Statistical Methods and Data Analysis

O.P. Jindal Global University via Coursera

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Overview

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Welcome to the Statistical Methods and Data Analysis course! This course serves as an introduction to the statistical and computation methods that have become indispensable tools for those pursuing careers in public policy. Alongside offering the necessary background in basic and applied statistics, the course will also introduce you to the powerful R programming interface. For statistical methods, the course focuses on understanding and application of different concepts and tools of statistics. You will be introduced to data visualization, which is an indispensable tool in this period of vast information around us. In this course, you will learn how to summarize data using descriptive statistics. Next, you will learn about sampling and how to make inferences about the population from a sample via probability theory. You will understand the difference between experimental and observational data. You will learn how to analyze experimental data using tests of significance. For observational data, you will learn correlation analysis and regression analysis. Finally, the course will help you to learn about regression with big data. For programming skills, you will learn R as a programming language for statistical computing. R is a free software environment for statistical computing and has lots of support information available on the Internet. At the end of this course, you will have the confidence of executing your research project using R.

Syllabus

Data Visualization

Statistical methods, by definition, are tools for identifying patterns in large datasets. This module takes the first step towards statistical analysis by exploring various strategies for visualizing data, an increasingly important skill in today’s era of big data. This module explains the different forms of data, types of plots, and charts used to depict the different forms of data. In addition, the module focuses on different visualization techniques appropriate for big data.

Descriptive Statistics

While data visualization gives us a ‘first cut’ in the empirical world, knowing what the data ‘looks like’ will not take us far towards identifying relationships between variables — the focal point of policymaking. At the minimum, identification requires that the researcher be able to summarize large amounts of information in the form of descriptive statistics. This module explains the measures of central tendency and dispersion for ungrouped data and for grouped data. The measures of central tendency and dispersion for ungrouped data include mean, median, mode, standard deviation, skewness, and kurtosis. The means of central tendency and dispersion for grouped data include grouped mean, grouped standard deviation, grouped mode, and grouped median.

Probability Distributions

Except in the rarest of cases when data on the entire population is available for all attributes of interest to the researcher, social scientists must draw inferences about a population from a sample drawn from that population. This module focuses on the statistical reasoning involved in studying the uncertainty attached to sample statistics. For making inferences about the population from a sample, the module explains the fundamentals of probability theory. In addition, the module explains the concepts of random variables and function of random variables. Finally, the module covers the concepts and applications of the binomial and normal distributions.

Sampling

This module discusses the various strategies available to researchers for drawing samples from a population and the first principles involved in determining sample size. The module explains the sampling strategies for sampling from a population. In addition, the module explains how to measure the accuracy of sample estimates. Finally, the module focuses on statistical inference. The goal of statistical inference is to make a statement about something that is not observed based on something that is observed, within a certain level of uncertainty. The module will discuss the Central Limit Theorem (CLT) and the concept of the confidence interval, which allow us to make such statements.

Tests of Significance

This module introduces the critical distinction between experimental data and observational data. In addition, the module explores statistical inference in the context of experimental data using tests of significance. You will also learn about observational data and the problem of confounding, controlled experiment, and natural experiment. The module focuses on the concepts and methods for analyzing statistical significance, including analytical framework, one sample t-test, two sample t-test, and ANOVA.

Correlation and Regression

This module introduces the foundational model for statistical inference with observational data, namely, the ordinary least squares (OLS) regression, paying particular attention to the conditions under which the OLS estimator is the best linear unbiased estimator (BLUE). You will learn about the concept of association, which helps to understand the relationship between two variables. You will also learn about the measures of association appropriate for each variable type: lambda coefficient for nominal variables, gamma coefficient for ordinal variables, and correlation coefficient for interval-ratio variables. Finally, the module focuses on regression analysis by explaining bivariate OLS and multivariate OLS.

Measurement Error, Complex Residual Structures, and Limited Dependent Variables

This module focuses on advanced modeling strategies in settings where the best linear unbiased estimator (BLUE) assumptions are violated. You will learn about how to get valid ordinary least squares (OLS) estimates when one or the other key assumption on regression errors for OLS estimates to be BLUE is violated. In particular, you will learn how to detect and correct OLS estimates for reverse causality, heteroscedasticity, and serial correlation. Next, under violations of BLUE assumptions on model and variable specification, you will learn how to model nominal and ordinal dependent variables.

Regression with Big Data

Running regression models on large-scale datasets with millions of observations and thousands of variables can be a daunting task. This module examines the strategies for building regression models when dealing with such datasets. For conducting big data regression analysis with nominal dependent variables, you will learn the concepts of decision tree, pruning, cross-validation, and random forest. You will also learn about the penalized regression approach, which is useful for running big data regressions when the dependent variable is an interval-ratio variable.