The document discusses the process of data analysis and interpretation in research, outlining its importance and the steps involved. It defines data analysis as the statistical treatment of data and categorizes data into four levels: nominal, ordinal, interval, and ratio, each with its own characteristics and measures of central tendency. Additionally, it highlights the role of statistics in evaluating research data and emphasizes the necessity of clear presentation and interpretation of research findings.

1. DATAANALYSIS &
DATA INTERPETATION
Prepared by Mr. Abhinav Bhatt

2. INTRODUCTION:
Analysis is a process which
enters into research in one form or
another from the very beginning. It
may be fair to say that research
consists in general of two larger
steps the gathering data, & analysis
of these data, but no amount of
analysis can validity extract from
the data factors which are not
present.

3. CONT…
• The analysis & interpretation of
data involve the objective material
in the possession of the researcher
& his subjective reactions & desire
to drive from the data the inherent
meanings in that relation to the
problem.

4. CONT…
• To avoid making conclusions or
interpretations from insufficient or
invalid data, the final analysis
must be anticipated in details,
when plans are being made for
collecting information.

5. DATAANALYSIS:
• DEFINITION:
Data analysis means statistical
computation or statistical treatment of
data.
Data analysis generally includes
categorized includes categorizing of
data, ordering of data, so that the
hypothesis can tested & the answers to
the research questions can be obtained.
Data analysis is based on the
research objectives.

6. STEPS OF DATAANALYSIS:
Data analysis consists of the
following steps :
• Deciding purposes of data analysis.
• Recognizing the data in hand.
• Reformulating hypotheses in terms
of statistical hypotheses (null
hypothesis)

7. CONT…
• Setting the level of significance.
• Choosing an appropriate statistical
test.
• Doing the statistical test.
• Evaluating the test.
• Interpreting the research hypothesis
on the basis of statistical findings.

8. PURPOSES OF DATAANALYSIS:
• To reduce data to intelligible &
interpretable form so that the relationships
between the researches variables can be
studied tested, established or rejected.
• To assess the significance of the difference
between the means.
• To assess the difference between
proportions.
• To evaluate the degree of correlations
between the variables or the
characteristics.

9. CONT…
• In statistical term, the data is called
the level of measurements & the data
analysis refers to the statistical
computation or the statistical
treatment of the data.
• Measurement is central to the
process of data analysis. The term
measure refers to the dimensions or
characteristics of the variable with
reference to some units of
measurement.

10. CONT…
• Measurement is the quantification
of data, done by ascribing
numerical values or scores to the
variables, according to statistical
rules so that these characteristics or
the at attributes can be measured
quantitively.

11. DATA CLASSIFICATION:
• In statistical term, the data is
classified under four levels
according to its characteristics.
This classification is as follows:
I)Nominal level data.
II) Ordinal level data.
III) Ratio level data.
IV) Interval level data.

12. I) Nominal level data:
• This is the first level data which is
mutually exclusive, which is assigned in
the named categories & the frequency the
each category is counted.
• In the nominal level data, the measure of
central tendency or the category is called
the mode.

13. CONT….
• When two categories of data occur
in the same frequency it is called
bimodal.
• When more than two categories of
data occur in the same frequency,
the data is called multi-modal.

14. CONT….
• Example:
Age group distribution of 20 children
1, 1, 2, 3, 3, 5, 6, (7), (7), 8, (7), (7),
(7,) (7), (7), 8, 9, 6, 8
• The mode is (7) since, it is the most
frequently occurring data.
• Nominal level data is counted data & it
is used for statistical analysis in those
situations where counting is the only
feasible method of quantification.

15. II) Ordinal level data:
• The ordinal level data is the second
level data which can be put into a
rank such as, the data is put on a
scale which has a rule of order
such as high, medium, low or from
the highest to the lowest etc.

16. CONT….
• The level implies ranking. The
middle measurement of the rank is
identified as the median which is
the measures of the central
tendency in the ordinal level data

17. CONT…
• Example:
• Weight of the 10 children in kilogram.
• Ungrouped: 25, 28, 25, 25, 30, 32, 25, 25,
21, 28, 25, and 25.
• Ranking: 21, 25, 25, 25, 25, 25, 25, 25,
28, 28, 30, 32.
• Median: 25
• Ordinal level data has no absolute
values, when ranking is done, ranking
spaces them equally but value wise they
are not equally spaced.
•

18. IV)Ratio level data:
• In ratio level data, there are some
rules of order (ordinal, quality) &
equal interval (internal quality).
In addition, there is also an
absolute zero point.
• In this, the individual scores are
added & then the total sum of all the
scores is divided by the total
number of the subjects.

19. CONT…
• The data which is obtained is
called ratio level data. This is the
most precise & also highest.
This is also the most accurate
measure of data because it is
measured on a scale with true
zero point.

20. CONT…
• The number & can be added,
subtracted, multiplied, divided &
can also be expressed in ratio
relationship.
• The average or the measure of
central tendency of the ratio
level data is referred to as
mean.

21. IV) Internal level data:
• This is the third level data which is
measured on the interval scale. But
in this, the limitation of the scale
which is used is, it has no absolute
zero (0) & therefore no fixed
beginning point.
• But the scale has equal spaces or
intervals or relative distance between
the units as well as a rule of order.
The measure of the central tendency
is the mean

22. CONT…
• Example:
• A student has scored the
following marks in (6) subjects of
100 each, such as 80, 85, 86, 100, 96,
90.
• The mean (average) is (89).
• Total score of all the 6 subject =Mean
Number of subjects

23. SUMMARY OF DATA, ITS
CHARACTERISTICS & ITS MEASURES
OF CENTRAL TENDENCY:

24. SR.
NO
DATA
LEVEL
CHARACTERISTI
CS
MEASUR
ES OF
CENTRA
L
TENDEN
CY
1 Nominal Measured on a scale
of frequency of
categories
Mode (M)
2 Ordinal Measured on no scale
but can be ranked
Median
(Md)
3 Interval Measured on a scale
with no true zero
Mean (M)
4 Ratio Measured on a scale
with absolute zero
Mean(M)

25. STATISTICS:
• DEFINITION OF STATISTICAL:
• Statistics is a mathematical technique
which is applied for statistical
computation or statistical treatment of
the quantitative or numerical data for
measurement, for evaluation & for
interpretation, purpose.

26. • Statistics, which are computed from
the samples, are used to estimate the
population parameter from which the
sample is drawn.
• Statistical population is the total
number of things, events or
phenomena having common
attributes. Statistical sample is a
fraction of the statistical population
CONT…

27. CONT…
• Statistical also represents a tool for
evaluating or analyzing the information
that the researcher gathers, during the
course of data collection.
• The type of data analysis needs to
match the research approach. The types
of statistics, to be used for the data
analysis, depend upon the research
approach. Also the researcher must
know what type of data, the researcher
has at hand.

28. STATISTICAL SYMBOLS:
• BLACKBOARD

29. CATEGORIES OF STATISTICS:
• CATEGORIES OF STATISTICS:
• Data analysis is done with structural
statistical methods. There are two broad
categories which are as follows:
1. Descriptive or deterministic statistics for
data analysis.
2. Inferential statistics for data analysis.
•

30. Descriptive or deterministic statistics
for data analysis.
• In a quantitative research approach,
the descriptive statistical analysis is
used. Descriptive analysis is done
with the data in hand. The researcher
makes attempts to describe the results
in the context of the responses that are
received during the data collection
process.

31. CONT….
• In a quantitative research
approach, the descriptive
statistical analysis is used.
Descriptive analysis is done with
the data in hand. The researcher
makes attempts to describe the
results in the context of the
responses that are received
during the data collection
process.

32. CONT…
• In qualitative data analysis the result
are generated from the research
sample & the generalization is done
for the research population. The
variability of the data & the
relationship amongst the data are
determined by the descriptive
statistics.

33. CONT…
• The relationships amongst the data
refer to the associations amongst the
data. In descriptive statistics, most
commonly the numerical values or
scores are ascribed to the numerical
values or scores are ascribed to the
objects or the characteristics of the
objects or the events & then
measurements of these scores are
done.

34. CONT….
• In descriptive statistics, the levels of
measurements are statistically described
through the statements of measurements
which reflect the centre of distribution of
or the central tendency. These statements
are the following:
• Mean (M)
• Median (Md)
• Mode (Mo)

35. CONT…
• Following are the appropriate statistical
measures of the descriptive statistics:
• The frequency distribution.
• The measures of central tendency or
averages.
• The measures of variance or variance or
variability or spread or depression.
• The graphic distribution & percentile.
• The normal distribution curve.
• The measures of relationships.

36. CONT….
• The frequency distribution:
• The frequency distribution is a statistical
technique through which the whole data is
brought into some order without much
loss of the factual information. Frequency
is denoted by “f”.
• These can be done in a tubular from or a
graphic from.
• The tabular form is shown below:
• Ungrouped scores: 50

37. 75 52 95 72 51 66 81 93 76 52
77 68 50 81 53 67 94 98 75 59
80 69 61 89 90 77 86 98 62 79
74 10
0
61 96 92 77 86 99 57 93
56 92 74 73 97 78 87 79 54 98

38. (1)
Class
intervals
(2)
Tallies
(3)
Class- interval
frequency
50- 55 ||||, | 6
56-60 ||| 3
61-65 ||| 3
66-70 |||| 4
71-75 ||||, | 6
76-80 ||||, ||| 8
81-85 || 2
86-90 |||| 5
91-95 ||||, | 6

39. CONT…
• The original ungrouped score (total no.
50). The ungrouped 50 scores in the Box
below are grouped in a frequency
distribution, in Table VI.
• In the first column of the table, the class
intervals are serially listed from the
smallest score to the largest score. Each
class interval covers 5 scores.
• In the second column, tallies or the class,
- intervals are placed.
• In the third column, the class intervals or
the frequency (f) is written

40. Drawing up a frequency distribution
in a graphic form:
The first way of representing a
frequency distribution graphically, is by
means of a polygon.
ON OHP

41. CONT….
b) The measurement of the central
tendency or averages:
• The measures of the central
tendency or the averages are
described below which are as
follows.
• Mean (M)
• Median (Md)
• Mode(Mo)

42. Mean (M):-
• The mean or the arithmetic mean is
described as the most stable measures of
central tendency for the variables
measured at the interval level. It is the
sum of all the individual values divided
by the individual values divided by the
number of subjects. It is also called the
average. This is the most accurate
measure. This is also the most
commonly used measure of the central
tendency.

43. CONT….
• Example: A student has scored the
following marks in (6) subjects out of
100 each:
• 80, 85, 86, 100, 96, 90
• The mean is M=
= 537 = 89
6
X- Total of all scores.
N- No. of marks.

44. Median:
• The median is described central
tendency which lies exactly at the
middle rank when all the values are
arranged & ranked in order of size
from the highest to the lowest order. It
is the central point on a scale of
observation so that, equal number of
items or things lie on either side of the
central point.

45. CONT…
• Example:
• Two situations may arise when the median is to
be computed from the ungrouped data in two
different ways such as, when the total number of
scores (N) is odd & when the total number of
scores (N) is even.
• When number of scores or N is odd such as:
11, 11, 12, 14, 16, 16, 16, 17, 18
• The median score is the midscore= 16
• When number of scores or N is even such as:
11, 11, 12, 14, 15, 16, 16, 16, 16, 17
• The median score is midscore= 15

46. Mode:
• The mode is described as the score or
the measure of central tendency of
the variables or the scores which
occur most frequently. The mode can
be used for measuring variables at
any level.

47. CONT….
• Example:
• If the scores are: 7, 6, 7, 5, 4, 9, 7,
7, 7, 6, and 7
• Mode = 7 most frequently
occurring score.
• The most frequently occurring
score of the mode is (7). Therefore
the mode of the variable is (7).

48. C) The measures of variance
or variability:
The measures of variability describe how
scattered or how spread the scores are
around their central tendency. Following
are the measures which indicate the
variability.
1) Minimum measures, maximum measure
& range.
2) Variance.
3) Standard deviation.

49. 1) Minimum measures, maximum
measure & range:
• The maximum measure denotes the
largest value in the scores.
• The minimum measure denotes the
smallest value in the scores.
• The range denotes the measurement
of difference between the minimum
value & the maximum value.

50. CONT…
• Example: suppose there are 25
children whose ages are the
following:
• 4, 4, 5, 8, 10, 11, 12, 12, 12, 13, 14.
15, 15, 16, 18, 16, 16, 18, 18, 20:
• The lowest score is = 4
• The highest score is = 20
• The range is = 4- 20

51. 2) Variance:
• The variance is the way of
measuring about how closely the
individual variable scores cluster
around the mean. Variance can be
experimental variance, which is the
observed difference between two
sample- means & error- variance,
which is the sampling error facts.

52. 3) Standard deviation:
• It refers to the spread of the results away
from the mean. It is the positive square
root of the variance. It is the measure of
spread or dispersion of the individual
values around the means.
• The standard deviation is the most stable
index of variability. In short it is called
SD & the symbol of the SD is the Greek
letter- sigma

53. CONT…
• The SD is calculated on the
measurements of the interval &
ratio data. Sometimes, the SD is
used to compare two groups

54. d) The graphic distribution &
percentile:
• Graphic distribution:
• The graphic distribution is done in
two ways. One is cumulative
frequency graphing & the other is
cumulative percentile graphing
curve (0 give).
• Example:
• Scores (ungrouped) = (50)

55. 75 52 95 72 51 66 81 76 52
77 68 50 81 53 67 94 75 59
80 69 61 89 90 77 86 62 79
74 100 61 96 92 77 86 57 93
56 92 74 73 97 78 87 54 98

56. Grouped scores f Cumulative
frequency (cum.f)
95-100 7 50
90-95 6 43
85-90 5 37
80-85 2 32
75-80 8 30
70-75 6 22
65-70 4 16
60-65 3 12
55-60 3 9
50-55 6 6

57. CUMULATIVE FREQUENCY GRAPH
• OHP

58. PERCENTILE:
• Percentiles are points in a continuos
distribution, below which lies the given
percentage of the total score or N. in the
cumulative percent curve or 0 give, the
frequencies are expressed as cumulative
percents of N on the Y-axis instead of
cumulative frequencies.

59. CONT….
• Percentile rank is the point in the
distribution below which a given
percentage of scores falls.
• Example: scores 52, 43, 34, 25, 25
• The score (34) occupies the 50th
percentile rank.

60. e) The normal distribution curve:
• The normal distribution curve is
depicted through the normal curve. It
is one of the many varieties of
possible curves. It is a mathematical
form which is also called the curve
of normal distribution & which
corresponds with the theory of
probability. In statistical term, the
probability of a given variable is
described as expected frequency of
occurrence.

61. DATA INTERPRETATION:
• INTRODUCTION:
• In a research study, the data
analysis & the data interpretation
involve application of deductive &
inductive logic to the research
process. The data is analysed &
synthesized to verity hypothesis to
general new principles & theories.

62. DEFINITION:
• Data interpretation means that the
results of the data analysis are
studied & then making inferences
about the relations & drawing
conclusions about these relations.

63. CONT….
• After the data analysis or the statistical
computation of the data, data
interpretation is done from the results
of the data analysis.
• It is necessary that the research
findings are presented in a clear,
accessible & understandable terms.

64. • Data interpretation is a critical
process in which 3 types of
validity are to be ascertained.
These are the following:
a) Explanatory validity.
b) Ecological validity.
c) Methodological validity.

65. Cont….
a) Explanatory validity:
• It refers to the selected conceptual
theory of the research study & the
adequacy of its relationship with the
statistical findings.
b) The ecological validity:
• It refers to the adequacy of the
relationship between the sample & the
research study design.

66. Cont…
c) The methodological validity:
• It refers to the adequacy of the
degree of the methods used to test
conceptual theory.
• It is important that errors should be
checked & to be eliminated from the
data interpretation.

67. Cont…
• It is of almost importance that incorrect,
faulty interpretation is to be guarded, to
make the interpretation, the researcher
need to be careful about personal biases
& need to take all precautions to
eliminate them.
• The interpretation should necessarily
reflect the testing of the hypothesis &
not providing the hypothesis.

68. Cont…
• In the interpretation the researcher
should not make any attempt to
emphasize the convictions held by the
researcher.
• The interpretation should be supported
by the logical findings of the
scientifically data analysis. The
researcher must make the interpretation
of the research results on the basis of
the reality.

69. THE SUCCESS OF DATAANALYSIS &
INTERPRETATION DEPENDS UPON
THE FOLLOWING FACTORS:
• poster

70. STEPTS OF FORMULATING &
TESTIG A STATISTICAL
HYPOTHESIS:
• Selecting the measures on which the
research will be based.
• Specifying the general characteristics of
the population & the parameters which
will be examined & investigated.
• Formulating a hypothesis about the
population based upon population
characteristics.

71. Cont…
• Identifying & determining the statistics
by which the hypothesis is to be tested.
• Determining the distribution of
statistics.
• Selecting the level of significance.
• Find out the level of rejection on the
basis of the level of significance.

72. Cont….
• Drawing a random sample from the
population.
• Computing the value of the statistics
specified earlier, for the sample.
• Determining whether the computed
statistical values is in the level of
rejection.
• Rejecting the hypothesis if the
statistical value is in the level of
rejection, otherwise accepting the
hypothesis.

73. SUMMARY:
• CONCLUSION:

74. BIBLIOGRAPHY:

75. THANK YOU