This presents an overview about relevance and significance of statistics as a valid tool in enhancing quality of research. It also touches upon some misuse and abuse of statistics.

1. Relevance of Statistics in
Research
Dr S G Deshmukh
ABV-Indian Institute of Information Technology &
Management Gwalior
15 Feb 2018
FDP on Statistics and Research Methodology (15-21 Feb, 2018)

2. Opening remarks..
“all knowledge is, in the final analysis, history.
All sciences are, in the abstract,
mathematics and all methods of acquiring
knowledge are essentially statistics.”
C. R. Rao, in the preface of his famous book
“Statistics and Truth”, 1997, World Scientific
2

3. Typically, such research wants to:
 Describe the structure, hierarchy and
organization of societies
 Identify regularities/anomalies that are worth
explaining
 Construct and test explanations for such
patterns and regularities
 Address societal problems, suggest
interventions, implement changes
Theories to explain why certain things
happen. Causes and effects.

4. Research is …….
 Knowledge acquisition gained
through reasoning
through intuition/gut feelings
but most importantly through the use of
appropriate methods/tools/techniques
That is where the role of statistics comes into
picture !
4

5. Research in pursuit of knowledge
 Attributional:
Attributing a measurement (definition) to a particular
Concept.
 Growth, Leadership, Managerial Efficiency
 Relational:
Relating a phenomenon with its determinants
 Explaining behavior
 Classificational:
Understanding by categorizing on the basis of some
indicators
 Taxonomy, Innovators Vs Followers, Leaders Vs Laggards5

6. Basic Elements of the Scientific
Method
 Empiricism: Enquiry is conducted through
observation and verified/validated through
evidence
 Determinism: Events occur according to
regular laws and causes. The goal of research
is to discover/unfold these
 Scepticism: Our proposition is open to analysis
scrutiny and critique- That is how body of
knowledge progresses !
6

7. Typical Scientific Method
1. Choose a question to investigate
2. Identify a hypothesis related to the question
3. Make testable predictions in the hypothesis
4. Design an experiment to answer hypothesis
question
5. Collect data in experiment
6. Determine results and assess their validity
7. Determine if results support or refute your
hypothesis
7

8. Some basic features of research
process
 Always involves bringing together three sets of things:
 some content that is of interest
 some ideas that give meaning to that content, and
 some techniques or procedures by means of which those ideas and
content can be studied.
 These three sets of things more formally, as three distinct, though
interrelated domains:
 The Substantive domain, from which we draw contents that seem
worthy of our study and attention;
 The Conceptual domain, from which we draw ideas that seem likely to
give meaning to our results; and
 The Methodological domain, from which we draw techniques that seem
useful in conducting that research.
8

9. Stepping into research
 Method and Methodology
 Method refers to the techniques and Methodology to the
strategy
 Logic as an Essence of Philosophy
 Inference depends on the law of Causation
 Deductive and Inductive are methods Non Exclusive
 Structuralism as the holistic approach
 Why Philosophy?
 In Search of Knowledge, Understanding of Nature and
Meaning of Universe.
 Creation of Theories OR Universality about Basic things.
 In-depth knowledge of a phenomenon
9

10. Two models : AROHA & AVAROHA
A - Algorithm
A – Approach V - Variables
R – Review A - Arrangement
O - Objectives R - Results
H - Hypothesis O - Objectivity
A - Analysis H – Humanistic
A – Analytical Rigour
10
Source: Deshpande R S, Institute for Social & Economic Change, B’lore

11. How to get into a research topic?
 Searching for new evidence from facts and
concluding with a new hypothesis.
 It should be net addition to the existing knowledge
or at least a new interpretation of that.
 It should be crystal clear in its meaning.
 It should have a hypothesis which is not a
statement of existing facts.
 It should be empirically analyzable.11

12. Criteria of good research
 Good research is systematic- structured with
specified steps taken in specified sequence in
accordance with well-defined rules
 Good research is logical: logical reasoning makes
research more meaningful in the context of decision
making
 Good research is empirical: dealing with concrete
data that provides the basis for external validity to
research results.
 Good research is replicable
 Good research is also visible : sharing with
community, peers and the society at large
12

13. Credit: Prof N K Sharma(IITK)
13

14. What is Statistics ?
A collection of methods for planning
experiments, obtaining data, and then
organizing, summarizing, presenting,
analyzing, interpreting, and drawing
conclusions based on the data
https://www.amazon.in/Business-Statistics-2e-Naval-Bajpai/dp/8131797007

15. 15
Statistics
 The science of data to answer research
questions
Formulate a research question(s) (hypothesis)
Collect data
Analyze and summarize data
Draw conclusions to answer research question(s)
 Statistical Inference
In the presence of variation

16. Why are statistics important in
research?
 Communication
 Credibility
 Convergence
 Answered in Quora by Stan Paxtan, Apr 2016
 https://www.quora.com/Why-are-statistics-important-in-
research
16

17. Why do we need statistics? ..1..
 Measure things
 Examine relationships
 Make predictions
 Test hypotheses
 Construct concepts and develop theories
 Explore issues

18. Why do we need statistics? ..2..
 Explain activities or attitudes
 Describe what is happening
 Present information
 Make comparisons to find similarities and
differences
 Draw conclusions about populations
based only on sample results.

19. Common reasons for rejection of
a paper ..
 Incomplete data such as too small a sample size or missing or poor controls
 Poor analysis such as using inappropriate statistical tests or a lack of
statistics altogether
 Inappropriate methodology for answering your hypothesis or using old
methodology that has been surpassed by newer, more powerful methods
that provide more robust results
 Weak research motive where your hypothesis is not clear or scientifically
valid, or your data does not answer the question posed
 Inaccurate conclusions on assumptions that are not supported by your data
Source: Springer Nature Guidelines
https://www.springer.com/gp/authors-editors/authorandreviewertutorials/submitting-to-a-journal-and-
peer-review/what-is-open-access/10285582 19

20. Language of statistics
 Variable and Constant
 Discrete and Continuous
 Population and Sample
 Parameter and Statistic

21. Population vs Sample
 Population — the whole
a collection of persons, objects, or items under
study
 Census — gathering data from the entire
population
 Sample — a portion of the whole
a subset of the population
21

22. 22
Parameter vs. Statistic
 Parameter — descriptive measure of the
population
Usually represented by Greek letters
 Statistic — descriptive measure of a sample
Usually represented by Roman letters

23. Examples
 Parameter
51% of the entire population of the Gwalior is
Female
 Statistic
Based on a sample from the IIITM population
is was determined that 23.2% consider
themselves as addict to internet.

24. 24
Variation
 What if everyone:
Looked the same
Thought the same
Believed the same
 How many people would you have to interview
to know everything about the population with
regard to looks, thoughts, and beliefs?

25. 25
 Populations with variation
Everyone looks different
Everyone thinks different
Everyone believes different
 Interviews or observations are required on
multiple members of the population for valid
conclusions about population characteristics.
Variation

26. 26
Variation
 Variation is everywhere
Individuals
Repeated measurements on the same individual
Almost everything varies over time
 Because variation is everywhere, statistical
conclusions are not certain.
Probability statement
Confidence statement
Margin of error

27. 27
Understanding Data
Individuals & Variables
 Individuals – objects described by a set of data.
May be people, animals, or things
Also called subjects or units.
 Variables – any characteristic of an individual.
A variable can take different values for different
individuals.

28. Statistics as a tool in research
Types of Research Questions
 Descriptive (What does X look like?)
 Correlational (Is there an association between X
and Y? As X increases, what does Y do?)
 Experimental (Do changes in X cause changes in
Y?)
Different statistical procedures allow us to
answer the different kinds of research
questions

29. 29
Statistical concepts & tools
 Data representation
 Various Probability Distributions
 Discrete (Binomial, Geometric, Poisson, Uniform etc.)
 Continuous (Uniform, Exponential, Normal etc.)
 Central Limit Theorem
 Moment generating functions
 Distribution of Sample Means
 Point Estimates
 Confidence Interval
 Type I and Type II errors
 Hypothesis Testing
 Regression: simple/multiple
 Anova, DOE
 Non-parametric tests

30. 30
Common concern: Bias
Statistics- Collection of data
Sample Surveys Experimentsvs.
Population “Snapshot”
Impose treatment
on subjects/units
Observe response to
imposed treatment
Bias:
Systematically favors certain outcomes

31. 31
Commonly used tables
 Standard normal variate
 t
 Chi-square
 F
 Non-parametric

32. 32
Central Limit Theorem
 Most theory about sample means depends on
assumptions that the mean comes from a normal
distribution.
 The Central Limit Theorem says that for any
population, if the sample size is large enough, the
sample means will be approximately normally
distributed with the mean equal to the population
mean and standard deviation equal to the population
standard deviation σ divided by the square root of n
(σ/√n).

33. 33
Normal distribution
 Mother of all !
Standard normal variate (Z) ~ N(, 2 )
2 : Chi-Square – Square of Z
t distribution –small sample size
F Distribution ~ Ratio of 2
Approximation to Discrete : Binomial etc.

34. Recall..
Descriptive Statistics
Describes data usually through the use of graphs, charts and
pictures. Simple calculations like mean, range, mode, etc., may
also be used.
Inferential Statistics
Uses sample data to make inferences (draw
conclusions) about an entire population

35. 1. Center: A representative or average value that indicates where the
middle of the data set is located
2. Variation: A measure of the amount that the values vary among
themselves or how data is dispersed
3. Distribution: The nature or shape of the distribution of data (such
as bell-shaped, uniform, or skewed)
4. Outliers: Sample values that lie very far away from the vast
majority of other sample values
5. Time: Changing characteristics of the data over time
Recall:
Important Characteristics of Data

36. 36
Statistical significance
 Significance is a statistical term that tells how sure you are that
a difference or relationship exists. To say that a significant
difference or relationship exists only tells half the story.
 We might be very sure that a relationship exists, but is it a
strong, moderate, or weak relationship? After finding a
significant relationship, it is important to evaluate its strength.
 Significant relationships can be strong or weak. Significant
differences can be large or small. It just depends on your
sample size.

37. Steps in a test of hypothesis
 1. Define problem. :Determine H0 and HA. Select Alpha .
 2. Collect data
 3. Calculate xbar as an estimate of µ and s as an estimate of
σ.
 4. Check assumptions:
 Sample size n is reasonably large (n ≥ 30) so can use
normal distribution and estimate σ with s.
 Check for outliers or strong skewness in pop. dist.
 5. Calculate Standard Score
 6. Compare with Tabulated value to make conclusions.
 7. Make conclusions in context of the problem.


38. 38
If statistic is higher than the critical
value from the table
The finding is significant.
Reject the null hypothesis.
The probability is small that the difference or
relationship happened by chance, and p is less
than the critical alpha level (p < alpha ).

39. 39
Regression and Correlation
 Regression analysis is the process of
constructing a mathematical model or function
that can be used to predict or determine one
variable by another variable.
 Correlation is a measure of the degree of
relatedness of two variables.

40. 40
Simple Regression analysis
 bivariate (two variables) linear regression -- the
most elementary regression model
dependent variable, the variable to be
predicted, usually called Y
independent variable, the predictor or
explanatory variable, usually called X

41. 41
Regression models
 Probabilistic Regression Model
Y = 0 + 1X + 
 0 and 1 are population parameters
 0 and 1 are estimated by sample statistics b0 and b1

42. 42
Parametric vs Nonparametric
Statistics
 Parametric Statistics are statistical techniques based on assumptions about
the population from which the sample data are collected.
 Assumption that data being analyzed are randomly selected from a
normally distributed population.
 Requires quantitative measurement that yield interval or ratio level data.
 Nonparametric Statistics are based on fewer assumptions about the population and the
parameters.
 Sometimes called “distribution-free” statistics.
 A variety of nonparametric statistics are available for use with nominal or ordinal
data.
 RUN TEST
 MANN-WHITNEY
 CHI-SQUARE
 KRUSKAL-WALLIS
 Etc.

43. 43
Which test to use?
Goal Measurement
(from Gaussian
Population)
Rank, Score, or Measurement
(from Non- Gaussian
Population)
Describe one group Mean, SD Median, interquartile range
Compare one group to a
hypothetical value
One-sample t test Wilcoxon test
Compare two unpaired
groups
Unpaired t test Mann-Whitney test
Compare two paired
groups
Paired t test Wilcoxon test
Compare three or
more unmatched
groups
One-way ANOVA Kruskal-Wallis test

44. 44
Importance of data origin..
 Good data – intelligent human effort
 Bad data – laziness, lack of understanding, or a
desire to mislead
 Know where the data come from
 Understand statistics
 Example: Did you know that 45% of statistics
are made up on the spot????

45. 45
Manipulating the facts
 Data collection – sampling and measurement
biases, ignoring influential variables
 Data summarization – graphically
misrepresenting data, choosing misleading
statistics
 Statistical Inference – reporting invalid
conclusions and interpretations

46. 46
Manipulating data collection
 Sampling biases:
One group in a population is overrepresented
compared to another.
Example: “New Longitudinal Study Finds that
Having a Working Mother Does No Significant Harm
to Children.”
The sample was not representative of average
or higher income families.

47. 47
Manipulating data production
 Ignoring influential variables:
 Reporting results without considering important influential
variables.
 Example – Differences in pay due to gender
 “As of 2016, full-time employed women earned on average
only about 76 percent as much as full-time employed men”
 Does this difference show that women are discriminated
against?
 Occupation has been ignored.
 More men have received training for higher paying jobs.

48.  Bad Samples
 Small Samples
 Loaded Questions
 Misleading Graphs
 Precise Numbers
 Distorted Percentages
 Partial Pictures
 Deliberate Distortions
Abuses of Statistics

49. Abuses of Statistics ..1..
 Bad Samples
Inappropriate methods to collect data. BIAS Example: using
yellow pages (phone book) to sample data.
 Small Samples
Size of the sample could be a question mark
 Loaded Questions
Survey questions can be worked to elicit a desired response

50. Some students collected the following data on
lunch preferences.
How was data collected?

51. Issues:
 Sample size
 Was sample representative?
 Was the survey question biased?
 How was the survey conducted?
 Is the graph constructed accurately?
Is their conclusion valid?

52. Their conclusion is not valid (it may still be
true). You need more information about the
sample and size of sample as well as the
survey itself.
Remarks..

53.  Misleading graphs
 Precise Numbers
 Distorted Percentages
 Partial Pictures
 Deliberate Distortions
Abuses of Statistics ..2..

54. Bachelor
Degree Diploma
Misleading graphs:
Salaries of People with Bachelor’s Degrees and with
Diplomas
Rs 40,000
30,000
25,000
20,000
Rs 40,500
Rs 24,400
35,000
$40,000
20,000
10,000
0
Rs 40,500
Rs 24,400
30,000
Bachelor
Degree Diploma
(a) (b)(test question)

55. Misleading graphs:
Alpha’s profits over a 5 year period.

56.  Precise Numbers
There are 103,215,02 households in a Metro town.
This is actually an estimate and it would be best to say
there are about 1.03 Crore households.
 Distorted Percentages
100% improvement doesn’t mean perfect.
 Deliberate Distortions
Lies, Lies, all Lies
Abuses of Statistics ..3..

57. Abuses of Statistics
 Partial Pictures
“Ninety percent of all our cars sold in Gwalior the
last 10 years are still on the road.”
Problem: What if the 90% were sold in the last 3
years?

58. Some research hypotheses
 “If you know the outcome of your research, then
you are not doing research”-Einstein.
 Hypothesis:””-The relationship between Emotional
Intelligence and job performance will be stronger for
individuals whose job involves greater amount of
interpersonal interaction
 Hunch says true, So says the research findings. Axiomatic
hypothesis testing.(Source XXX,Vol.14,no.4,Oct.-
Dec.2010,pp.250-252).
 There is no new light by such like researches.
 Statistical packages such as SPSS,LISREL have
made as if you are doing in-depth research l

59. Spurious Correlations by
Tyler Vigen (Author)

60. r=0.9978

61. Web exercise
 Demo exercise : Spurious correlations
 http://www.tylervigen.com/
 Interesting article on improbability !
 http://www.jmp.com/landing/hand_improbability-
principle.shtml

62. 62
Checklist for
A Statistical Project ..1..
 Statement of purpose/question of interest
 Summary of data collection e.g. random sample, stratified sample, available
data
 Identify possible sources of bias
 Why do you believe sample was representative?
 Summarize the data (concise, well-labeled, easy to read)
 Numerical or quantitative data
 Graphs: Pie diagram or histogram
 Measures of central tendency (e.g. mean or median)
 Measures of spread (e.g. range, SD, IQR)
 A check for outliers (e.g. z scores,)
 A check for normality (prob. plot, 68-95-99.7 rule) if needed by your analysis
 Quantitative data
 Proportion in each category

63. 63
Checklist for
A Statistical Project :2..
 Statistical inference
 Quantitative data -e.g. confidence intervals for mean(s), hypothesis test for
mean(s), regression, ANOVA
 Qualitative data
 Include a discussion of why our method is appropriate
 Diagnostics
 Verification of any assumptions made during statistical inference
 Interpretation/Explanation of results
 What does it all mean?
 Use the above summaries to justify your interpretation
 Suggest reasons for what you have observed
 Overall conclusion, recommendations, future scope
 References

64. 64
Quotable quotes !!
 Every model is an approximation. It is the data that are real !
 All models are wrong ; some models are useful.
 Discovering the unexpected is more important than confirming the known !
 Among the factors to be considered there will usually be the vital few and the
trivial many ( Juran)
 There’s never been a signal without noise !
 Not everything that can be counted counts and not everything that counts
can be counted (Albert Einstein)

65. Online resources available on
Statistics..
 Quora
 YouTube
 TED Talks
 Blogs
65

66. Some YouTube presentations..
Sn Title Link Duration
1 Choosing which statistical test to use
- statistics help
https://www.youtube.com/wat
ch?v=rulIUAN0U3w
9.32
minutes
2 Intro to Hypothesis Testing in
Statistics - Hypothesis Testing
Statistics Problems & Examples
https://www.youtube.com/wat
ch?v=VK-rnA3-41c
23.40
minutes
3 Null and Alternate Hypothesis -
Statistical Hypothesis Testing
https://www.youtube.com/wat
ch?v=_Qlxt0HmuOo
14.51
minutes
4 What is a p-value? https://www.youtube.com/wat
ch?v=HTZ8YKgD0MI
5.43
minutes

67. TED Talks on Statistics
Sn Title Link
1 Why you should love statistics | Alan
Smith
https://www.ted.com/talks/alan_smith_
why_we_re_so_bad_at_statistics?refe
rrer=playlist-statistically_speaking
2 How juries are fooled by statistics? Peter
Donnelly
https://www.ted.com/talks/peter_donne
lly_shows_how_stats_fool_juries?refer
rer=playlist-statistically_speaking
67

68. An interesting blog:
Not awful and boring ideas for teaching
statistics
 http://notawfulandboring.blogspot.in/
 By Jess Hartnett, Gannon University's Department of
Psychology and Counseling.
Statistically funny
 Blog by Hilda Bastian, National Institutes of Health, USA
 https://statistically-funny.blogspot.in/
68

69. Useful resource
 Prof J P Verma, Professor of Statistics at
LNIPE, Gwalior and author of several books on
statistics
 Visit : http://jpverma.org/
And get complimentary material
(presentations ) on statistics..
69

70. Summary :
Relevance of statistics in research
 Validity
Will this study help answer the research
question?(Content validity?)
 Analysis
What analysis, & how should this be interpreted
and reported?(Stat. packages?)
 Efficiency
Is the experiment the correct size,
making best use of resources?(Time, budget?)

71. Information literacy & statistics**
 First generation of literacy is when you know
how to read and write.
 Second generation of literacy is when you are
computer literate
 Third generation - it is critical for all of us to be
information literate
And, one of the purposes of statistics is to bring
about information literacy in the society
**Dr K C Chakrabarty, “Uses and misuses of statistics” address by Deputy Governor of
the Reserve Bank of India, at the DST Centre for Interdisciplinary Mathematical
Sciences, Faculty of Science, BHU, 20 March 2012.
71

72. Thank you
Deshmukh.sg@gmail.com