RM_Week_5_Unit_04.ppsx...................

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1. DRP 901 -ResearchandPublicationEthics
Unit-IV: Data analysis -II Design of Experiments
ANOVA -Error Analysis
Correlation and Regression
Simulation
Optimization (Definition and Examples only).
01
Course InstructorLProf.Dr.A.G.Srinivasan–
Addl. Dean (Research)

2. DRP 901 -ResearchandPublicationEthics
Unit-IV: Data analysis -II Design of Experiments
•BASIC PRINCIPLES OF EXPERIMENTAL DESIGNS
•Professor Fisher has enumerated three principles of experimental
designs:
•(1) Principle of Replication
•(2) the Principle of Randomization
•(3) Principle of Local Control.
Course InstructorLProf.Dr.A.G.Srinivasan–
Addl. Dean (Research)

3. DRP 901 -ResearchandPublicationEthics
Unit-IV: Data analysis -II Design of Experiments
•According to the Principle of Replication;
•The experiment should be repeated more than once.
•Thus, each treatment is applied in many experimental units instead of
one.
Course InstructorLProf.Dr.A.G.Srinivasan–
Addl. Dean (Research)

4. DRP 901 -ResearchandPublicationEthics
Unit-IV: Data analysis -II Design of Experiments
•The Principle of Randomization provides protection, when we
conduct an experiment, against the effect of extraneous factors by
randomization.
•In other words, this principle indicates that we should design or plan
the experiment in such a way that the variations caused by
extraneous factors can all be combined under the general heading of
“chance.”
Course InstructorLProf.Dr.A.G.Srinivasan–
Addl. Dean (Research)

5. DRP 901 -ResearchandPublicationEthics
Unit-IV: Data analysis -II Design of Experiments
•The Principle of Local Control is another important principle of
experimental designs.
•Under this extraneous factor, the known source of variability, is made
to vary deliberately over as wide a range as necessary
•This needs to be done in such a way that the variability it causes can
be measured and hence eliminated from the experimental error.
Course InstructorLProf.Dr.A.G.Srinivasan–
Addl. Dean (Research)

6. DRP 901 -ResearchandPublicationEthics
Unit-IV: Data analysis -II Design of Experiments
•Important experiment designs are as follows:
•(a) Informal experimental designs:
•(i) Before-and-after without control design.
•(ii) After-only with control design.
•(iii) Before-and-after with control design.
Course InstructorLProf.Dr.A.G.Srinivasan–
Addl. Dean (Research)

7. DRP 901 -ResearchandPublicationEthics
Unit-IV: Data analysis -II Design of Experiments
•(b) Formal experimental designs:
•(i) Completely randomized design (C.R. Design).
•(ii) Randomized block design (R.B. Design).
•(iii) Latin square design (L.S. Design).
•(iv) Factorial designs.
Course InstructorLProf.Dr.A.G.Srinivasan–
Addl. Dean (Research)

8. DRP 901 -ResearchandPublicationEthics
Unit-IV: Data analysis -II Design of Experiments
•ANOVA is essentially a procedure for testing the difference among different
groups of data for homogeneity.
•“The essence of ANOVA is that the total amount of variation in a set of data is
broken down into two types, that amount which can be attributed to chance and
that amount which can be attributed to specified causes.”
•1: There may be variation between samples and also within sample
•items.
•ANOVA consists in splitting the variance for analytical purposes.
Course InstructorLProf.Dr.A.G.Srinivasan–
Addl. Dean (Research)

9. DRP 901 -ResearchandPublicationEthics
Unit-IV: Data analysis -II Design of Experiments
•Hence, it is a method of analyzing the variance to which a response is
subject into its various components corresponding to various sources
of variation.
Course InstructorLProf.Dr.A.G.Srinivasan–
Addl. Dean (Research)

10. DRP 901 -ResearchandPublicationEthics
Unit-IV: Data analysis –II
Course InstructorLProf.Dr.A.G.Srinivasan–
Addl. Dean (Research)

11. DRP 901 -ResearchandPublicationEthics
Unit-IV: Data analysis –II
Course InstructorLProf.Dr.A.G.Srinivasan–
Addl. Dean (Research)

12. DRP 901 -ResearchandPublicationEthics
Unit-IV: Data analysis –II
Course InstructorLProf.Dr.A.G.Srinivasan–
Addl. Dean (Research)

13. DRP 901 -ResearchandPublicationEthics
Unit-IV: Data analysis –II
Course InstructorLProf.Dr.A.G.Srinivasan–
Addl. Dean (Research)

14. DRP 901 -ResearchandPublicationEthics
Unit-IV: Data analysis –II
Course InstructorLProf.Dr.A.G.Srinivasan–
Addl. Dean (Research)

15. DRP 901 -ResearchandPublicationEthics
Unit-IV: Data analysis –II
Course InstructorLProf.Dr.A.G.Srinivasan–
Addl. Dean (Research)

16. DRP 901 -ResearchandPublicationEthics
Unit-IV: Error Analysis
•Overview of Error Analysis
•What is an error?
•Anerroris a form in learner language that isinaccurate, meaning it is
different from the forms used by others
Course InstructorLProf.Dr.A.G.Srinivasan–
Addl. Dean (Research)

17. DRP 901 -ResearchandPublicationEthics
What is error analysis?
•Errors and Data Analysis Types of errors:
•1)Precision errors –these are random errors. These could also be
called repeatability errors.
•They are caused by fluctuations in some part (or parts) of the data
acquisition.
•These errors can be treated by statistical analysis.
Course InstructorLProf.Dr.A.G.Srinivasan–
Addl. Dean (Research)

18. DRP 901 -ResearchandPublicationEthics
What is error analysis?
•2)Bias errors –These are systematic errors. Zero offset, scale errors
(nonlinear output vs input) , hysteresis, calibration errors, etc.
•If these are hidden, they are essentially impossible to correct.
•These are often negligible in instruments used for calibration for a
long time.
•But new instruments and devices can easily have bias errors. For
instance,
•when reducing scales from meters and millimeters to a scale of
nanometers bias errors can creep in due to unforeseen new effects.
Course InstructorLProf.Dr.A.G.Srinivasan–
Addl. Dean (Research)

19. DRP 901 -ResearchandPublicationEthics
•3)Analysis errors –wrong theory or wrong analysis applied to data,
which are used to ”fit” the data.
•This is usually not considered as a error in the data acquisition, but
nevertheless can waste a lot of time.
Course InstructorLProf.Dr.A.G.Srinivasan–
Addl. Dean (Research)

20. DRP 901 -ResearchandPublicationEthics
Unit-IV: Correlation and Regression
•Correlation and Regression
•Correlation and regression are the two most commonly used
techniques for investigating the relationship between quantitative
variables.
•Here regression refers to linear regression. Correlation is used to give
the relationship between the variables whereas linear regression uses
an equation to express this relationship.
•.
Course InstructorLProf.Dr.A.G.Srinivasan–
Addl. Dean (Research)

21. DRP 901 -ResearchandPublicationEthics
Unit-IV: Correlation and Regression
•Correlation and regression are used to define some form of
association between quantitative variables that are assumed to have
a linear relationship.
Course InstructorLProf.Dr.A.G.Srinivasan–
Addl. Dean (Research)

22. DRP 901 -ResearchandPublicationEthics
Unit-IV: Correlation and Regression
•What are Correlation and Regression?
•Correlation and regression are statistical measurements that are
used to give a relationship between two variables.
•For example, suppose a person is driving an expensive car then it is
assumed that she must be financially well.
•To numerically quantify this relationship, correlation and regression
are used.
Course InstructorLProf.Dr.A.G.Srinivasan–
Addl. Dean (Research)

23. DRP 901 -ResearchandPublicationEthics
Unit-IV: Correlation and Regression
•Correlation can be defined as a measurement that is used to
quantify the relationship between variables.
•If an increase (or decrease) in one variable causes a corresponding
increase (or decrease) in another then the two variables are said to
be directly correlated.
Course InstructorLProf.Dr.A.G.Srinivasan–
Addl. Dean (Research)

24. DRP 901 -ResearchandPublicationEthics
Unit-IV: Correlation and Regression
•Similarly, if an increase in one causes a decrease in another or vice
versa, then the variables are said to be indirectly correlated.
•If a change in an independent variable does not cause a change in
the dependent variable then they are uncorrelated.
•Thus, correlation can be positive (direct correlation), negative
(indirect correlation), or zero.
•This relationship is given by the correlation coefficient.
Course InstructorLProf.Dr.A.G.Srinivasan–
Addl. Dean (Research)

25. DRP 901 -ResearchandPublicationEthics
Unit-IV: Correlation and Regression
•Regression Definition
•Regression can be defined as a measurement that is used to quantify
how the change in one variable will affect another variable.
•Regression is used to find the cause and effect between two variables.
Linear regression is the most commonly used type of regression
because it is easier to analyze as compared to the rest
•Linear regression is used to find the line that is the best fit to establish
a relationship between variables.
Course InstructorLProf.Dr.A.G.Srinivasan–
Addl. Dean (Research)

26. DRP 901 -ResearchandPublicationEthics
Unit-IV: Correlation and Regression
Course InstructorLProf.Dr.A.G.Srinivasan–
Addl. Dean (Research)

27. DRP 901 -ResearchandPublicationEthics
Unit-IV: Simulation
For a detailed discussion refer:
Discrete Event System Simulation by Jerry Banks et al 2013
Pearson Education.
Course InstructorLProf.Dr.A.G.Srinivasan–
Addl. Dean (Research)

28. DRP 901 -ResearchandPublicationEthics
Unit-IV: Optimization
Refer Operations Research by HamdyA Taha2016 Pearson;
10th edition
Course InstructorLProf.Dr.A.G.Srinivasan–
Addl. Dean (Research)

29. DRP 901 -ResearchandPublicationEthics
References:
https://courses.physics.illinois.edu/phys403/sp2012/lectur
es/error%20and%20data%20analysis.pdf
https://www.cuemath.com/data/correlation-and-
regression/
Course InstructorLProf.Dr.A.G.Srinivasan–
Addl. Dean (Research)

30. DRP 901 -ResearchandPublicationEthics
References:
Kothari, C R 2004, Research Methodology: Methods and
Techniques 2nd Edition, New Age International Publication.
PanneerselvamR 2014, Research Methodology 2nd Edition,
PHI learning & Pvt.Ltd.
3. Anderson B H, Dursaton, & Poole M, 1997, Thesis and
assignment writing, WileyEastern.
4. Venkataraman, M 2015, An introduction to Intellectual
property rights VenkataramanM, Publications.
Course InstructorLProf.Dr.A.G.Srinivasan–
Addl. Dean (Research)