biostatist

PracticalPresentation of data

Types of Tables:
Simple Table :including one variable (quantitative or qualitative ) and the corresponding frequencyCross tabulation: Two–dimensional tables: two variables are cross classified Three-dimensional tables: three variables are cross-classified (eg. outcome of treatment by age and sex) Contingency table: demonstrating the relationship between two or more variables. observations on a number of categorical variables are cross-classified.

3-Graphical and Pictorial presentation of data 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 dependent variable (frequency or relative frequency or other indicator)

Arithmetic scale line graph:

This is particularly beneficial to present the trend of one or more sets of data. In general the Y-axis is 2/3 the X-axis An equal distance represents an equal quantity anywhere on an axis. The slop of the line indicates the rate of increase or decrease Two or more lines following a parallel path indicate identical rates of increase or decrease

Trends in Cardiovascular Operations & Procedures United States: 1979-2002

Source: CDC/NCHS.


Histogram: This is a graphical presentation of frequency distribution in which rectangle proportional in the area to the frequencies are erected on the horizontal axis. The base lines are continuous (because we are dealing with continues variables). The width of the rectangles should be equal.

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)


Criteria of 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

More than one set can be demonstrated on the same graph, to direct comparison. It is only appropriate when the variables on the horizontal axis are continues. It provides information about underlying characteristics of data . The area under the frequency polygon is equal to the area under the equivalent histogram.

Frequency Polygon

Frequency Polygon

Cumulative frequency polygon, & cumulative frequency charts

The cumulative frequency are plotted against the upper tabulated value for each class . It is used to estimate by interpolation the frequency of occurrence of a value of the variable less than or equal to a specified value.


<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


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 (%)

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

Showing the relation

A single and effective form to examine the relation between two quantitative variables is using a scattered points graph. Each point correspond at one subject.

Scatter diagram

The pattern is indicative of the relationship between two variables, which might be linear (if they follow straight line) or curvilinear (if the pattern doesn't follow straight line)

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 .



Diagrammatic "Graphical“ or "Figure“: For categorical data Bar chart; This is a graphical presentation of the (relative) frequencies or magnitudes by rectangles of constant width drawn with length proportional to the (relative) frequencies or magnitudes concerned.

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.

Criteria of 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.

Representing the simple frequency table using the bar chart

We can represent the simple frequency table using the bar chart.


Estimated Direct and Indirect Costs of Cardiovascular Diseases and Stroke United States: 2005
Source: Heart Disease and Stroke Statistics – 2005 Update.

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 DiseasesE Diabetes MellitusF Alzheimer’s Disease Source: CDC/NCHS

Component bar chart:

It is a type of charts based on proportion. A bar chart that shows the component parts of the aggregate represented by the total length of the bar. It uses bars that are either shaded or colored to show the relative contribution of each of its components


Picto-gram ((Picto-chart)): This is a graphical representation of the (relative) frequencies by using symbols (drawing or picture) relevant to the subject matter. Symbols of different size should not be used. A unit value of the data should be represented by standard symbol which may repeat to represent magnitude, Each symbol represents a fixed number of units.

Pictograms

Pie chart: This is a graphical presentation of the  (relative) frequencies or magnitudes by a circle whose area represent the total  frequency and which is divided into  segments which represent the proportional  composition of total frequency.

Pie chart

It is mostly used in presentation of qualitative data. It is a type of charts based on proportionIt uses wedge-shaped portions of a circle to illustrate the relative contribution of each part to the total (division of the whole into segments).To demonstrate the angle 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.

Most Myocardial Infarctions Are Caused by 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.)

Map charts:

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



Flow chart
It is used to illustrate the sequence of a series of events. It is characterized by multiple arrows

Development of Atherosclerotic Plaques

Normal
Fatty streak
Foam cells
Lipid-rich plaque
Lipid core
Fibrous cap
Thrombus
Ross R. Nature. 1993;362:801-809.

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

Exercise (1)

The followings are the DBP measurements (mmHg) of 60 individuals. Make a suitable graphical or pictorial presentation
No.
DBP (mmHg)
3
65-69
5
70-74
9
75-79
18
80-84
13
85-89
9
90-94
3
95-99
60
Total

Exercise (2)

The following are the proportions of the commonest ten cancers in Iraq, 1995 Make a suitable graphical or pictorial presentation
% of total CA
Primary site
14.3
Breast
11.2
Bronchus &lung
7.4
Urinary Bladder
6.2
Non-Hodgkin Lymphoma
5.9
Larynx
5.2
Leukemia
4.8
Brain & other CNS
4.3
Skin
3.6
Stomach
3.0
Hodgkin Lymphoma

Exercise (3)

The following is the distribution of TB cases registered in City X. Make a suitable graphical or pictorial presentation
No.
Type of TB
360
Smear +ve PTB
240
Smear –ve PTB 200
Extra PTB
800
Total

Exercise (4)

The followings are the distribution of meningitis cases by their cause , Ibn Al-Khateeb Hospital, 1999. Make a suitable graphical or pictorial presentation
Total
Female No.
Male No.
Agent
252
84
168
Viral
126
42
84
Bacterial
42
21
21
TB
420
147
273
Total