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Biostatistics Presentation of data DR. AMEER KADHIM HUSSEIN M.B.CH.B.FICMS (COM.)
Biostatistics
Presentation of data
DR. AMEER KADHIM HUSSEIN
M.B.CH.B.FICMS (COM.)
PRESENTATION OF DATA
1. Mathematical presentation (measures of
central tendency and measures of
dispersion).
2. Tabular presentation.
3. Graphical presentation.
4. Pictorial presentation.
(Map chart).
TABULAR PRESENTATION
Presentation of data in tables make them
into a compact, concise and readily
comprehensible form. They can display
the characteristics of data more efficiently
than the raw data.
TYPES OF TABLES
1.Simple Table including one variable (quantitative or
qualitative) and the corresponding frequency.
2. Cross tabulation is a tabular method for simultaneously
summarizing the data for two
categorical variables.
CRITERIA FOR PROPER TABLE
1.Simple. 2.Understandable and self explanatory (all symbols should be explained in details in a foot note,each row or column should be labeled clearly, units of the data should be clearly mentioned,the title should be clear, precise, and should answer the questions, what? where? and when? and totals should be shown. 3.The title should be separated from the body of the table by lines or spaces. 4.Avoid too much ruling. 5.If the data are not original, their source should be mentioned as a foot note or in the title.
GRAPHICAL AND PICTORIAL
PRESENTATION
The use of diagrams or pictures to describe the
distribution or characteristics of one or more
sets of data in a compact and readily
comprehensible form. They can provide a
better visual presentation
of characteristics of data than
tabular presentation.
1. Vertical and horizontal scales should be clearly
labeled and units identified.
2. Keep graphs as simple as possible – avoid too
many bars or lines – two or three is appropriate –
more than four is probably too many.
3. Graphs are designed to provide a “snapshot” of
the results – use tables for details.
4. Avoid presentation of numbers
in the body of a graph.
Criteria For proper graph
Qualitative Data:
Tabular presentation include:
1. Frequency distribution.
2. Relative frequency distribution.
3. Percent frequency distribution.
4. Cross tabulation.
Graphical presentation include:
1.Bar chart.
2. Pie chart.
Tabular and Graphical Presentation of data
Quantitative data
Tabular presentation include:
1. Frequency distribution.
2. Relative frequency distribution.
3. Cumulative frequency.
4. Cumulative relative frequency.
Graphical presentation include:
1. Histogram.
2. Frequency polygon.
3. Scatter diagrams.
4. Line graph.
Tabular and Graphical Presentation of data
Qualitative Data
Frequency: It determines the number of
observations falling into each category.
Relative frequency: It determines the proportion
of observation in the particular class relative to
the total observations.
A relative frequency distribution
is a tabular summary of a set of data showing the
relative frequency for each class.
The percent frequency of a class is the relative
frequency multiplied by 100.
FREQUENCY DISTRIBUTION
FREQUENCY DISTRIBUTION
Example:
A sample of 10 students were examined by
certain teacher and the results of examination
was as below:
1. good 2. very good 3. good
4. excellent 5. poor 6. very good
7. good 8. poor 9. excellent
10. poor
FREQUENCY DISTRIBUTION
Frequency Results
3 poor
3 good
2 Very good
2 excellent
10 Total
RELATIVE FREQUENCY AND PERCENT
FREQUENCY DISTRIBUTION
Percent
frequency
Relative
frequency Results
30% 0.3 poor
30% 0.3 good
20% 0.2 Very good
20% 0.2 excellent
100% 1 Total
BAR GRAPH
A bar graph is a graphical device for depicting qualitative data. On the horizontal axis we specify the labels that are used for each of the classes. A frequency, relative frequency, or percent frequency scale can be used for the vertical axis. Using a bar of fixed width drawn above each class label, we extend the height appropriately. The bars are separated to emphasize the fact that each class is a separate category.
BAR GRAPH
0%
10%
20%
30%
PoorGood
Very goodExcellent
30% 30%
20% 20%
PIE CHART
The pie chart is a commonly used graphical device for presenting relative frequency distributions for qualitative data. First draw a circle; then use the relative frequencies to subdivide the circle into sectors that correspond to the relative frequency for each class. Since there are 360 degrees in a circle, a class with a relative frequency of 0.25 would consume 0.25(360) = 90 degrees of the circle.
PIE CHART
30%
30%
20%
20%
Poor
Good
Very good
Excellent
CROSS-TABULATIONS
Cross-tabulation : is a tabular method for simultaneously summarizing the data for two categorical variables. Steps for Constructing a Cross-tabulation
1. Put the categories of one variable at the top of each column, and the categories of the other variable at the beginning of each row.
2. For each row and column combination, enter the number of observations that fall in the two categories.
3.The bottom of the table gives the column totals, and the right-hand column gives the row totals.
CROSS-TABULATIONS
Total
Group
Gender Control Case
40 10 30 Male
60 40 20 Female
100 50 50 Total
Table: Distribution of case and control groups by gender
CLUSTERED BAR GRAPHS
Clustered bar graphs are useful for comparing two
categorical variables and are often used in conjunction
with cross-tabulations . (we can use frequency or
relative frequency ).
Quantitative Data
To group a set of observations, we select a set of
contagious, non overlapping intervals, such that each
value in the set of observation can be placed in one, and
only one, of the interval, and no single observation
should be missed.
The interval is called: Class interval
THE FREQUENCY DISTRIBUTION
Number of class interval : Too few intervals are not good because information will be lost. Too many intervals are not helpful to summarize the data.
A commonly followed rule is that number of class interval should be not fewer than 6 and not more than 15.
The specific guidance to decide the number of classes is (Sturges formula).
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, but can be regard as guide only. The number of class intervals obtain by sturges rule can be increase or decrease for convenience and clear presentation.
THE FREQUENCY DISTRIBUTION
Range: It is the difference between the largest and the smallest
observation in the data set.
The Width of the interval (w):
Class intervals generally should be of the same width, but
sometimes this is impossible to do. Width of class interval can be
obtain by the following formula:
W= Width of the class interval , R= Range , K= Number of class
intervals.
To make the summarization more comprehensible, the class width
may be 5 or 10 or the multiples of 10.
THE FREQUENCY DISTRIBUTION
Frequency: It determines the number of observations falling into
each class interval.
Relative frequency: It determines the proportion of observation in
the particular class interval relative to the total observations in the
set.
Cumulative frequency: 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: This 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.
THE FREQUENCY 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 Mid-interval (midpoint):
It can be computed by adding the lower bound of the interval plus
the upper bound of it and then divide by 2.
THE FREQUENCY DISTRIBUTION
91 78 93 57 75 52 99 80 97 62
71 69 72 89 66 75 79 75 72 76
104 74 62 68 97 105 77 65 80 109
85 97 88 68 83 68 71 69 67 74
62 82 98 101 79 105 79 69 62 73
The following are the heart rate of 50 patients
1. Number of classes :
(K) = 1+3.322 Log 50
= 1+3.322 (1.69)
= 1+ 5.64 = 6.64 6
2. Width of class interval
W = R/K
= 109 – 52 /6 = 57/6 = 9.5 10
ANSWER
Frequency, cumulative frequency, relative frequency
and cumulative relative frequency distribution of
heart rate of 50 patients
Cumulative
relative
frequency
Relative
frequency
Cumulative
frequency
Frequency Class
interval
0.04 0.04 2 2 50-59
0.3 0.26 15 13 60-69
0.62 0.32 31 16 70-79
0.76 0.14 38 7 80-89
0.9 0.14 45 7 90-99
1 0.1 50 5 100-109
1 50 Total
Example: The following are the hemoglobin values
(g/100ml) of 30 children receiving treatment for hemolytic anemia.
10.0 8.7 6.7 7.8 8.9 10.8
9.7 9.9 8.5 7.5 9.0 10.0
9.1 9.1 8.4 10.6 10.2 8.5
8.6 9.7 9.7 9.6 10.2 11.4
12.2 9.4 9.3 8.4 8.2 9.2
Order the sample observations by size,
6.7 7.5 7.8 8.2 8.4 8.4
8.5 8.5 8.6 8.7 8.9 9.0
9.1 9.1 9.2 9.3 9.4 9.6
9.7 9.7 9.7 9.9 10.0 10.0
10.2 10.2 10.6 10.8 11.4 12.2
No. of classes = 1+ 3.322 (Log10 30) 6
Width = (12.2 – 6.7) / 6 1
Cumulative
relative
frequency
Relative
frequency
Cumulative
frequency Midpoint Frequency
True class
limits
0.033 0.033 1 7 1 6.5 -7.5
0.2 0.167 6 8 5 7.5 - 8.5
0.567 0.367 17 9 11 8.5 - 9.5
0.867 0.300 26 10 9 9.5-10.5
0.967 0.100 29 11 3 10.5 - 11.5
1 0.033 30 12 1 11.5 - 12.5
1 30 Total
A common graphical presentation of quantitative data is a
histogram.
The variable of interest is placed on the horizontal axis.
A rectangle is drawn above each class interval with its height
corresponding to the interval’s frequency, relative frequency, or
percent frequency.
Unlike a bar graph, a histogram has no natural separation between
rectangles of adjacent classes.
To draw the histogram, the true classes limits should be used.
They can be computed by subtracting 0.5 from the lower limit and
adding 0.5 to the upper limit for each interval.
HISTOGRAM
0
2
4
6
8
10
12N
o. o
f ch
ildre
n
Hemoglobin values (g/100ml)Fig ( ) Hemoglobin values of children receiving
treatment for hemolytic anemia
6.5 7.5 8.5 9.5 10.5 11.5 12.5
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.
SCATTER DIAGRAM
A scatter diagram is a graphical presentation of
the relationship between two quantitative
variables.
One variable is shown on the horizontal axis and
the other variable is shown on the vertical axis.
The general pattern of the plotted points suggests
the overall relationship between the variables.
SCATTER DIAGRAM
LINE GRAPH
A line graph is used to show trend of events with passage of time and
show how frequency of particular event change over time. Time
could be (Seconds - Minutes - Hours – Days - Weeks - Months –
Years - Decades - Centuries – etc).
Money spent this week
$0.00
$5.00
$10.00
$15.00
$20.00
$25.00
Mon. Tues. Wed. Thurs. Fri.
Day
Am
outn
of $
LINE GRAPH
Calories burned while running
0
20
40
60
80
100
120
140
160
180
200
220
240
30 60 90 120
150
180
210
240
270
Hours
Cal
orie
s
PICTORIAL PRESENTATION
Small pictures or symbols are used to present data.
For example: picture of no horn on road near a hospital.
1. PICTOGRAM
PICTORIAL PRESENTATION
These maps are prepared to show the geographical distribution of
frequencies of a characteristic.
2. MAP DIAGRAM OR SPOT MAP
Thank you
