**About the Course**

Observations from
biological laboratory experiments, clinical trials, and health surveys always
carry some amount of uncertainty. In many cases, especially for the laboratory
experiments, it is inevitable to just ignore this uncertainty due to large
variation in observations. Tools from statistics are very useful in analyzing
this uncertainty and filtering noise from data. Also, due to advancement of
microscopy and molecular tools, a rich data can be generated from experiments.
To make sense of this data, we need to integrate this data a model using tools
from statistics. In this course, we will discuss about different statistical
tools required to

(i) analyze our observations,

(ii) design new experiments, and

(iii) integrate large number of observations in single unified model.

We will discuss about both the theory of these tools and will do hand-on exercise on open source software R.

**Intended Audience:**

BE Biotech/Biosciences/Bioengineering,MSc Biotech/Bio sciences/Bioengineering,PhD Biotech/Biosciences/Bioengineering.It is taught as a core course for M. Tech Biomedical Engineering students at IIT Bombay.

**Pre-requisites **

Basic knowledge of 12th standard mathematics is sufficient.

**Core/Elective ,UG/PG**

It can be taught both as a core and as an elective to students depending on their background.

**Industries that will recognize this course**

Biotech companies, pharma companies and omics
companies may be interested in this course.

(i) analyze our observations,

(ii) design new experiments, and

(iii) integrate large number of observations in single unified model.

We will discuss about both the theory of these tools and will do hand-on exercise on open source software R.

BE Biotech/Biosciences/Bioengineering,MSc Biotech/Bio sciences/Bioengineering,PhD Biotech/Biosciences/Bioengineering.It is taught as a core course for M. Tech Biomedical Engineering students at IIT Bombay.

Basic knowledge of 12th standard mathematics is sufficient.

It can be taught both as a core and as an elective to students depending on their background.

Dr.Shamik Sen joined IIT Bombay in July 2010 as an Assistant Professor in the Department of Biosciences and Bioengineering. Dr. Sen earned a B.E. in Mechanical Engineering from Jadavpur University, Kolkata, and a M. Tech in Mechanical Engineering from IIT Kanpur. He then completed his PhD in Mechanical Engineering from University of Pennsylvania, where he worked in the area of mechanobiology.

He
is currently working in the area of mechanobiology where he is integrating
mechanics and biology for probing stem cell biology and cancer cell biology. He
is combining experiments with simulations for addressing his research
questions.

**Course Plan**

**Week
1**

Lecture 1. Introduction to the course

Lecture 2. Data representation and plotting

Lecture 3. Arithmetic mean

Lecture 4. Geometric mean

Lecture 5. Measure of Variability, Standard deviation

**Suggested Reading**

1. Introduction to Probability & Statistics - Medenhall, Beaver, Beaver 14th Edition

2. Introduction to Probability and statistics for engineers and scientists, S M Ross, 3rd Edition

**Certification Exam :**

**Certificate :**

Lecture 1. Introduction to the course

Lecture 2. Data representation and plotting

Lecture 3. Arithmetic mean

Lecture 4. Geometric mean

Lecture 5. Measure of Variability, Standard deviation

**Week
2**

Lecture 6. SME, Z-Score, Box plot

Lecture 8. Kurtosis, R programming

Lecture 9. R programming

Lecture 10. Correlation

**Week
3**

Lecture 11. Correlation and Regression

Lecture 12. Correlation and Regression
Part-II

Lecture 13. Interpolation and
extrapolation

Lecture 14. Nonlinear data fitting

Lecture 15. Concept of Probability: introduction
and basics

**Week
4**

Lecture 16. counting principle,
Permutations, and Combinations

Lecture 17. Conditional probability

Lecture 18. Conditional probability and
Random variables

Lecture 19. Random variables,
Probability mass function, and Probability density function

Lecture 20. Expectation, Variance and
Covariance

**Week
5**

Lecture 21. Expectation, Variance and
Covariance Part-II

Lecture 22. Binomial random variables
and Moment generating function

Lecture 23. Probability distribution:
Poisson distribution and Uniform distribution Part-I

Lecture 24. Uniform distribution Part-II
and Normal distribution Part-I

Lecture 25. Normal distribution Part-II
and Exponential distribution

**Week
6**

Lecture 26. Sampling distributions and Central
limit theorem Part-I

Lecture 27. Sampling distributions and
Central limit theorem Part-II

Lecture 28. Central limit theorem
Part-III and Sampling distributions of sample mean

Lecture 29. Central limit theorem - IV
and Confidence intervals

Lecture 30. Confidence intervals Part-
II

**Week
7**

Lecture 31. Test of Hypothesis - 1

Lecture 32. Test of Hypothesis - 2 (1
tailed and 2 tailed Test of Hypothesis, p-value)

Lecture 33. Test of Hypothesis - 3 (1
tailed and 2 tailed Test of Hypothesis, p-value)

Lecture 34. Test of Hypothesis - 4 (Type
-1 and Type -2 error)

Lecture 35. T-test

**Week
8**

Lecture 36. 1 tailed and 2 tailed
T-distribution, Chi-square test

Lecture 37. ANOVA - 1

Lecture 38. ANOVA - 2

Lecture 39. ANOVA - 3

Lecture 40. ANOVA for linear regression,
Block Design

1. Introduction to Probability & Statistics - Medenhall, Beaver, Beaver 14th Edition

2. Introduction to Probability and statistics for engineers and scientists, S M Ross, 3rd Edition

- The exam is optional for a fee.Exams will be on 26 March 2017.
- Time : Shift 1: 9 AM -12 Noon;Shift 2 : 2 PM-5 PM
- Any one shift can be chosen to write the exam for a course.
- Registration URL : Announcements will be made when the registration form is open for registrations.
- The online Registration form has to be filled and the certification exam fee needs to be paid.More details will be made available when the exam registration form is published.

- Final score will be calculated as : 25% assignment score + 75% final exam score.
- 25% assignment score is calculated as 25% of average of 8 weeks course : Best 6 out of 8 assignments
- E-Certificate will be given to those who register and write the exam and score greater than or equal to 40% final score. Certificate will have your name, photograph and the score in the final exam with the breakup. It will have the logos of NPTEL and IIT Bombay. It will be e-verifiable at nptel.ac.in/noc.