Introduction to Biostatistics

COURSE PLAN: Observations from biological laboratory experiments, clinical trials, and health surveys always carry some amount of uncertainty. In many cases, especially for 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 the advancement of microscopy and molecular tools, rich data can be generated from experiments. To make sense of this data, we need to integrate this data into a model using tools from statistics. In this course, we will discuss different statistical tools required to (i) analyze our observations, (ii) design new experiments, and (iii) integrate a large number of observations in a single unified model.

Introduction to the course.
Data representation and plotting.
Arithmetic mean.
Geometric mean.
Measure of Variability, Standard deviation.
SME, Z-Score, Box plot.
Moments, Skewness.
Kurtosis, R programming.
R programming.
Correlation.
Correlation and Regression.
Correlation and Regression Part-II.
Interpolation and extrapolation.
Nonlinear data fitting.
Concept of Probability: Introduction and basics.
Counting principle, Permutations, and Combinations.
Conditional probability.
Conditional probability and Random variables.
Expectation, Variance and Covariance Part - II.
Binomial random variables and Moment generating function.
Random variables, Probability mass function, and Probability density function.
Expectation, Variance and Covariance.
Probability distribution : Poisson distribution and Uniform distribution Part-I.
Uniform distribution Part-II and Normal distribution Part-I.
Normal distribution Part-II and Exponential distribution.
Sampling distributions and Central limit theorem Part-I.
Sampling distributions and Central limit theorem Part-II.
Central limit theorem Part-III and Sampling distributions of sample mean.
Central limit theorem - IV and Confidence intervals.
Confidence intervals Part- II.
Test of Hypothesis - 1.
Test of Hypothesis - 2 (1 tailed and 2 tailed Test of Hypothesis, p-value).
Test of Hypothesis - 3 (1 tailed and 2 tailed Test of Hypothesis, p-value).
Test of Hypothesis - 4 (Type -1 and Type -2 error).
T-test.
1 tailed and 2 tailed T-distribution, Chi-square test.
ANOVA - 1.
ANOVA - 2.
ANOVA - 3.
ANOVA for linear regression, Block Design.