Bio statistics 1

Biostatistics 1Biostatistics 1
Sivasankaran V
Clinical Research Professional
Bangalore

BiostatisticsBiostatistics
The application of statistics to a wide range of topics
in biology.
some statistical methods are more heavily
used in health applications than elsewhere
e.g : survival analysis, longitudinal data
analysis

BiostatisticsBiostatistics
It is the science which deals with development and
application of the most appropriate methods for
the:
Collection of data.
Presentation of the collected data.
Analysis and interpretation of the results.
Making decisions on the basis of such analysis

Statistics
The study and use of theory and methods for the analysis of data arising from
random processes The study and use of theory and methods for the analysis of
data arising from random processes
Statistics provides some of the most fundamental tools and techniques of the
scientific method
• forming hypotheses
• designing experiments and observational studies
• gathering data
• summarizing data
• drawing inferences from data e g testing hypotheses

Other definitions for “Statistics”
 Frequently used in referral to recorded data
 Denotes characteristics calculated for a set of data :
sample mean

Role of Biostatisticians
 To guide the design of an experiment or survey
prior to data collection
 To analyze data using proper statistical
procedures and techniques
 To present and interpret the results to researchers
and other decision makers

Sources of
data
Records Surveys Experiments
Comprehensive Sample

Types of dataTypes of data
Constan
t Variable
s

Quantitative
continuous
Types of variables
Quantitative variables Qualitative variables
Quantitative
descrete
Qualitative
nominal
Qualitative
ordinal

Data
 Data are observations of random
variables made on the elements of a
population or sample.
Data are the
1.Quantities -numbers or
2.Qualities -attributes
are measured or observed that are to be collected
and or analyzed

 Numerical presentationNumerical presentation
 Graphical presentationGraphical presentation
 Mathematical presentationMathematical presentation
Methods of presentation of data

1- Numerical presentation
Tabular presentation (simple – complex)
Simple frequency distribution Table (S.F.D.T.)
Title
Name of variableName of variable
(Units of variable)(Units of variable)
FrequencyFrequency %%
--
- Categories- Categories
--
TotalTotal

Table (I): Distribution of 50 patients at the surgical
department of Alexandria hospital in May 2008
according to their ABO blood groups
BloodBlood
groupgroup
AA
BB
ABAB
OO
1212
1818
55
1515
2424
3636
1010
3030
TotalTotal 5050 100100

Table (II): Distribution of 50 patients at the surgical
department of Alexandria hospital in May 2008
according to their age
AgeAge
(years)(years)
20-<3020-<30
30-30-
40-40-
50+50+
1212
1818
55
1515
2424
3636
1010
3030
TotalTotal 5050 100100

Complex frequency distribution Table
Table (III): Distribution of 20 lung cancer patients at the chest
department of Alexandria hospital and 40 controls in May 2008
according to smoking
Smoking
Lung cancer
Total
Cases Control
No. % No. % No. %
Smoker 15 75% 8 20% 23 38.33
Non
smoker
5 25% 32 80% 37 61.67
Total 20 100 40 100 60 100

Complex frequency distribution Table
Table (IV): Distribution of 60 patients at the chest department of
Alexandria hospital in May 2008 according to smoking & lung
cancer
Smoking
Lung cancer
Total
positive negative
No. % No. % No. %
Smoker 15 65.2 8 34.8 23 100
Non
smoker
5 13.5 32 86.5 37 100
Total 20 33.3 40 66.7 60 100

2- Graphical presentation
 Graphs drawn using Cartesian
coordinates
• Line graph
• Frequency polygon
• Frequency curve
• Histogram
• Bar graph
• Scatter plot
 Pie chart
 Statistical maps
rules

Line Graph
 A line graph is preferred when emphasis isA line graph is preferred when emphasis is
on the trend of the time series over theon the trend of the time series over the
period rather than on the comparison ofperiod rather than on the comparison of
relative size of the different figures in therelative size of the different figures in the
series.series.

Line Graph
0
10
20
30
40
50
60
1960 1970 1980 1990 2000
Year
MMR/1000
Year MMR
1960 50
1970 45
1980 26
1990 15
2000 12
Figure (1): Maternal mortality rate of
(country), 1960-2000

Graphical representation
 HistogramHistogram
 Histogram is specialHistogram is special
kind of bar diagramkind of bar diagram
used to present aused to present a
frequency distributionfrequency distribution
of a characteristicof a characteristic
measured on ameasured on a
continuous scalecontinuous scale
 Frequency PolygonFrequency Polygon
 A frequency polygon is aA frequency polygon is a
variation of histogram.variation of histogram.
 Instead rectangles areInstead rectangles are
erected over the intervals,erected over the intervals,
points are plotted at thepoints are plotted at the
midpoints of the tops of themidpoints of the tops of the
corresponding rectangles incorresponding rectangles in
a histogram. Points area histogram. Points are
joined by straight line.joined by straight line.

Frequency polygon
Age
(years)
Sex Mid-point of
intervalMales Female
s
20 - 3 (12%) 2 (10%) (20+30) / 2 = 25
30 - 9 (36%) 6 (30%) (30+40) / 2 = 35
40- 7 (8%) 5 (25%) (40+50) / 2 = 45
50 - 4 (16%) 3 (15%) (50+60) / 2 = 55
60 - 70 2 (8%) 4 (20%) (60+70) / 2 = 65
Total 25(100%) 20(100%)

Frequency polygon
Age
Sex
M-P
M F
20- (12%) (10%) 25
30- (36%) (30%) 35
40- (8%) (25%) 45
50- (16%) (15%) 55
60-70 (8%) (20%) 65
0
5
10
15
20
25
30
35
40
25 35 45 55 65
Age
%
Males Females
Figure (2): Distribution of 45 patients at (place)
, in (time) by age and sex

0
1
2
3
4
5
6
7
8
9
20- 30- 40- 50- 60-69
Age in years
Frequency
Female
Male
Frequency curve

HistogramHistogram
0
5
10
15
20
25
30
35
0
25
30
40
45
60
65
Age (years)
%
Figure (2): Distribution of 100 cholera patients at
(place) , in (time) by age

Presentation by space:
Data are classified by location of occurance
 BAR CHARTBAR CHART
 Bar diagram isBar diagram is
commonly used tocommonly used to
provide visualprovide visual
comparison of figurescomparison of figures
in a time seriesin a time series
 MULTIPLE BAR CHART.MULTIPLE BAR CHART.
 This is another type of barThis is another type of bar
diagram used fordiagram used for
comparison purpose.comparison purpose.

Bar chart
0
5
10
15
20
25
30
35
40
45
%
Single Married Divorced Widowed
Marital status

Multiple Bar chart
0
10
20
30
40
50
%
Single Married Divorced Widowed
Marital status
Male
Female

PIE CHART
Pie chart is chosen when
component parts of the figure to
each category are to be shown.
Pie chart is a circular diagram.

Pie chart
Deletion
3%
Inversion
18%
Translocation
79%

Doughnut chart
Hospital A
Hospital B
DM
IHD
Renal

3-Mathematical presentation
Summery statistics
Measures of locationMeasures of location
1- Measures of central tendency1- Measures of central tendency
2- Measures of non central locations2- Measures of non central locations
(Quartiles, Percentiles )(Quartiles, Percentiles )
Measures of dispersionMeasures of dispersion

Classification of Measures of
central tendency

Central Tendency for Non
frequency data

Central Tendency for grouped
data

Mean
 Arithmetic mean (mean)Arithmetic mean (mean)
Sum of all observationsSum of all observations
Number of observationsNumber of observations

1- Measures of central tendency (cont.)
 MedianMedian
the observation which lies in the middle ofthe observation which lies in the middle of
the ordered observation.the ordered observation.
Summery statistics

Median for odd number and even
number

Calculate Median for ungrouped
data

Advantage and disadvantage of
Central tendency

Measures of dispersion
 RangeRange
 VarianceVariance
 Standard deviationStandard deviation
 Semi-interquartile rangeSemi-interquartile range
 Coefficient of variationCoefficient of variation
 ““Standard error”Standard error”

Range
 The range of group of observations is theThe range of group of observations is the
interval between the smallest and the biggestinterval between the smallest and the biggest
observation.observation.
 Range = Xmax-Xmin= A-BRange = Xmax-Xmin= A-B

Variance
 An amount of difference or change in theAn amount of difference or change in the
observations or in dataobservations or in data
 The square of the standard deviationThe square of the standard deviation
 Varience = S squareVarience = S square

Standard Deviation
 The standard deviation is the square root ofThe standard deviation is the square root of
the average of the squared deviations of thethe average of the squared deviations of the
observations from the arithmatic meanobservations from the arithmatic mean
 Standard Deviation =Standard Deviation =

Standard deviation SD
7 7
7 7 7
7
7
8
7 7 7
6
3 2
7 8
13
9Mean = 7
SD=0
Mean = 7
SD=0.63
Mean = 7
SD=4.04

Standard error of mean SE
A measure of variability among means of samples
selected from certain population

Bio statistics 1

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