Quantitative Methods

… one of the core Subjects in Public Management

QuantitativeMethods3Subject description

This public management subject, within the Analysis
and Skills domain, covers the principles and techniques of quantitative methods that are most useful in analyzing public policy. The core topics and concepts of Quantitative Methods are listed below and organized by topic, as they are in Atlas104 Quantitative Methods.

The topics and concepts for this subject reflect those taught in the required courses of highly regarded programs. See, for example, the detailed comparison of syllabi for the first-year required courses in quantitative methods at Harvard HKS, Michigan Ford, NYU Wagner, and Wisconsin La Follette in Comparing Course Workload – Quantitative Methods. These are well captured in the remarkable open access resource created by a team of professors led by Rice University:

OnlineStatBook, Online Statistics Education – An Interactive Multimedia Course of Study, at http://onlinestatbook.com/2/index.html, PDF version entitled Introduction to Statistics at http://onlinestatbook.com/Online_Statistics_Education.pdf, accessed 13 May 2016.

We have therefore used OnlineStatBook to help structure the sequence of topics and concept within topics. Indeed, as a temporary measure until we have time to create Atlas pages for each of the concepts we use section headings from OnlineStatBook as the concept name with the link pointing directly to the page on OnlineStatBook.

Core normed topics
The Study of Quantitative Methods

Describing Distributions

Bivariate Data

Probability Theory

Research Design

Normal Distributions and Advanced Graphs

Sampling Distributions

Estimation and Hypothesis Testing

Tests of Means and Power

Regression

Analysis of Variance

Transformation, Chi Square, Distribution Free Tests, and Effect Size

Core concepts and terms
The Study of Quantitative Methods

What are Statistics?

Importance of Statistics

Descriptive Statistics

Inferential Statistics

Variables

Percentiles

Levels of Measurement

Distributions

Summation Notation

Linear Transformations

Logarithms

Describing Distributions

Qualitative Variables

Quantitative Variables

Stem and Leaf Displays

Histograms

Frequency Polygons

Box Plots

Box Plot Demonstration

Bar Charts

Line Graphs

Dot Plots

Central Tendency

What is Central Tendency

Measures of Central Tendency

Median and Mean

Additional Measures

Comparing measures

Variability

Measures of Variability

Estimating Variance Simulation

Shape

Effects of Transformations

Variance Sum Law I

Bivariate Data

Introduction to Bivariate Data

Values of the Pearson Correlation

Guessing Correlations Simulation

Properties of Pearson’s r

Computing Pearson’s r

Restriction of Range

Variance Sum Law II

Probability

Introduction to Probability

Basic Concepts

Conditional Probability

Gambler’s Fallacy

Permutations and Combinations

Birthday Simulation

Binomial Distribution

Binomial Demonstration

Poisson Distribution

Multinomial Distribution

Hypergeometric Distribution

Base Rates

Bayes’ Theorem

Monty Hall Problem

 

 

Research Design

Scientific Method

Measurement

Basics of Data Collection

Sampling Bias

Experimental Designs

Causation

Normal Distributions and Advanced Graphs

Introduction to Normal Distributions

History

Areas of Normal Distributions

Varieties of Normal Distributions

Standard Normal

Normal Approximation to the Binomial

Q-Q Plots

Contour Plots

3D Plots

Sampling Distributions

Introduction to Sampling

Sample Size

Central Limit Theorem

Sampling Distribution of the Mean

Sampling Distribution of Difference Between Means

Sampling Distribution of Pearson’s r

Sampling Distribution of a Proportion

Estimation and Hypothesis Testing

Introduction to Estimation

Degrees of Freedom

Characteristics of Estimators

Bias and Variability Simulation

Confidence Intervals

Introduction to Confidence Intervals

Confidence Interval for the Mean

t distribution

Confidence Interval Simulation

Confidence Interval for the Difference Between Means

Confidence Interval for Pearson’s Correlation

Confidence Interval for a Proportion

Introduction to Hypothesis Testing

Significance Testing

Type I and Type II Errors

One- and Two-Tailed Tests

Interpreting Significant Results

Interpreting Non-Significant Results

Steps in Hypothesis Testing

Significance Testing and Confidence Intervals

Misconceptions

 

Tests of Means and Power

Single Mean

t Distribution Demo

Difference between Two Means (Independent Groups)

Robustness Simulation

All Pairwise Comparisons Among Means

Specific Comparisons

Difference between Two Means (Correlated Pairs)

Correlated t Simulation

Specific Comparisons (Correlated Observations)

Pairwise Comparisons (Correlated Observations)

Power and Null Hypothesis

Example Calculations

Power Demo 1

Power Demo 2

Factors Affecting Power

Regression

Introduction to Simple Linear Regression

Linear Fit Demo

Partitioning Sums of Squares

Standard Error of the Estimate

Inferential Statistics for b and r

Influential Observations

Regression Toward the Mean

Introduction to Multiple Regression

Analysis of Variance

Introduction to ANOVA

ANOVA Designs

One-Factor ANOVA (Between-Subjects)

One-Way Comparisons

Multi-Factor ANOVA (Between-Subjects)

Unequal Sample Sizes

Tests Supplementing ANOVA

Within-Subjects ANOVA

Power of Within-Subjects Designs

Transformation, Chi Square, Distribution Free Tests, and Effect Size

Log

Tukey’s Ladder of Powers

Box-Cox Transformations

Chi Square Distribution

One-Way Tables (Testing Goodness of Fit)

Testing Distributions Demo

Contingency Tables

2 x 2 Table Simulation

Benefits of Distribution-Free Tests

Randomization Tests – Association (Pearson’s r)

Randomized Tests – Contingency Tables (Fisher’s Exact Test)

Rank Randomization Tests – Two Conditions (Mann-Whitney U, Wilcoxon Rank Sum)

Rank Randomization Tests – Two or More Conditions (Kruskal-Wallis)

Rank Randomization Tests – Association (Spearman’s ρ)

Proportions

Difference between Means

Variance Explained

 

Open access resources

Khan Academy, Probability and Statistics, at https://www.khanacademy.org/math/probability, accessed 12 May 2016.

OnlineStatBook, Online Statistics Education – An Interactive Multimedia Course of Study, at http://onlinestatbook.com/2/index.html, PDF version entitled Introduction to Statistics at http://onlinestatbook.com/Online_Statistics_Education.pdf, accessed 13 May 2016.

Glossary in the OnlineStatBook, at http://onlinestatbook.com/2/glossary/index.html, accessed 13 May 2016.

Saylor Academy Open Textbooks, Introductory Statistics, HTML version at https://saylordotorg.github.io/text_introductory-statistics/, PDF version at http://www.saylor.org/site/textbooks/Introductory%20Statistics.pdf, accessed 11 May 2016.

Comparison of topics from open access resources

The table below lists the topic headings in OnlineStatBook, the Saylor Academy book, Introductory Statistics, and in the Khan Academy course Probability and Statistics, and aligns them with the first-draft Atlas topic.

Atlas Quantitative Methods
OnlineStatBook
Saylor Academy Introductory Statistics Online Textbook
Khan Academy Probability and Statistics
The Study of Quantitative Methods Introduction Chapter 1: Introduction Independent and dependent events

 

Describing Distributions Graphing Distributions

Summarizing Distributions

Chapter 2: Descriptive Statistics Descriptive statistics
Bivariate Data Describing Bivariate Data Chapter 4: Discrete Random Variables

Chapter 5: Continuous Random Variables

Probability Probability Chapter 3: Basic Concepts of Probability Probability and combinatorics

 

Research Design Research Design Statistical studies

 

Normal Distributions and Advanced Graphs Normal Distribution

Advanced Graphs

Random variables and probability distributions
Sampling Distributions Sampling Distributions Chapter 6: Sampling Distributions
Estimation and Hypothesis Testing Estimation

Logic of Hypothesis Testing

Chapter 7: Estimation

Chapter 8: Testing Hypotheses

Inferential statistics
Tests of Means and Power Tests of Means

Power

Chapter 9: Two-Sample Problems
Regression Regression Chapter 10: Correlation and Regression Regression
Analysis of Variance Analysis of Variance
Transformation, Chi Square, Distribution Free Tests, and Effect Size Transformations

Chi Square

Distribution Free Tests

Effect Size

Chapter 11: Chi-Square Tests and F-Tests

Page created by: Ian Clark, last modified on 15 May 2016.

Image: Scope, at http://www.scope-mr.ch/en/services/methods/, accessed 10 March 2016.