The document outlines the process of data analysis, emphasizing the steps involved in quantitative data analysis such as data preparation, descriptive statistics, and drawing inferences through inferential statistics. It details various measurement scales, including nominal, ordinal, interval, and ratio, highlighting their properties and uses in research. Additionally, it covers different methods of data presentation, including tables and graphical representations like bar diagrams and pie charts, stressing the importance of clarity and accuracy in conveying information.

1. ANALYSIS
OF
DATA
Dr. Jitender Kaushal
Associate Professor

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Introduction
• Important phase of research process
• Involves computation of certain measures
along with searching for patterns of
relationship that exists among groups
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Introduction
• Data collection is followed by the analysis and
interpretation of data, where collected data are analysed
and interpreted in accordance with study objectives
• Analysis and interpretation of data includes
compilation
editing
coding
classification
presentation of data
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Definition
• Analysis is the process of organizing and
synthesizing the data so as to answer the
research questions and test hypothesis
Purpose
• To describe the data in meaningful terms
• To analyze the data so that patterns of
relationship can be detected
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Steps of Quantitative Data Analysis
1. Data preparation: Involves following steps
Compilation: Includes gathering all the collected data
and arranging it in orderly manner
Editing: Involves checking the gathered data for
accuracy, utility and completeness
Coding: Numerous replies can be reduced to a small
number of classes through coding
• Code is an abbreviation, a symbol, a number or an
alphabet which is assigned by the researcher to
every schedule item
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Steps of Quantitative Data Analysis
Classification: divide and arrange the entire data into
the different categories, groups or classes on the
basis of common characteristics
Tabulation: Involves orderly arrangement of data in
columns and rows
2. Describing the data: Descriptive statistics are used
to describe the basic features of data and to provide
simple summaries about the sample
Percentage, means of central tendency and means of
dispersion are the examples of descriptive statistics
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Steps of Quantitative Data Analysis
3. Drawing the inferences of data: Inferential
statistics helps in drawing inferences from the data
For example, finding the difference, relationship and
association between two more variables by the
help of parametric and non parametric statistical
tests
4. Interpretation of data: Refers to critical
examination of the analyzed study results to draw
inferences and conclusions
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SCALES OF MEASUREMENTS
• Measurement is the assignment of numbers to
objects according to specific rules, to
characterize quantities of attribute
There are four level of measurements:
 Nominal measurement
 Ordinal measurement
 Interval measurement
 Ratio measurement
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PROPERTIES OF MEASUREMENT
SCALE
Identity: Each value on the measurement scale has a unique
meaning
Magnitude: Value on the measurement scale have an
ordered relationship to one another. That is some values
are larger and some are smaller
Equal intervals: Scale units along the scale are equal to one
another. This means, for example, that the difference
between 1 and 2 would be equal to the difference
between 19 and 20
A minimum value of zero: the scale has a true zero point,
below which no values exist
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NOMINAL LEVEL MEASUREMENT
• Lowest of the four levels of measurement
• Only satisfies the identity property of
measurement
• Consists of categories that are not more or less
than each other but are different from one
another in some way
• They have no quantitative values
• For example: Gender: Male, Female
• Habitat: Urban, Rural, Slums
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ORDINAL LEVEL MEASUREMENT
• Has the property of both identity and magnitude
• Each value on the ordinal scale has a unique
meaning, and it has an ordered relationship to every
other value on the scale
• Rank objects based on their relative standing on a
specific attribute
• For example: Health status: Poor, Fair,Good
• Income status: Low income, Middle income, Upper
income
• Central tendency: Median
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INTERVAL LEVEL MEASUREMENT
• Has the property of identity, magnitude and equal intervals
• There is more or less, equal numerical distance between
intervals
• For example: Fahrenheit scale to measure temperature
• This scale is made up of equal temperature units, so that
the difference between 40 and 50 degrees Fahrenheit is
equal to the difference between 50 and 60 degrees
Fahrenheit
• With an interval scale, you know not only whether different
values are bigger or smaller, you also know how much
bigger or smaller they are
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INTERVAL LEVEL MEASUREMENT
• For example, suppose it is 60 degrees
Fahrenheit on Monday and 70 degrees on
Tuesday. You know not only that it was hotter
on Tuesday, you also know that it was 10
degrees hotter
• Central tendency:
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RATIO LEVEL MEASUREMENT
• It is the highest level of measurement
• Satisfies all four properties of measurement
• For example: Each value on the weight scale has a
unique meaning, weights can be rank ordered, units
along the weight scale are equal to one another, and
the scale has a minimum value of zero
• Weight scale have a minimum value of zero because
objects at rest can be weightless, but they cannot
have negative weight
• Central tendency:
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Solve the problem
• Which of the following measurement properties is
satisfied by the centigrade scale?
1. Magnitude
2. Equal intervals
3. A minimum value of zero
A) 1 only
B) 2 only
C) 3 only
D) 1 and 2 only
E) 2 and 3 only
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DESCRIPTIVE STATISTICS
• Used to organize and summarize the data to
draw meaningful interpretations
Classification
• Measures to condense data
Frequency and percentage distribution
Tabulation
Graphic presentations
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DESCRIPTIVE STATISTICS
• Measures of central tendency
• Measures of dispersion
• Measures of relationship (correlation
coefficient)
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MEASURES TO CONDENSE DATA
• An appropriate presentation of data involves
organization of data in such a manner that
meaningful conclusions and inferences can
drawn to answer the research question
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TABLES
• First step before data can be used for further
statistical analysis and interpretation
• Tabulation means the systematic presentation of the
information contained in the data in rows and
columns
General principles of tabulation
• Table should be precise, understandable and self
explanatory
• Every table should have title
• Title must describe the content clearly and precisely
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TABLES
• Items should be arranged alphabetically or
according to size, importance and causal
relationship to facilitate comparison
• The unit of measurement must be clearly
stated
• Totals can be placed at the bottom of the
column
• Two or three small tables are to be preferred to
one large one
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Parts of a table
A good statistical table must contain:
Table number: It should be placed at the top of
the table
Title: Should be brief, concise and self
explanatory
Subheads: Should be given below the title in a
prominent type usually enclosed in brackets
for further description of the content of the
table
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Parts of a table
Caption and stubs: Captions are headings for vertical
columns and stubs are the headings for horizontal rows
Body of table: Arrangement of the data according to
description given in the form of captions and stubs
compose the body of the table
Footnotes: When some characteristics cannot be
adequately explained in the body of the table, footnotes
are used to explain those items
Source note: used when secondary data is used, to
mention the source from which these data are retrieved
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Types of the table
Frequency Distribution Table:
• Presents the frequency and distribution of the information
collected
• Table 10.1 Socio demographic profile of patients
S . No. Socio demographic variables N=60
f (%)
1 Age (in years)
20 – 40 18 (30.0)
41 – 60 42 (70.0)
2 Gender
Male 39 (65.0)
Female 21 (35.0)
3 Marital status
Married 52 (86.7)
Unmarried 08 (13.3)
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Types of the table
Contingency Table:
• Tables that report on the frequency distribution of
nominal variables simultaneously and that include the
totals are known as contingency tables
• Also known as cross tables
• Presents frequency distribution of two or more
variables to establish the relationship or association
between them
• Tables could be 2 x 2, 2 x 3 and 3 x 3, depending on
the number of variables
• These tables are generally used in Chi square test
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Types of the table
• Table 10.2 Type of ventilation and daily bowel movements
among patients
S.No. Bowel
movements
Mode of ventilation N=60
f (%)
χ2
value
Spontaneous
ventilation
f (%)
Mechanical
ventilation
f (%)
Present 391 (64.0) 32 (29.4) 423 45.87*
Absent 220 (36.0) 77 (70.6) 297
Total 611 109 720 df=1
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Types of the table
• Multiple Response Tables: When classification of the
cases is to be done into categories that are neither
exclusive nor exhaustive (observation cannot be beyond
these categories), a multiple response table is used
• For example, a patient can have two or more
complaints. In such cases sum total of
frequencies would exceed the total number of
subjects and may lead to confusion
• Therefore, the total number of subjects in cases
of multiple responses is given as base, and from
this we calculate the percentages.
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Types of the table
• Table 10.3 Factors contributing to sleep deprivation among
patients
• * Each patient has more than one factor
S.No. Factors* N=60
f (%)
1 Blood sampling 35 (58.3)
2 Diagnostic test 33 (55.0)
3 Medication 33 (55.0)
4 Vital signs monitoring 32 (53.3)
5 Noise 32 (53.3)
6 Bright lights 30 (50.0)
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Types of the table
Miscellaneous tables:
• When the presentation of data cannot be classified
under any other type
• These tables are used to present data other than
frequency or percentage distributions such as mean,
median, mode, range, standard deviation and so on
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GRAPHS AND DIAGRAMS
Graphical presentation of data
There are certain rules to effectively present the information in the graphical
representation. They are:
• Suitable Title: Make sure that the appropriate title is given to the graph which
indicates the subject of the presentation.
• Measurement Unit: Mention the measurement unit in the graph.
• Proper Scale: To represent the data in an accurate manner, choose a proper scale.
• Index: Index the appropriate colours, shades, lines, design in the graphs for better
understanding.
• Data Sources: Include the source of information wherever it is necessary at the
bottom of the graph.
• Keep it Simple: Construct a graph in an easy way that everyone can understand.
• Neat: Choose the correct size, fonts, colours etc in such a way that the graph should
be a visual aid for the presentation of information.
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Constructing Diagrams / Graphs
While constructing a diagram or graph the following points
should be considered:
• They must have a title and an index.
• The proportion between width and height should be balanced
• Footnotes must be appropriate
• principal of simplicity must be kept in mind
• Neatness and cleanliness in construction of graph must be
ensured
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Types of Diagrams and Graphs
Commonly used diagrams and graphs are:
• Bar diagram
• Pie chart
• Histogram
• Frequency polygon
• Line graphs
• Cumulative frequency curve
• Scattered diagrams
• Pictograms
• Map diagrams
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BAR DIAGRAM
• Useful for displaying nominal and ordinal data
• Easy method for visual comparison of the
magnitude of different frequencies
• The width of the bars should be uniform
throughout the diagram
• The gap between one bar and another should
be uniform throughout
• Bars may be vertical or horizontal
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Types of Bar Diagram
Simple Bar Diagram
Multiple Bar Diagram
Proportion bar Diagram
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Pie Diagram
• A pie chart is a type of graph that represents the data
in the circular graph.
• The slices of pie show the relative size of the data.
• It is a type of pictorial representation of data.
• A pie chart requires a list of categorical variables and
the numerical variables.
• Here, the term “pie” represents the whole, and the
“slices” represent the parts of the whole.
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Formula
To work out with the percentage for a pie chart, follow the
steps given below:
• Categorize the data
• Calculate the total
• Divide the categories
• Convert into percentages
• Finally, calculate the degrees
• Therefore, the pie chart formula is given as
• (Given Data/Total value of Data) × 360°
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How to Create a Pie Chart?
• Imagine a teacher surveys her class on the
basis of their favourite Sports
• Step 1: First, Enter the data into the table.
Football Hockey Cricket Basketball Badminton
10 5 5 10 10
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Step 2: Add all the values in the table to get the total.
• i.e. Total students are 40 in this case.
Step 3: Next, divide each value by the total and
multiply by 100 to get a per cent:
Football Hockey Cricket Basketball Badminton
(10/40) × 100
=25%
(5/ 40) × 100
=12.5%
(5/40) ×100
=12.5%
(10/ 40) ×100
=25%
(10/40)× 100
=25%
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• Step 4: Next to know how many degrees for each “pie sector”
we need, we will take a full circle of 360° and follow the
calculations below:
• The central angle of each component = (Value of each
component/sum of values of all the components) 360°
✕
• Now you can draw a pie chart.
Football Hockey Cricket Basketball Badminton
(10/40) × 360°
=90°
(5/ 40) × 360°
=45°
(5/40) × 360°
=45°
(10/ 40) × 360°
=90°
(10/40) × 360°
=90°
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• Step 5: Draw a circle and use the protractor to
measure the degree of each sector.
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Histogram
• A histogram is a graphical representation of a
grouped frequency distribution with continuous
classes
• Histogram is a diagram involving rectangles whose
area is proportional to the frequency of a variable and
width is equal to the class interval.
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How to Make Histogram?
You need to follow the below steps to construct a histogram.
• Begin by marking the class intervals on the X-axis and frequencies on the Y-
axis.
• The scales for both the axs have to be the same.
• Class intervals need to be exclusive.
• Draw rectangles with bases as class intervals and corresponding frequencies
as heights.
• A rectangle is built on each class interval since the class limits are marked on
the horizontal axis, and the frequencies are indicated on the vertical axis.
• The height of each rectangle is proportional to the corresponding class
frequency if the intervals are equal.
• The area of every individual rectangle is proportional to the corresponding
class frequency if the intervals are unequal.
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Histogram Example
• Question: The following table gives the life times of
400 neon lamps. Draw the histogram for the below
data.
Lifetime (in hours) Number of lamps
300 – 400 14
400 – 500 56
500 – 600 60
600 – 700 86
700 – 800 74
800 – 900 62
900 – 1000 48
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Frequency Polygon
• A frequency polygon is almost identical to a
histogram
• Frequency polygons are the pictorial or graphical
representation of data set
• It is used to compare sets of data or to display a
cumulative frequency distribution.
• Frequency polygons are a visually substantial method
of representing quantitative data and its frequencies.
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Steps to Draw Frequency Polygon
To draw frequency polygons, first we need to draw histogram and
then follow the below steps:
Step 1- Choose the class interval and mark the values on the
horizontal axes
Step 2- Mark the mid value of each interval on the horizontal axes.
Step 3- Mark the frequency of the class on the vertical axes.
Step 4- Corresponding to the frequency of each class interval,
mark a point at the height in the middle of the class interval
Step 5- Connect these points using the line segment.
Step 6- The obtained representation is a frequency polygon.
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Example
• Example 1: In a batch of 400
students, the height of
students is given in the
following table. Represent it
through a frequency
polygon. Height (cm) No. of students
(Frequency)
140 – 150 74
150 - 160 163
160 - 170 135
170 - 180 28
Total 400
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Solution: Following steps are to be followed to
construct a histogram from the given data:
• The heights are represented on the horizontal axes on a suitable scale as
shown.
• The number of students is represented on the vertical axes on a suitable scale
as shown.
• Now rectangular bars of widths equal to the class- size and the length of the
bars corresponding to a frequency of the class interval is drawn.
• ABCDEF represents the given data graphically in form of frequency polygon as:
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• Frequency polygons can also be drawn
independently without drawing histograms.
• For this, the midpoints of the class intervals known
as class marks are used to plot the points.
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Line Graph
• It is mostly used where data is collected over a long
period of time
• On x-axis, values of independent variables are taken
and values of dependent variables are taken on y-
axis
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Cumulative frequency curve or Ogive
• This graph represents the data ofa cumulative
frequency distribution
• For drawing ogive, an ordinary frequency distribution
table is converted into cumulative frequency table
• The cumulative frequencies are then plotted
corresponding to the upper limits of the classes
• The points corresponding to cumulative frequency at
each upper limit of the classes are joined by a free hand
curve
• The diagram made is called Ogive
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Height of 50 students
Height (cm) Frequency Cumulative
frequency
145 - 155 3 3
155 - 165 9 12
165 - 175 21 33
175 - 185 13 46
185 - 195 4 50
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Scattered or Dotted diagram
• It is a graphic presentation that shows the nature
of correlation between two variable characters x
and y on the similar features or characteristics
• E.g. height and weight in men 20yrs old
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Scattered or Dotted diagram
• The following table gives the height and weight of 10
students in a class
Height
(cm)
180 150 158 165 175 163 145 195 180 155
Weight
(Kg)
65 154 55 61 60 54 50 63 65 50
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Negative corelation
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Pictograms or Picture diagram
• This method is used to impress the frequency of the
occurence of events to common people, such as
attacks, deaths, number of operations, admissions,
accidents etc.
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Map diagram or Spot map
• These maps are
prepared to show
geographical
distribution of
frequency of
characteristics
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