Master the essential skills to land a job as statistician! Using statistics, you can help solve real-world problems in business, engineering, the sciences, and many other fields. In this track, you'll learn how to use statistical methods to explore and model data, draw conclusions from a wide variety of datasets, and interpret and report findings.

A statistician collects and analyzes data and helps companies make sense of quantitative data, including spotting trends and making predictions.

with R

Statistician

This chapter introduces terminology of datasets and data frames in R.

Language of data

In this chapter, you will learn about observational studies and experiments, scope of inference, and Simpson's paradox.

Study types and cautionary tales

This chapter defines various sampling strategies and their benefits/drawbacks as well as principles of experimental design.

Sampling strategies and experimental design

Apply terminology, principles, and R code learned in the first three chapters of this course to a case study looking at how the physical appearance of instructors impacts their students' course evaluations.

Case study

Course evaluation

UC Berkeley admissions

US state regions

Scientists seek to answer questions using rigorous methods and careful observations. These observations—collected from the likes of field notes, surveys, and experiments—form the backbone of a statistical investigation and are called data. Statistics is the study of how best to collect, analyze, and draw conclusions from data. It is helpful to put statistics in the context of a general process of investigation: 1) identify a question or problem; 2) collect relevant data on the topic; 3) analyze the data; and 4) form a conclusion. In this course, you'll focus on the first two steps of the process.

Introduction to the Tidyverse

Taught by Dr. Mine of Duke University, this course introduces the first part of statistical analysis: identifying a question and collecting relevant data.

Introduction to Data in R

Learn the language of data, study types,  sampling strategies, and experimental design.

Probability & Statistics

In this chapter, you will learn how to create graphical and numerical summaries of two categorical variables.

Exploring Categorical Data

In this chapter, you will learn how to graphically summarize numerical data.

Exploring Numerical Data

Now that we've looked at exploring categorical and numerical data, you'll learn some useful statistics for describing distributions of data.

Numerical Summaries

Apply what you've learned to explore and summarize a real world dataset in this case study of email spam.

Case Study

Cars data

Comics data

Immigration data

Raw life expectancy data

Names data

Raw U.S. income data

When your dataset is represented as a table or a database, it's difficult to observe much about it beyond its size and the types of variables it contains. In this course, you'll learn how to use graphical and numerical techniques to begin uncovering the structure of your data. Which variables suggest interesting relationships? Which observations are unusual? By the end of the course, you'll be able to answer these questions and more, while generating graphics that are both insightful and beautiful.

Learn how to use graphical and numerical techniques to begin uncovering the structure of your data.

Exploratory Data Analysis in R

This chapter will introduce you to some background theory and terminology for modeling, in particular, the general modeling framework, the difference between modeling for explanation and modeling for prediction, and the modeling problem. Furthermore, you'll start performing your first exploratory data analysis, a crucial first step before any formal modeling.

Introduction to Modeling

Equipped with your understanding of the general modeling framework, in this chapter, we'll cover basic linear regression where you'll keep things simple and model the outcome variable y as a function of a single explanatory/ predictor variable x. We'll use both numerical and categorical x variables. The outcome variable of interest in this chapter will be teaching evaluation scores of instructors at the University of Texas, Austin.

Modeling with Basic Regression

In the previous chapter, you learned about basic regression using either a single numerical or a categorical predictor. But why limit ourselves to using only one variable to inform your explanations/predictions? You will now extend basic regression to multiple regression, which allows for incorporation of more than one explanatory or one predictor variable in your models. You'll be modeling house prices using a dataset of houses in the Seattle, WA metropolitan area. 

Modeling with Multiple Regression

In the previous chapters, you fit various models to explain or predict an outcome variable of interest. However, how do we know which models to choose? Model assessment measures allow you to assess how well an explanatory model "fits" a set of data or how accurate a predictive model is. Based on these measures, you'll learn about criteria for determining which models are "best". 

Model Assessment and Selection

In this course, you will learn to model with data. Models attempt to capture the relationship between an outcome variable of interest and a series of explanatory/predictor variables. Such models can be used for both explanatory purposes, e.g. "Does knowing professors' ages help explain their teaching evaluation scores?", and predictive purposes, e.g., "How well can we predict a house's price based on its size and condition?" You will leverage your tidyverse skills to construct and interpret such models. This course centers around the use of linear regression, one of the most commonly-used and easy to understand approaches to modeling. Such modeling and thinking is used in a wide variety of fields, including statistics, causal inference, machine learning, and artificial intelligence.

Working with Data in the Tidyverse

Explore Linear Regression in a tidy framework. 

Modeling with Data in the Tidyverse

In this chapter, you will learn techniques for exploring bivariate relationships.

Visualizing two variables

This chapter introduces correlation as a means of quantifying bivariate relationships.

Correlation

With the notion of correlation under your belt, we'll now turn our attention to simple linear models in this chapter.

Simple linear regression

This chapter looks at how to interpret the coefficients in a regression model.

Interpreting regression models

In this final chapter, you'll learn how to assess the "fit" of a simple linear regression model.

Model Fit

Ultimately, data analysis is about understanding relationships among variables. Exploring data with multiple variables requires new, more complex tools, but enables a richer set of comparisons. In this course, you will learn how to describe relationships between two numerical quantities. You will characterize these relationships graphically, in the form of summary statistics, and through simple linear regression models.

Learn how to describe relationships between two numerical quantities and characterize these relationships graphically through simple linear regression models.

Correlation and Regression in R

Learn how to describe relationships between two numerical quantities and characterize these relationships graphically.

In this chapter you'll learn about the class of linear models called "parallel slopes models." These include one numeric and one categorical explanatory variable.

Parallel Slopes

This chapter covers model evaluation. By looking at different properties of the model, including the adjusted R-squared, you'll learn to compare models so that you can select the best one. You'll also learn about interaction terms in linear models.

Evaluating and extending parallel slopes model

This chapter will show you how to add two, three, and even more numeric explanatory variables to a linear model.

Multiple Regression

In this chapter you'll learn about using logistic regression, a generalized linear model (GLM), to predict a binary outcome and classify observations.

Logistic Regression

Explore the relationship between price and the quality of food, service, and decor for Italian restaurants in NYC.

Case Study: Italian restaurants in NYC

Average SAT scores by state

New York City Zagat restaurant reviews

In this course you'll take your skills with simple linear regression to the next level. By learning multiple and logistic regression techniques you will gain the skills to model and predict both numeric and categorical outcomes using multiple input variables. You'll also learn how to fit, visualize, and interpret these models. Then you'll apply your skills to learn about Italian restaurants in New York City!

In this course you'll learn to add multiple variables to linear models and to use logistic regression for classification.

Multiple and Logistic Regression in R

In this chapter, you will investigate how repeated samples taken from a population can vary.  It is the variability in samples that allow you to make claims about the population of interest.  It is important to remember that the research claims of interest focus on the population while the information available comes only from the sample data.

Introduction to ideas of inference

In this chapter, you will gain the tools and knowledge to complete a full hypothesis test.  That is, given a dataset, you will know whether or not is appropriate to reject the null hypothesis in favor of the research claim of interest.

Completing a randomization test: gender discrimination

You will continue learning about hypothesis testing with a new example and the same structure of randomization tests.  In this chapter, however, the focus will be on different errors (type I and type II), how they are made, when one is worse than another, and how things like sample size and effect size impact the error rates.

Hypothesis testing errors: opportunity cost

As a complement to hypothesis testing, confidence intervals allow you to estimate a population parameter.  Recall that your interest is always in some characteristic of the population, but you only have incomplete information to estimate the parameter using sample data.  Here, the parameter is the true proportion of successes in a population.  Bootstrapping is used to estimate the variability needed to form the confidence interval.

Confidence intervals

All polls

Polling data

Big discrimination dataset

New discrimination dataset

Small discrimination dataset

One of the foundational aspects of statistical analysis is inference, or the process of drawing conclusions about a larger population from a sample of data. Although counter intuitive, the standard practice is to attempt to disprove a research claim that is not of interest. For example, to show that one medical treatment is better than another, we can assume that the two treatments lead to equal survival rates only to then be disproved by the data. Additionally, we introduce the idea of a p-value, or the degree of disagreement between the data and the hypothesis. We also dive into confidence intervals, which measure the magnitude of the effect of interest (e.g. how much better one treatment is than another).

Learn the practice of drawing conclusions about a population from a sample of data, a process known as statistical inference. 

Foundations of Inference in R

Learn how to draw conclusions about a population from a sample of data via a process known as statistical inference.

Foundations of Inference

One of the simplest and most common examples of a random phenomenon is a coin flip: an event that is either "yes" or "no" with some probability. Here you'll learn about the binomial distribution, which describes the behavior of a combination of yes/no trials and how to predict and simulate its behavior.

The binomial distribution

In this chapter you'll learn to combine multiple probabilities, such as the probability two events both happen or that at least one happens, and confirm each with random simulations. You'll also learn some of the properties of adding and multiplying random variables.

Laws of probability

Bayesian statistics is a mathematically rigorous method for updating your beliefs based on evidence. In this chapter, you'll learn to apply Bayes' theorem to draw conclusions about whether a coin is fair or biased, and back it up with simulations.

Bayesian statistics

So far we've been talking about the binomial distribution, but this is one of many probability distributions a random variable can take. In this chapter we'll introduce three more that are related to the binomial: the normal, the Poisson, and the geometric.

Related distributions

Probability is the study of making predictions about random phenomena. In this course, you'll learn about the concepts of random variables, distributions, and conditioning, using the example of coin flips. You'll also gain intuition for how to solve probability problems through random simulation. These principles will help you understand statistical inference and can be applied to draw conclusions from data.

Introduction to R

In this course, you'll learn about the concepts of random variables, distributions, and conditioning.

Foundations of Probability in R

Chapter 1 introduces you to missing data, explaining what missing values are, their behavior in R, how to detect them, and how to count them. We then introduce missing data summaries and how to summarise missingness across cases, variables, and how to explore across groups within the data. Finally, we discuss missing data visualizations, how to produce overview visualizations for the entire dataset and over variables, cases, and other summaries, and how to explore these across groups.


Why care about missing data?

In chapter two, you will learn how to uncover hidden missing values like "missing" or "N/A" and replace them with `NA`. You will learn how to efficiently handle implicit missing values - those values implied to be missing, but not explicitly listed. We also cover how to explore missing data dependence, discussing Missing Completely at Random (MCAR), Missing At Random (MAR), Missing Not At Random (MNAR), and what they mean for your data analysis.

Wrangling and tidying up missing values

In this chapter, you will learn about workflows for working with missing data. We introduce special data structures, the shadow matrix, and nabular data, and demonstrate how to use them in workflows for exploring missing data so that you can link summaries of missingness back to values in the data. You will learn how to use ggplot to explore and visualize how values changes as other variables go missing. Finally, you learn how to visualize missingness across two variables, and how and why to visualize missings in a scatterplot. 


Testing missing relationships

In this chapter, you will learn about filling in the missing values in your data, which is called imputation. You will learn how to impute and track missing values, and what the good and bad features of imputations are so that you can explore, visualise, and evaluate the imputed data against the original values. You will learn how to use, evaluate, and compare different imputation models, and explore how different imputation models affect the inferences you can draw from the models.


Connecting the dots (Imputation)

Missing data is part of any real world data analysis. It can crop up in unexpected places, making analyses challenging to understand. In this course, you will learn how to use tidyverse tools and the naniar R package to visualize missing values. You'll tidy missing values so they can be used in analysis and explore missing values to find bias in the data. Lastly, you'll reveal other underlying patterns of missingness. You will also learn how to "fill in the blanks" of missing values with imputation models, and how to visualize, assess, and make decisions based on these imputed datasets.

Make it easy to visualise, explore, and impute missing data with naniar, a tidyverse friendly approach to missing data.

Dealing With Missing Data in R

Importing & Cleaning Data

An introduction to key parts of experimental design plus some power and sample size calculations.

Introduction to Experimental Design

Explore the Lending Club dataset plus build and validate basic experiments, including an A/B test.

Basic Experiments

Use the NHANES data to build a RCBD and BIBD experiment, including model validation and design tips to make sure the BIBD is valid.

Randomized Complete (& Balanced Incomplete) Block Designs

Evaluate the NYC SAT scores data and deal with its missing values, then evaluate Latin Square, Graeco-Latin Square, and Factorial experiments.

Latin Squares, Graeco-Latin Squares, & Factorial experiments

sample of Lending Club data

NHANES Body Measures

NHANES Demographics

NHANES final combined dataset

NHANES Medical Conditions

NYC SAT Scores

Experimental design is a crucial part of data analysis in any field, whether you work in business, health or tech. If you want to use data to answer a question, you need to design an experiment! In this course you will learn about basic experimental design, including block and factorial designs, and commonly used statistical tests, such as the t-tests and ANOVAs. You will use built-in R data and real world datasets including the CDC NHANES survey, SAT Scores from NY Public Schools, and Lending Club Loan Data. Following the course, you will be able to design and analyze your own experiments!

In this course you'll learn about basic experimental design, a crucial part of any data analysis.

Experimental Design in R

Short case study on building and analyzing an A/B experiment.

Chapter 1: Mini case study in A/B Testing

In this chapter we'll continue with our case study, now moving to our statistical analysis. We'll also discuss how to do follow-up experiment planning.

Chapter 2: Mini case study in A/B Testing Part 2

In this chapter we'll dive deeper into the core concepts of A/B testing. This will include discussing A/B testing research questions, assumptions and types of A/B testing, as well as what confounding variables and side effects are.

Chapter 3: Experimental Design in A/B Testing

In the final chapter we'll go over more types of statistical tests and power analyses for different A/B testing designs. We'll also introduce the concepts of stopping rules, sequential analysis, and multivariate analysis.

Chapter 4: Statistical Analyses in A/B Testing

Click dataset

Experiment dataset

Data Visualization Website - April 2018

In this course, you will learn the foundations of A/B testing, including hypothesis testing, experimental design, and confounding variables. You will also be exposed to a couple more advanced topics, sequential analysis and multivariate testing. The first dataset will be a generated example of a cat adoption website. You will investigate if changing the homepage image affects conversion rates (the percentage of people who click a specific button). For the remainder of the course you will use another generated dataset of a hypothetical data visualization website.

Intermediate R

Learn A/B testing: including hypothesis testing, experimental design, and confounding variables.

A/B Testing in R

This chapter will introduce you to Bayesian data analysis and give you a feel for how it works.

What is Bayesian Data Analysis?

In this chapter we will take a detailed look at the foundations of Bayesian inference.

How does Bayesian inference work?

This chapter will show you four reasons why Bayesian data analysis is a useful tool to have in your data science tool belt.

Why use Bayesian Data Analysis?

Learn what Bayes theorem is all about and how to use it for statistical inference.

Bayesian inference with Bayes' theorem

Learn about using the Normal distribution to analyze continuous data and try out a tool for practical Bayesian analysis in R.

More parameters, more data, and more Bayes

Bayesian data analysis is an approach to statistical modeling and machine learning that is becoming more and more popular. It provides a uniform framework to build problem specific models that can be used for both statistical inference and for prediction. This course will introduce you to Bayesian data analysis: What it is, how it works, and why it is a useful tool to have in your data science toolbox.

Learn what Bayesian data analysis is, how it works, and why it is a useful tool to have in your data science toolbox.

Fundamentals of Bayesian Data Analysis

Fundamentals of Bayesian Data Analysis in R

In this chapter, you will learn about the key objects in linear algebra, such as vectors and matrices. You will understand why they are important and how they interact with each other.

Introduction to Linear Algebra

Many machine learning algorithms boil down to solving a matrix-vector equation.  In this chapter, you learn what matrix-vector equations are trying to accomplish and how to solve them in R.

Matrix-Vector Equations

Matrix operations are complex. Eigenvalue/eigenvector analyses allow you
to decompose these operations into simpler ones for the sake of image recognition, genomic analysis, and more!

Eigenvalues and Eigenvectors

“Big Data” is ubiquitous in data science and its applications.  However, redundancy in these datasets can be problematic.  In this chapter, we learn about principal component analysis and how it can be used in dimension reduction.

Principal Component Analysis

NFL Player dataset

WNBA Massey Matrix dataset

WNBA Point Differentials dataset

Linear algebra is one of the most important set of tools in applied mathematics and data science. In this course, you’ll learn how to work with vectors and matrices, solve matrix-vector equations, perform eigenvalue/eigenvector analyses and use principal component analysis to do dimension reduction on real-world datasets. All analyses will be performed in R, one of the world’s most-popular programming languages.

This course is an introduction to linear algebra, one of the most important mathematical topics underpinning data science.


Linear Algebra for Data Science in R

In this chapter you will learn how to perform statistical inference on a single parameter that describes categorical data. This includes both resampling based methods and approximation based methods for a single proportion.

Inference for a single parameter

This chapter dives deeper into performing hypothesis tests and creating confidence intervals for a single parameter. Then, you'll learn how to perform inference on a difference between two proportions. Finally, this chapter wraps up with an exploration of what happens when you know the null hypothesis is true.

Proportions: testing and power

This part of the course will teach you how to use both resampling methods and classical methods to test for the indepence of two categorical variables. This chapter covers how to perform a Chi-squared test.

Comparing many parameters: independence

The course wraps up with two case studies using election data. Here, you'll learn how to use a Chi-squared test to check goodness-of-fit. You'll study election results from Iran and Iowa and test if Benford's law applies to these datasets.

Comparing many parameters: goodness of fit

GSS data

Iowa election data

Iran election data

Categorical data is all around us. It's in the latest opinion polling numbers, in the data that lead to new breakthroughs in genomics, and in the troves of data that internet companies collect to sell products to you. In this course you'll learn techniques for parsing the signal from the noise; tools for identifying when structure in this data represents interesting phenomena and when it is just random noise.

In this course you'll learn how to leverage statistical techniques for working with categorical data.

Inference for Categorical Data in R

Bayesian models combine prior insights with insights from observed data to form updated, posterior insights about a parameter. In this chapter, you will review these Bayesian concepts in the context of the foundational Beta-Binomial model for a proportion parameter. You will also learn how to use the rjags package to define, compile, and simulate this model in R.

Introduction to Bayesian Modeling

The two-parameter Normal-Normal Bayesian model provides a simple foundation for Normal regression models.  In this chapter, you will engineer the Normal-Normal and define, compile, and simulate this model using rjags.  You will also explore the magic of the Markov chain mechanics behind rjags simulation.

Bayesian Models & Markov Chains

In this chapter, you will extend the Normal-Normal model to a simple Bayesian regression model.  Within this context, you will explore how to use rjags simulation output to conduct posterior inference.  Specifically, you will construct posterior estimates of regression parameters using posterior means & credible intervals, you will test hypotheses using posterior probabilities, and you will construct posterior predictive distributions for new observations.

Bayesian Inference & Prediction

The Bayesian approach to statistics and machine learning is logical, flexible, and intuitive. In this course, you will engineer and analyze a family of foundational, generalizable Bayesian models. These range in scope from fundamental one-parameter models to intermediate multivariate & generalized linear regression models.  The popularity of such Bayesian models has grown along with the availability of computing resources required for their implementation. You will utilize one of these resources - the rjags package in R. Combining the power of R with the JAGS (Just Another Gibbs Sampler) engine, rjags provides a framework for Bayesian modeling, inference, and prediction.

In this course, you'll learn how to implement more advanced Bayesian models using RJAGS.

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