Statistical Inference: Inference means to draw the conclusions, when decisions are taken
with the help of statistical techniques then it is called statistical inference. It helps to take
decision under uncertainty.
Procedure of Statistical Inference: There are two procedures of statistical inference-
A) Estimation: This procedure helps in estimation of population parameters and setting
up the confidence intervals for them.
B) Tests of Statistical Hypothesis: In this procedure the following terms come up
which are defined as:
Statistical Hypothesis: A statistical hypothesis is a statement about
population parameter which we want to verify on the basis of information
available from a sample. This hypothesis are classified in two groups-
Null Hypothesis (H₀): It is a hypothesis that is tested by a decision maker.
Decision makers should take up the neutral or null attitude of regarding
outcome of the test.
Alternative Hypothesis (H₁): The acceptance or rejection of H₀ is meaningful
only when it is being tested against an alternative hypothesis.
Example: There are two drugs A and B. We have to test that which drug is
superior A or B, then
H₀: There is no difference between the effects of two drugs.
H₁: There is difference between the effects of two drugs.
(a) Effect of A ≠ Effect of B
(b) Effect of A < Effect of B
(c) Effect of A > Effect of B
Degree of Freedom (df): Number of independent observations are called the
degree of freedom.
Errors: In testing of hypothesis, four possible situations come up which are
True Situation Decision from sample
H₀ is true Correct Type I error (α)
H₀ is false
Type I error: The error of rejecting H
Type II error: The error of accepting H
Level of Significance
error. It is always fixed in advance before collecting the information. A level
is called level of significance
Size of the test: Probability of committing type I error is called the size of the
test. In general α and size of the test are equal i.e. α=0.05 or α=0.01, α=0.001.
Power of the test
the power function of the test hypothesis H
H₁. The value of power function at a parameter point is called the power of the
test at that point.
statistic is known as its standard error.
Most Powerful Test
number of tests. We try to choose that test for which type II error is minimum.
Critical Regions (Left, two
Procedure of hypothesis testing
• Frame H₀ and H₁.
• Fixed α (Level of significance).
• Apply appropriate tests, multiple range, non
• Compare the calculated value with
Type II error (β) Correct
H₀, when it is true is called type I error.
H₀, when it is false is called type II
Significance: Experimenter fixes the level of committing type I
(α), which does not exceed the level fixed in
test: The probability of type II error is known as β. 1
H₀ against the alternative hypothesis
₁. : The standard deviation of the sampling distribution of a
Test: For the fixed level of significance, there are a large
s two-sided, Right sided)
non-parametric tests or others and calculate the
tabulated value and take the decision
If calculated < tab. Accept H₀
Calculated > tab. Reject H₀.
₀, ₀, f 1-β is called
Quality concern of Social science Research: Issues and
Understanding what ‘science’ is all about….(Encarta Dictionary, 2009)
Study of physical world:
especially by using systematic
Branch of science: a particular area of study
Systematic body of knowledge
a particular subject. Something studied or performed methodically
is the object of careful study or that is
1. Social sciences
2. Physical sciences or natural sciences
3. Life sciences
4. Management sciences, etc.
Social science: Science of society…
What ‘Research’ involves…
Research = “to go about seeking
Research is basically a creative
stock of knowledge and help in devising new
society a better place.
Research has also been defined variously as:
Data / information / facts collection
A studious inquiry or examination…
Empirical research is not derived from application of logic; rather, it is
: The study of the physical and natural world and phenomena,
observation and experiment.
or knowledge of the physical world.
knowledge: A systematically organized body of knowledge
methodically: An activity that
carried out according to a developed
nces seeking” or ‘search’ (French “recherché”)
work conducted in a systematic manner to
applications that would make the
for advancement of knowledge
Revisiting the purpose of research
Well-being of the society…
The current massive data availability
Rapid and monumental changes and implications on the future of the professions
e.g. technology ‘disruptions’ rendering traditional approaches antiquated, opaque,
and unaffordable (Susskind &Susskind, 2015)
The Recurring Question of ‘Methodology’ and ‘Methods’
Methodology is the general research strategy
to undertake the research, the methods you will use, + the theoretical justification fo
using the methods
‘Methodology’ is not synonym for method…
Methods captures the means or modes for collecting data (publication research,
interviews, surveys, etc.) and in some cases, how you want to analyze, compute or
infer from the result.
Exploratory research-Helping to identify and define research problems
Constructive research- Testing theories and proposing solutions
Empirical Research-Testing the feasibility of solution using real
Two major types of empirical social research design (Gorard, 2013)
Formal Social Research Process…
- The BIG PICTURE
– the Internet age / smart phones
– outlining the way in which you want
Wider Variety of Data Sets… For All Social Sciences Subjects
Errors in Data Analytics
Are ‘Numbers’ the End?
Far too many reviews are dominated by dry discussions of
a creative exercise, not a drill where people
Increased awareness of statistical errors
Why Exercising Good Judgement is
Analytical tools are as important to the modern executive as pliers and screwdrivers
are necessary to the auto mechanic.
Like a mechanic, the analyst must know his business well enough to choose the
proper statistical tool to solve the problem at hand.
numbers… The review should be
Resolving Several Social Questions in Organizational Settings …
What are your competitors doing to increase market share?
What are your competitors doing differently in the area of customer service?
How are your best-in-class competitors handling cost, quality, technology and HR?
Does your organization have the cost structure (or capital structure) that will allow it
to compete profitably?
Assume your organization needs a new organogram; what new sales management
skills will be required?
How sensible is this? One research approach to every problem?
“I suppose it is tempting, if the only tool you have is a hammer, to treat every problem as if it
were a nail.” - Abraham Maslow
Minimizing Statistical Errors- Further Tips…
Understand the underlying business theory / issues / questions first before performing
statistical analysis – this is pivotal to drafting meaningful questionnaires.
The central point of statistics is problem-solving – how are your analyses helping
your organization or country to make better decisions or policies?
Don’t carelessly round up data – check to ensure that your data add up – data
The need to produce better decisions and insights from the massive data amount
generated in today’s world of business and science.
Technology – Computers now perform most of the calculations that once dominated
statistics and related courses
Use Statistical packages / software carefully – interpretation of results must make
sense to you first before it can make sense to your audience
Minimizing Statistical Errors
Data normalization and standardization: now a major issue…
Basically, to normalize data, traditionally this means to fit the data within unity (1),
so all data values will take on a value of 0 to 1 (Ben Etzkom, 2012). Where
applicable, data should be normalized or standardized to bring all of the variables
into proportion with one another.
This is important so that the coefficients associated with each variable will scale
appropriately to adjust for the disparity in the variable sizes, thereby reflecting
meaningful relative activity between each variable, i.e., a positive coefficient will
mean that the variable acts positively towards the objective function, and vice versa.
Associated with software entrepreneurs Brian M. Rom & Kathleen Ferguson, PMPT
is an expanded risk-return paradigm designed to address the major practical
limitations of CAPM/MPT – the assumption that of a discrete, normal (meanvariance)
distribution that may not accurately reflect investment reality.
Thus, the lognormal distribution was introduced as a more robust model for the
pattern of investment returns.
Avoiding Data Confusion / Mis-Handling…
Qualitative data – Categorical - Discrete - Nominal – Ordinal (Likert scale) – we
cannot easily measure or count; e.g. gender, behaviour, quality…
Performing purely quantitative techniques such multiplication and division on
categorical data will yield meaningless results.
Don’t put ordinal data in a pie chart!
Don’t carelessly round off data particularly in pie charts.
Be careful with elaborate graphs
Clarity in knowledge of Mean, Mode, & Median…
Quantitative data – data that we can easily measure and count; e.g. age, weight,
height, sales, production output, prices…Numerical – Continuous – Interval – Ratio
Time series (trend analysis) – changing values of a variable over time / at different
Cross-sectional data – data that measure attributes of different objects at the same
time – one-shot data.
Panel Data – Data collected on various objects (individuals, countries, etc.) for
sequential periods – a combination of time-series and cross- sectional data.
Statistical Inference: Inference means to draw the conclusions, when decisions are taken