Statistical Analysis

Module 1 - Random Variables, Probability Distributions

 Motivate the use of statistical methods for managerial decision making

Discuss the concepts of probability distributions and random variables

Review methods of representing data, pictorially and through summary statistics

Module 2 - Properties Of Normal Distribution

Introduce standard normal distribution

Discuss applications of normal distribution

Module 3 - Sampling Distributions And The Central Limit Theorem

Introduce the concept of statistical inference

Recognize the existence of sample-to-sample variations

Understand central limit theorem and its implications for statistical inference

Module 4 - Confidence Intervals (I)

Introduce the concept of confidence intervals as a way to make statistical inferences

Calculate confidence intervals for population mean with known and unknown population

Module 5 - Confidence Intervals (II)

Calculate confidence intervals for population proportions

Calculate confidence intervals for population variance

Quantify minimum sample sizes to achieve certain margin of error in predictions

Module 6 - Hypothesis Tests (I)

Learn how to state null and alternative hypotheses

Understand type-I and type-II errors

Conduct one-sided hypothesis test for population proportion / mean

Module 7 - Hypothesis Tests (II)

Conduct two-sided hypothesis tests for population proportion / mean

Module 8 - Comparison Of Two Populations

 Compare the means using paired observations

Test for the difference of two population means using independent samples

Test for the difference of two population proportions

Module 9 - Analysis Of Variance

Introduce Design of Experiments

Conduct one way Analysis of Variance (ANOVA)

Module 10 - Nonparametric Statistics

Introduce the notion of statistical tests on ordinal data

Test for the difference between mean ranks using paired observations

Compare mean ranks in two independent samples parametric Statistics

Module 11 - Introduction To Regression Methods

Bivariate data

Scatter plot

Compare mean ranks in two independent samples

Covariance

Correlation coefficient

Uses and issues

Linear regression

Covariance

Assumptions

Module 12 - Several Regressors

Scatter plot matrix

Multiple linear regression

Ordinary Least Squares method (OLS)

Basic regression summary

Interpretation of coefficient estimates

standard errors

t-values and p-values

Basic tests

ANOVA table

Module 13 - Regression Models For Count Data

Generalized Linear Models

Binary and multinomial logistic regressions

Poisson regression

Zero-inflated Poisson regression

Negative Binomial regression

Module 14 - Missing Value Analysis

Missing value patterns: Missing completely at random (MCAR). Missing at random (MAR). Missing not at random (MNAR)

List wise deletion. Pairwise deletion

Various imputation methods: Hot deck imputation. Mean substitution. Regression imputation. EM imputation

Module 15 - Survival Analysis

Censoring and truncation. Characteristics of survival analysis data

Time-to-event data. Hazard and survival functions

Kaplan-Meier estimate of survival function–

Cox proportional hazards model (ph), estimation and its analysis. Extensions

Stratified ph; ph with time-varying covariates–

Parametric survival analysis with standard distributions

Accelerated failure time models

Module 16 - Design Of Experiments

Basic concepts: randomization, replication and control

Experimental design for testing differences in several means: Completely randomized and randomized–complete block designs. Cross-over designs

Two-level factorial experiments full and fractional. Plackett-Burman designs

Designs for three or more levels. Taguchi designs. Response surface designs

Case-Control designs for campaign evaluation

Designs for conjoint analysis