presentation of datain qualitative data we are counting the number of observations in each category....

PRESENTATION OF DATATabular presentation

Data summarizationIs the organization of data in a way for easy

understanding.

It is the first step of data interpretation (analysis).

Consists of the following steps:

1) Data entering.

2) Ordered array.

3) Summarization

Data entering

Generally, computers are used for data entry.

Nowadays, many software are developed for data entering, presentation and data analysis.

Examples of statistical software:

MS Excel.

Epi-Info.

SPSS.

Stata.

Ordered array

It is the first step in the process of data organization after data entering.

An ordered array is a listing of values from the smallest value to the largest value.

It enables one to determine quickly the largest and smallest measurements.

It also enables to determine roughly proportion of people lying below and above certain value.

FREQUENCY DISTRIBUTIONTABLES

It determines the number of observations falling into each class

In qualitative data we are counting the number of observations in each category. These counts are called frequencies. And they are also presented as relative percentages of the total numbers.

In quantitative data frequencies can be counted by grouping data into equal intervals and counting frequency of event in each interval.

GROUPING DATA

To group a set of observations, we selecta set of contagious, non overlappingintervals, such that each value in the set ofobservation can be placed in one intervalonly, and no single observation should bemissed. The interval is called:

CLASS INTEVAL.

NUMBER OF CLASS INTERVALS

The number of class intervals should not

be too few because of the loss of important

information, and not too many because of

the loss of the needed summarization


When there is a priori classification of

that particular observation we can follow

that classification.

But when there is no such classification we

can follow the Sturge's Rule


Sturge's Rule:

k=1+3.322 log n

k= number of class intervals

n= number of observations in the set

The result should not be regarded as final,

modification is possible

WIDTH OF CLASS INTERVAL

The width of the class intervals should be the same, if possible.

RW=--------

K

W= Width of the class intervalR= Range (largest value – smallest value)K= Number of class intervals

RELATIVE FREQUENCY DISTRIBYTION

It determines the proportion of observation

in the particular class interval relative to the

total observations in the set.

CUMULATIVE FREQUENCY DISTRIBUTION This is calculated by adding the number of

observation in each class interval to the number of observations in the class interval above, starting from the second class interval onward.

CUMULATIVE RELATIVE FREQUENCY DISTRIBUTION

This is calculated by adding the relative

frequency in each class interval to the relative

frequency in the class interval above, starting

also from the second class interval onward.

CUMULATIVE DISTRIBUTION

Cumulative frequency and cumulative relative

frequency distributions are used to facilitate

obtaining information regarding the frequency or

relative frequency within two or more contagious

class intervals.

The following arethe number ofhours of 45 patientsslept following theadministration of acertain hypnoticdrug:

107717

23101212

57834

113158

513713

43171710

344411

57785

881813

Construct a table showing:

Frequency

Relative frequency

Cumulative frequency

Cumulative relative frequency distribution.

Number of class intervals:

K=1+3.322 log n

=1+3.322 log45

=1+3.322 X 1.653

=6.4

=6

Width of class interval:

R 17-1

W=------= ------- = 2.7 = 3

K 6

CUM.REL.

FREQUENCY

%

CUMULATIVE

FREQUENCY

RELATIVE

FREQUENCY

%

FREQUENCYCLASS

INTERVAL

(hour)

24.41124.4111-3

46.62122.2104-6

75.5 3428.9137-9

91.14115.6710-12

95.5434.4213-15

99.9454.42 16-18

99.945Total

The following are the weight (in ounces)

of malignant tumours removed from the

abdomen of 57 subjects:

28513641163112212211681

25521942243232222312632

45534643693349232413423

12543044473438242514274

57554345233542254415305

51564946223627266516366

23571247433731274317287

4248273850282518328

2849493938297419799

31502840213051202710

Construct a table showing :

Frequency

Relative frequency

Cumulative frequency

Cumulative relative frequency

Number of class intervals:K=1+3.322 log n

=1+3.322 log 57=1+3.322 X1.76= 6.8.3 = 7

Width of class interval:R 79-12 67

W=---------= ------------=-----------= 9.6 = 10K 7 7

Cum.Rel

Freq%

Rel.Freq

%

Cum.FreqFrequencyClass

interval

8.778.775510-19

42.1033.33241920-29

59.6417.54341030-39

82.4522.81471340-49

89.477.0251450-59

96.497.0255460-69

100.003.5157270-79

100.0057TOTAL

Tabular presentation

Presentation of data in tables so as to organize the data into a compact, concise and readily comprehensible form.

They can display the characteristics of data more efficiently than the raw data.

Types

Simple Table : including one variable (quantitativeor qualitative ) and the corresponding frequency

Cross tabulation: (Two–dimensional tables), twovariables are cross classified

Contingency table: demonstrating the relationshipbetween two or more variables

Graphical and Pictorial presentation of data

The use of diagrams or pictures to display distribution or characteristics of one or more sets of data in a compact and readily comprehensible form.

They can provide a better visual appreciation of characteristics of data than tabular presentation

Graphs

It is a pictorial display of quantitative data using a coordinate system , where the X is the horizontal axis and the Y is the vertical axis.

X-axis usually includes the independent variable (method of classification)

Y-axis includes the dependant variable

( frequency or relative frequency or other indicator)

Stem-and-Leaf Plot

Summarizes quantitative data.

Each data point is broken down into a “stem” and a “leaf.”

First, “stems” are aligned in a column.

Then, “leaves” are attached to the stems.

Stem-and-Leaf Plot

Stem-and-leaf of Shoes N = 139 Leaf Unit = 1.0

12 0 223334444444

63 0

555555555555566666666677777778888888888888999999999

(33) 1 000000000000011112222233333333444

43 1 555555556667777888

25 2 0000000000023

12 2 5557

8 3 0023

4 3

4 4 00

2 4

2 5 0

1 5

1 6

1 6

1 7

1 7 5

Histogram

Graphical display of frequency distribution of quantitative variable .

The values of the quantitative variable( as class interval) will be placed on the X-axis

( representing the width of the rectangles), and the corresponding frequency (or relative frequency) will be placed on the Y-axis (representing the height of the rectangles)

Histogram

The area is proportional to the height, and the frequencies in different categories can be directly compared by examining the relative height of the respective bar.

It is important that the class interval should be equal, otherwise the area should be compared.

Only one set of data can be shown in one histogram

Frequency Polygon

Another form of graphical presentation of frequency distribution of quantitative variables.

It is similar to the histogram , but instead of using rectangles to present data, the midpoint of the top of each rectangle are plotted , and connected together by straight lines.

Frequency Polygon

More than one set of data can be demonstrated on the same graph, to facilitate direct comparison.

It provides information about underlying characteristics of data .

The area under the frequency polygon is equal to the area under the equivalent histogram

Scatter diagram

A pair of measurements is plotted as a single point on a graph.

The value of one variable of each pair is plotted on the X axis and the value of the other variable is plotted on the Y axis

Scatter diagram

The pattern made by the plotted points is

indicative of the relationship between these

two variables, which might be linear (if they

follow straight line) or curvilinear (if the

pattern doesn't follow straight line)

Scatter diagram

A scatter diagram could suggest: No relationship: when one variable changes

with no change in the other variable ,or when the pattern is buzzard

Linear relationship: an increase in the 1st variable is associated with an increase (positive) or decrease (negative) in the 2nd variable, and the pattern follows a straight line.

Curvilinear (positive or negative) relationship: the pattern of increase or decrease will not follow a straight line .

0

0.5

1

1.5

2

2.5

3

0 1 2 3 4

l/m

in

l/min

correlation of two methods of cardiac output measurments

Series1

Bar chart

Used to present discrete or qualitative data

It includes separated bars of equal width

The method of classification of the variable is usually placed on the X-axis, and the Y-axis usually represents the corresponding frequency or relative frequency.

Bar chart

It can be used to present more than one set of data simultaneously using different colors , shades,... In this case a key should be used

Comparison will be made on the basis of the height of the bar (frequency). i.e.: the width of the bar has no value

It is important that the vertical axis should start at the zero, otherwise the heights of the bars are not proportional to the frequencies.

Estimated Direct and Indirect Costs of

Cardiovascular Diseases and Stroke

United States: 2005

Source: Heart Disease and Stroke Statistics – 2005 Update.

254.8

142.1

56.8 59.727.9

393.5

0

50

100

150

200

250

300

350

400

450

Heart

Dis

ease

Coro

nary

Heart

Dis

ease

Str

oke

Hypert

ensiv

e

Dis

ease

Congestive

Heart

Failu

re

Tota

l C

VD

*

Bil

lio

ns o

f D

oll

ars

434

289

69 6134

494

269

64 42 39

0

100

200

300

400

500

A B C D E A B D F E

Males

Females

Deaths in Thousands

Leading Causes of Death for

All Males and Females United States: 2002

A Total CVD

(Preliminary)

B Cancer

C Accidents

D Chronic Lower Respiratory Diseases

E Diabetes Mellitus

F Alzheimer’s Disease

Source: CDC/NCHS

Fig 3: Distribution of unvaccinated children below one year by governorates

0%

5%

10%

15%

20%

25%

30%

35%

Baghda

d

Anbar

Babylon

Was

sit

Basrah

Ninev

ah

Miss

an

Qadi

siya

Diyala

Kerbala

Taamem

Muthan

a

Thi q

ar

Najaf

Salah

Al Din

Suleim

aniya

Erbil

Duh

ok

Total

Governorates

% o

f u

nvaccin

ate

d c

hild

ren

Component bar chart

It is a type of charts based on proportion.

It uses bars that are either shaded or colored to show the relative contribution of each of its components

Fig 9: Reason for unvaccination for unvaccinated children

by governorates

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

Baghd

ad

Babylon

Basra

h

Missa

n

Diyala

Taam

em

Thi q

ar

Salah

Al d

inErb

il

Total

Governorates

% of other causes

% of the child abscent

% of not visited byvaccination team

<40 40-49 50-59 60-69 70-79 80+

Age (y)

17% 16% 16% 20% 20% 11%

Distribution of Hypertension Subtype in the untreated

Hypertensive Population in NHANES III by Age

ISH (SBP 140 mm Hg and DBP <90 mm Hg)

SDH (SBP 140 mm Hg and DBP 90 mm Hg)

IDH (SBP <140 mm Hg and DBP 90 mm Hg)

0

20

40

60

80

100

Numbers at top of bars represent the overall percentage distribution of untreated hypertension by

age.

Franklin et al. Hypertension 2001;37: 869-874.

Frequency of

hypertension

subtypes in all

untreated

hypertensives

(%)

POL-WARLTU-KAU

RUS-NOCUNK-GLA

FIN-NKARUS-NOI

RUS-MOC

CZE-CZEYUG-NOSRUS-MOI

BEL-CHAFRA-LIL

POL-TAR

FIN-KUOUNK-BELFIN-TUL

FRA-STRGER-EGE

ITA-FRI

GER-BREBEL-GHEUSA-STA

DEN-GLOGER-AUGSWE-GOT

NEZ-AUCITA-BRI

AUS-NEW

CAN-HALSWI-VAFICE-ICE

SWE-NSSWI-TIC

AUS-PER

FRA-TOUSPA-CATCHN-BEI

0 500 1000 1500 2000

Annual mortality rate per 100 000

CHD

Stroke

Other CVD

Non CVD

Men

UNK-GLA

POL-WARLTU-KAU

USA-STA

DEN-GLO

BEL-CHA

RUS-NOC

YUG-NOS

CZE-CZE

UNK-BELRUS-MOC

BEL-GHE

GER-EGE

RUS-NOI

RUS-MOI

NEZ-AUC

POL-TARFRA-LIL

AUS-NEW

CHN-BEI

CAN-HAL

GER-BRE

FIN-NKA

SWE-GOT

FIN-KUOITA-FRI

GER-AUG

FIN-TUL

FRA-STR

ICE-ICE

AUS-PER

ITA-BRISWE-NS

FRA-TOU

SPA-CAT

0 250 500 750 1000

Annual mortality rate per 100 000

Women

G3

Distribution of coronary risk factors among patients with chronic metabolic syndrome

48.8

27.5

53.866.3

93.1

17.5

010203040506070

8090

100

Rel

ativ

e fre

quen

cy (%

)

Hype

rtens

ion

Diabe

tes M

ellitu

s

Family

histo

ry of

ische

mic Hea

rt Di...

Smok

ing ha

bit

Dyslip

idemia

Obesit

y

Pictograms

It uses series of small identifying symbols to present the data. Each symbol represents a fixed number of units

Pie chart

It is a type of charts based on proportion

It uses wedge-shaped portions of a circle to illustrate the relative contribution of each part to the total (division of the whole into segments)

Pie chart

To demonstrate the angel of each wedge , we multiply the relative frequency of each division by 360 degrees.

Start at 12 o’clock,

It is preferable to arrange segments in order of their magnitude (starting with the largest), and proceed clockwise around the chart.

Percentage Breakdown of Deaths From

Cardiovascular DiseasesUnited States:2002 Preliminary

Source: CDC/NCHS.

18%

6%

5%

4%

0%0%

13%

53%

Coronary Heart Disease

Stroke

Congestive Heart Failure

High Blood Pressure

Diseases of the Arteries

Rheumatic Fever/Rheumatic

Heart Disease

Congenital Cardiovascular

Defects

Other

Most Myocardial Infarctions Are Causedby Low-Grade Stenoses

Pooled data from 4 studies: Ambrose et al, 1988; Little et al, 1988; Nobuyoshi et al, 1991; and Giroud et al, 1992.

(Adapted from Falk et al.)

Falk E et al, Circulation, 1995.

Box Plot

Summarizes quantitative data.

Vertical (or horizontal) axis represents measurement scale.

Lines in box represent the 25th percentile (“first quartile”), the 50th percentile (“median”), and the 75th percentile (“third quartile”), respectively.

Box and whisker plot

Largest non-outlying value

Upper

quartile

Lower

quartile

Smallest non-outlying value

*

oOutlying value

Extreme outlying value

Median

Box Whiskers

Outlying values

Box Plot

0

1

2

3

4

5

6

7

8

9

10

Hours

of sle

ep

Amount of sleep in past 24 hours

of Spring 1998 Stat 250 Students

Map charts

These are used to present the geographical distribution of one or more sets of data

Change in coronary event rate

Change in MONICA CHD mortality

Change in case fatality

Significant increase

Insignificant change

Significant decrease

Men

G24

Suggestions for the design and use of tables, graphs, and charts Choose the method most effective for data and

purpose

Point out one idea at a time

Limit the amount of data and include one kind of data in each presentation

Use adequate , properly located titles and labels

Mention the source , if it is not yours

Care and caution in proposing conclusions

Exercise

The following are the DBP measurements (mmHg) of 60 individuals.

Make a suitable graphical or pictorial presentation

No.DBP (mmHg)

365-69

570-74

975-79

1880-84

1385-89

990-94

395-99

60Total

DBP (mmHg) of 60 men

0

5

10

15

20

65-

69

70-

74

75-

79

80-

84

85-

89

90-

94

95-

99

years

No

.

Series1

Exercise

The following are the proportions of the commonest ten cancers in Iraq, 1995


% of total CAPrimary site

14.3Breast

11.2Bronchus &lung

7.4Urinary Bladder

6.2Non-Hodgkin

Lymphoma

5.9Larynx

5.2Leukemia

4.8Brain & other CNS

4.3Skin

3.6Stomach

3.0Hodgkin Lymphoma

Commonest 10 Ca in Iraq

02468

10121416

Bre

ast

Bro

nch

us

Uri

na

ry

No

n-

La

ryn

x

Le

uke

mia

Bra

in &

Skin

Sto

ma

ch

Ho

dg

kin

CA site

% o

f to

tal C

A

Series1

Exercise

The following is the distribution of TB cases registered in City X.


No.Type of TB

360Smear +ve PTB

240Smear –ve PTB

200Extra PTB

800Total

Types of TB

Smear +ve PTB

Smear –ve PTB

Extra PTB

Exercise

The following is the distribution of meningitis cases , Ibn Al-Khateeb Hospital, 1999.


TotalFemale

No.

Male

No.

Agent

25284168Viral

1264284Bacterial

422121TB

420147273Total

0%

20%

40%

60%

80%

100%

Viral Bacterial TB

%

type

Meningitis cases by type and sex

Series2

Series1

presentation of datain qualitative data we are counting the number of observations in each category....

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