t s c o re s o n t h e
 v a r i a b l e i s t h e r e f o r e s h a r e d b e t w e e n v e r y f e w r e s p o n d e n t s . Ta b l e s a n d d i a g r a m s
should
 p r e s e n t m a j o r f e a t u re s o f y o u r d a t a i n a s i m p l e a n d e a s i l y a s s i m i l a t e d f o r m . S o ,
sometimes
y ou wi l l h av e to us e ban ds of s cores rath er tha n in div i du al score v a lu es , j us t as
 y o u d i d f o r Ta b l e 2 . 2 . S o , i f w e a s ke d 1 0 0 p e o p l e t h e i r a g e s w e c o u l d c a t e g o r i s e t h e i r
repli es in to ban ds su ch as 0–9 y ear s, 10–19 y ea rs, 30–39 y ea rs, 40–49 ye ars an d a
fi n a l

 Ta b l e 2 . 3 D i s t r i b u t i o n o f s t u d e n t s ’ a t t i t u d e s t o w a r d s s t a t i s t i c s
 Re s p o n s e c a t e g o r y Va l u e Fre q u e n c y
 S t ro n g l y a g r e e 1 1 7
 A g re e 2 1 4
 N e i t h e r a g r e e n o r d i s a g re e 3 6
Di sa gree 4 2
 S t ro n g l y d i s a g r e e 5 1
FIGURE 2.5 Histogram of s tudents’ a ttitudes to wards s tatis tics

 2 0 PA RT 1 D E S C R I P T I V E S TAT I S T I C S
 c a t e g o r y o f t h o s e 5 0 y e a r s a n d o v e r. B y u s i n g b a n d s w e re d u c e t h e r i s k o f e m p t y
parts
 o f t h e t a b l e a n d a l l o w a n y t re n d s t o b e c o m e c l e a r ( Fi g u r e 2 . 6 ) .
How one cho oses the bands to use is an impo rtant question. The answ er is a bit
 o f l u c k a n d j u d g e m e n t , a n d a l o t o f t r i a l a n d e r r o r. I t i s v e r y t i m e - c o n s u m i n g t o re j i g
the ra nges of the bands when one is analysing the data by hand. One big a dvantage
of
 c o m p u t e r s i s t h a t t h e y w i l l re c o d e y o u r s c o r e s i n t o b a n d s re p e a t e d l y u n t i l y o u h a v e
tables w hich seem to do the job as well as pos sible. The criter io n is still whether the
table
 c o m m u n i c a t e s i n f o r m a t i o n e ff e c t i v e l y.

The one rule is that the bands ought to be of the same size – that is cover, for
ex ample, equal ranges of scores. Generally this is easy except at the upper and
lower
 e n d s o f t h e d i s t r i b u t i o n . Pe r h a p s y o u w i s h t o u s e ‘ o v e r 7 0 ’ a s y o u r u p p e r r a n g e .
This,
in modern practice, can be done as a bar of the same width as the others, but
must be
 v e r y c a re f u l l y m a r ke d . ( S t r i c t l y s p e a k i n g , t h e w i d t h o f t h e b a n d s h o u l d re p re s e n t
the
 r a n g e o f s c o re s i n v o l v e d a n d t h e h e i g h t re d u c e d i n t h e l i g h t o f t h i s . H o w e v e r ,
this is
 r a re l y d o n e i n m o d e r n p s y c h o l o g i c a l s t a t i s t i c s . )
 O n e m i g h t re d e fi n e t h e b a n d s o f s c o re s a n d g e n e r a t e a n o t h e r h i s t o g r a m b a s e d o n
 i d e n t i c a l d a t a b u t a d i ff e re n t s e t o f b a n d s ( Fi g u r e 2 . 7 ) .
 F I G U R E 2 . 6 U s e o f b a n d s o f s c o re s t o e n a b l e s i m p l e p re s e n t a t i o n
FIGURE 2.7 Histogram showing ‘collapsed’ categories
 C H A P T E R 2 D E S C R I B I N G VA R I A B L E S 2 1
 I t re q u i re s s o m e t h o u g h t t o d e c i d e w h i c h o f t h e d i a g r a m s i s b e s t f o r a p a r t i c u l a r
 p u r p o s e . T h e r e a re n o h a r d - a n d - f a s t r u l e s .

2 . 3 E rro r s t o a v o i d
T h e re a re a c o u p l e o f m i s t a ke s t h a t y o u c a n m a ke i n d r a w i n g u p t a b l e s a n d d i a g r a m s :
1 . D o n o t f o rg e t t o h e a d t h e t a b l e o r d i a g r a m w i t h a s u c c i n c t d e s c r i p t i o n o f w h a t i t
 c o n c e r n s . Yo u w i l l n o t i c e t h a t w e h a v e d o n e o u r b e s t t h r o u g h o u t t h i s c h a p t e r t o
s u p p l y e a c h t a b l e a n d d i a g r a m w i t h a c l e a r t i t l e .
2 . L a b e l e v e r y t h i n g o n t h e t a b l e o r d i a g r a m a s c l e a r l y a s p o s s i b l e . W h a t t h i s m e a n s i s
t h a t y o u h a v e t o m a r k y o u r b a r c h a r t s a n d h i s t o g r a m s i n a w a y t h a t t e l l s t h e re a d e r
w h a t e a c h b a r m e a n s . T h e n y o u m u s t i n d i c a t e w h a t t h e h e i g h t o f t h e b a r re f e r s t o –
 p r o b a b l y e i t h e r f r e q u e n c y o r p e r c e n t a g e f r e q u e n c y.
N o t e t h a t t h i s c h a p t e r h a s c o n c e n t r a t e d o n d e s c r i b i n g a s i n g l e v a r i a b l e a s c l e a r l y a s p o s s i b l e .
I n C h a p t e r 6 , m e t h o d s o f m a k i n g t a b l e s a n d d i a g r a m s s h o w i n g t h e re l a t i o n s h i p s
b e t w e e n t w o o r m o re v a r i a b l e s a re d e s c r i b e d .
 􀁺 Tr y t o m a k e y o u r t a b l e s a n d d i a g r a m s u s e f u l . I t i s n o t u s u a l l y t h e i r p u r p o s e t o r e c o r d t h e d a t a a s
y o u c o l l e c t e d i t i n y o u r re s e a rc h . O f c o u r s e y o u c a n l i s t y o u r d a t a i n t h e a p p e n d i x o f p ro j e c t s t h a t
y o u c a rr y o u t , b u t t h i s i s n o t u s e f u l a s a w a y o f i l l u s t r a t i n g t re n d s . I t i s p a r t o f a re s e a rc h e r ’ s j o b
t o m a ke t h e d a t a a c c e s s i b l e t o t h e re a d e r i n a s t r u c t u re d f o rm t h a t i s e a s i l y u n d e r s t o o d b y t h e
 r e a d e r.
􀁺 E s p e c i a l l y w h e n u s i n g c o m p u t e r s , i t i s v e r y e a s y t o g e n e r a t e u s e l e s s t a b l e s a n d d i a g r a m s . T h i s i s
u s u a l l y b e c a u s e c o m p u t e r a n a l y s i s e n c o u r a g e s y o u n o t t o ex a m i n e y o u r r a w d a t a i n a n y d e t a i l . T h i s
 i m p l i e s t h a t y o u s h o u l d a l w a y s r e g a r d y o u r fi r s t a n a l y s e s a s t e n t a t i v e a n d m e r e l y a s t e p t o w a r d s
 s o m e t h i n g b e t t e r.
􀁺 I f a t a b l e i s n o t c l e a r t o y o u , i t i s u n l i ke l y t o b e a n y c l e a re r t o a n y o n e e l s e .
􀁺 C h e c k e a c h t a b l e a n d d i a g r a m f o r c l e a r a n d f u l l l a b e l l i n g o f e a c h p a r t . E s p e c i a l l y , c h e c k t h a t
frequencies
a re c l e a r l y m a r ke d a s s u c h .
􀁺 C h e c k t h a t t h e re i s a c l e a r , h e l p f u l t i t l e t o e a c h t a b l e a n d d i a g r a m .