TABEL DATA YANG BERTUJUAN UNTUK SIMPLIFIKASI
ANALISIS STATISTIK BERURUSAN DENGAN DATA
MENTAH.
BAGAIMANA MELAKUKAN STRUKTURISASI SEHINGGA
DATA TERSEBUT DAPAT DIKOMUNIKASI SECARA
EFEKTIF.
TABEL DAN DIAGRAM HARUS JELAS DAN AKURAT DAN
Desc ri pti ve statisti cs are, by and large, rel ative ly si mpl e visual and
numeri cal tec hni ques
for descr ibing the major feature s of one’s data. Researchers m ay produc e
desc riptive
statistic s i n orde r to c omm uni cat e the major c harac ter istic s of the data t o
other s,
but in the fi rst instance they are used by resea rc her s themse lves i n order
to under stand
the distr ibution of partic ipant s’ responses in the researc h. Never rega rd
desc riptive
statistic al analysis as an unnec essary or tr ivial stage i n researc h. I t i s
proba bly more
informative tha n any other aspect o f data anal ysis. Box 2 .2 expla ins t he
cr uc ial role of
desc riptive statistic s i n researc h further.
The distinct ion between nominal (category) data and numerical scores
discussed in the
previous cha pter is importa nt in term s of the appropriate tables and
diagra ms 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
■ 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
t e n s i f n o t h u n d re d s o f d i ff e re 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 re v e a l i m p o r t a n t t re n d s . Fo r ex a m p l e , s i n c e t h e re s e a rc h i s
a b o u t
a h e a l t h i s s u e y o u m i g h t w i s h t o f o rm a c a t e g o r y m a d e u p o f t h o s e i n v o l v e d i n h e a l t h w o r k – s o m e m i g h t b e d e n t i s t s , s o m e n u r s e s , s o m e d o c t o r s , s o m e p a r a m e d i c s a n d s o
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 re 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 re n o h a rd - 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 rm
b ro a d e r c a t e g o r i e s . T h e f o l l o w i n g m i g h t b e u s e f u l r u l e s o f t h u m b :
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 re 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
Slices for a pie diagram
There is nothing diffi cult in constructing a pie diagram. Our
recommendation is that you turn each of your frequencies
into a percentage frequency. Since there are 360 degrees in a
circle, if you multiply each percentage frequency by 3.6
you will obtain the angle (in degrees) of the slice of the pie
which you need to mark out. In order to create the diagram,
you will require a protractor to measure the angles. However,
computer graph packages are standard at any university
or college and do an impressive job.
In Table 2.1, 25.00% of cases were students. In order to turn
this into the correct angle for the slice of the pie, you
simply need to multiply 25.00 by 3.6 to give an angle of 90
degrees.
One advantage of using computers is that they enable
experimentation with diff erent
schemes of categorising data in order to decide which is best for
your purposes. In this
case, you would use initially narrow categories for coding your
data. Then you can tell
the computer which of these to combine into broader categories.
Sometimes it is preferable to turn frequency tables into
diagrams. Good diagrams
are quickly understood and add variety to the presentation. The
main types of diagram
for nominal (category) data are
pie diagrams
and
bar charts
. A
pie diagram is a very
familiar form of presentation – it simply expresses each category
as a slice of a pie which
N o tic e th at th e
number of slic es is small – a multitude of slic es can be
c o nfusing. Ea ch
sli ce is c lear ly ma rked with i ts ca teg or y na me, a nd the percenta ge
frequenc y in ea ch
c a teg o ry a lso a ppea rs.
C H AP TER 2
DESCR IB IN G VAR IA BLES
1 7
l eg end o r key to identi fy the c o mp on ents to h el p c ope with th e ov ercro wdi ng
p ro bl em. In o th er wo rds, to o ma ny c a tego r ies ha v e resulted in a di agr am
w hic h is
fa r fro m ea sy to rea d – a ca rdina l si n in a ny stati stic al dia gr am.
A simple frequency ta ble migh t be mo re eff ec ti ve in this ca se.
A no ther ver y fa mi lia r fo rm o f sta tisti ca l dia gra m fo r no mina l (ca teg o ry) da ta
i s
th e
bar chart . Again these charts are very c ommon in the media. Basic ally
th ey a re
d ia gra ms in w hic h ba rs represent the siz e o f eac h c a tego r y. An exa mple is
sho w n in
The relative lengths (or heights) of the bars quickly reveal the main
trends in the data.
With a bar chart, there is very little to remember other than that the
bars have a standard
space separating them. The spaces indicate that the categories are
not in a numerical
order; they are frequencies of categories,
not scores.
It is hard to go wrong with a bar chart (that is not a challenge!) so
long as you
remember the following:
1. The heights of the bars represent frequencies (number of cases) in
a category.
2. Each bar should be clearly labelled as to the category it represents.
3. Too many bars make bar charts hard to follow.
FIGURE 2.3
A poor pie diagram
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 re p re s e n t v e r y f e w c a s e s . G e n e r a l l y , t h e i n f o rm a t i o n a b o u t s u b s t a n t i a l c a t e g o r i e s i s t h e m o s t i m p o r t a n t . ( S m a l 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 v e r t h e l e s s , i f i m p o r t a n t c a t e g o r i e s h a v e v e r y f e w e n t r i e s t h e n t h i s n e e d s re c o rd i n g .
S o , f o r e x a m p l e , a re s e a rc h e r w h o i s p a r t i c u l a r l y i n t e re s t e d i n o p p o r t u n i t i e s f o r 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 s u c h j o b s . I t i s i m p o r t a n t t o d r a w a t t e n t i o n t o t h i s i n t h e b a r c h a r t o f m a l e s a n d
f e m a l e s i n t o p m a n a g e m e n t . O n c e a g a i n , t h e re a re n o h a rd - a n d - f a s t r u l e s t o g u 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 f re q u e n c i e s o r p e rc e n t a g e f re q u e n c i e s .
7 . T h e b a r s s h o u l d b e o f e q u a l w i d t h .
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 re l i ke l y t o c o m e a c ro s s a v a r i a n t o f t h e b a r
c h a r t c a l l e d t h e p i c t o g r a m. I n t h i s , t h e b a r s o f t h e b a r c h a r t a re re p l a c e d b y v a r y i n g s i z e d
d r a w i n g s o f s o m e t h i n g e y e - c a t c h i n g t o d o w i t h y o u r c a t e g o r i e s . T h u s , p i c t u re s o f 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 , re p l a c e t h e b a r s . Pi c t o g r a m s a re r a re l y u s e d i n p ro f e s s i o n a l p re s e n t a t i o n s . T h e m a i n re a s o n i s t h a t p i c t u re s o f t h i n g s g e t w i d e r a s w e l l
a s t a l l e r a s t h e y i n c re a s e i n s i z e . T h i s c a n m i s re p re s e n t t h e re l a t i v e s i z e s o f t h e c a t e g o r i e s ,
■ 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 re d a t a
O n e c r u c i a l c o n s i d e r a t i o n w h e n d e c i d i n g w h a t t a b l e s a n d d i a g r a m s t o u s e f o r s c o re d a t a
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 re c o rd 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 v a r y
m a r ke d l y. S o , f o r ex 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 ro m n e w l y b o rn
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 re l y re c o rd e d a g e s t o t h e n e a re s t w h o l e y e a r
t h e n 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 re 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 w o u l d
l o o k h o rre n d o u s . I f w e re c o rd e d a g e t o t h e n e a re s t m o n t h , t h e n w e c o u l d m u l t i p l y
t h i s
n u m b e r o f a g e s b y 1 2 ! S u c h s c o re s c a n b e g ro u p e d i n t o b a n d s o r r a n g e s o f s c o re s
t o
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 ) .
M a n y p s y c h o l o g i c a l v a r i a b l e s h a v e a m u c h s m a l l e r r a n g e o f n u m e r i c a l v a l u e s . S o , f o r ex a m p l e , i t i s f a i r l y c o m m o n t o u s e q u e s t i o n s w h i c h p re - s p e c i fy j u s t a f e w
re s p o n s e
a l t e rn 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 re 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 :
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 rm o f s t a t i s t i c a l d i a g r a m t o re p re s e n t t h e s e d a t a . At
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
b a r s .
T h i s i s b e c a u s e t h e h i s t o g r a m d o e s n o t re p re s e n t d i s t i n c t u n re l a t e d c a t e g o r i e s b u t
d i ff e re 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 re 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 ro 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
q u e s t i o n ?
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 re s e a rc h i s t h a t t h e n u m b e r o f
re 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 rg e n u m b e r o f p o s s i b l e d i ff e re 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 re f o re s h a re d b e t w e e n v e r y f e w re 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
s h o u l d
p re 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 rm . S o , s o m e t i m e s
y o u w i l l h a v e t o u s e b a n d s o f s c o re s r a t h e r t h a n i n d i v i d u a l s c o re v a l u e s , j u s t a s
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
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 rd 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 re e 1 1 7 A g re e 2 1 4
N e i t h e r a g re e n o r d i s a g re e 3 6
D i s a g re e 4 2
S t ro n g l y d i s a g re e 5 1
F I G U R E 2 . 5 H i s t o g r a m o f s t u d e n t s ’ a t t i t u d e s t o w a rd s s t a t i s t i c s 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
p a r t s
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 re 2 . 6 ) .
H o w o n e c h o o s e s t h e b a n d s t o u s e i s a n i m p o r t a n t q u e s t i o n . T h e a n s w e r i s a b i t
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 rro 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 t h e r a n g e s o f t h e b a n d s w h e n o n e i s a n a l y s i n g t h e d a t a b y h a n d . O n e b i g a d v a n t a g e
o f
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 re 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 t a b l e s w h i c h s e e m t o d o t h e j o b a s w e l l a s p o s s i b l e . T h e c r i t e r i o n i s s t i l l w h e t h e r t h e
t a b l e
T h e o n e r u l e i s t h a t t h e b a n d s o u g h t t o b e o f t h e sa m e s i z e – t h a t i s c o v e r , f o r ex a m p l e , e q u a l r a n g e s o f s c o re s . G e n e r a l l y t h i s i s e a s y exc e p t a t t h e u p p e r a n d
l o w e r
e n d s o f t h e d i s t r i b u t i o n . Pe rh a p s y o u w i s h t o u se ‘ o v e r 7 0 ’ a s y o u r u p p e r r a n g e .
T h i s,
i n m o d e rn p r a c t i c e , c a n b e d o n e a s a b a r o f t h e sa m e w i d t h a s t h e o t h e r s , b u t m u s t b e
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
t h e
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 , t h i s i s
r a re l y d o n e i n m o d e rn p sy 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 st 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 re 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 si m p l e p re s e n t a t i o n F I G U R E 2 . 7 H i s t o g r a m s h o w i n g ‘ c o l l a p s e d ’ c a t e g o r i e s
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
2 . 3 E r r o r s t o a v o i d
T h e r e a r e a c o u p l e o f m i s t a k e s t h a t y o u c a n m a k e 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 r g 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 r e 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 r e 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 r e 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 r e v a r i a b l e s a r e 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 r e s e a r c 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 r o j e c t s t h a t
y o u c a r r 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 r e n d s . I t i s p a r t o f a r e s e a r c h e r ’ s j o b
t o m a k e t h e d a t a a c c e s s i b l e t o t h e r e a d e r i n a s t r u c t u r e d f o r m 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 e x 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 k e l y t o b e a n y c l e a r e 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 f r e q u e n c i e s
a r e c l e a r l y m a r k e d a s s u c h .
