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.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.INDUSTRY SUPPORT : Biotech companies, pharma companies and omics companies may be interested in this course.
Overview
Syllabus
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
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
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
