Learning Statistics: Concepts and Applications in R

Course No. 1480
Professor Talithia Williams, Ph.D.
Harvey Mudd College
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Course No. 1480
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What Will You Learn?

  • numbers How to use R and RStudio; how to import and export data, write code, and generate plots; how to customize R features.
  • numbers Fundamentals of descriptive statistics: e.g., normal distribution, central limit theorem, correlation.
  • numbers Fundamentals of statistical inference; e.g., hypothesis testing, regression, ANOVA.
  • numbers Advanced topics: e.g., experimental design, spatial statistics, time series analysis, Bayesian inference.

Course Overview

“Show me the data!” This is coin of the realm in science, medicine, business, education, journalism, and countless other fields. Of course, it’s more complicated than that, because raw data without interpretation is useless. What they mean is “Show me the statistics”—well-founded, persuasive distillations of data that support a claim under discussion.

The ability of statistics to extract insights from a random collection of facts is one of the most astonishing and useful feats of applied mathematics. That power is all the more accessible today through the statistical programming language R, a free, open-source computer language with millions of users worldwide—everyone from students and nonprofessionals to managers and researchers at the forefront of their disciplines.

In this era of big data, with a solid understanding of statistics and the tools for interpreting data, you don’t have to trust someone else’s analysis of medical treatments, financial returns, crop yields, voting trends, home prices, or any other interpretation of data. You can do it yourself.

Designed for those who appreciate math or want an introduction to an essential toolkit for thinking about the uncertainty inherent in all sorts of information, Learning Statistics: Concepts and Applications in R teaches you elementary statistical methods and how to apply them in R, which is made even more powerful when combined with the user interface of RStudio. (Both R and RStudio are free and downloadable for multiple platforms.)

In 24 challenging and in-depth half-hour lectures, award-winning Professor Talithia Williams of Harvey Mudd College walks you through major concepts of an introductory college-level statistics course, and beyond, using examples developed and presented in R. Compared with “canned” statistics packages, R brings users into a more hands-on, mind-engaging approach that is becoming the standard at top-tier statistics programs throughout the country.

An Associate Professor of Mathematics and the Associate Dean for Research and Experiential Learning at Harvey Mudd, Dr. Williams is a nationally recognized innovator in statistics education, noted for her popular TED Talk, “Own Your Body’s Data,” and she is cohost of the PBS NOVA series NOVA Wonders.

R You Ready for a Fresh Approach to Statistics?

In a course that repays multiple viewings, Professor Williams presents the most widely-used statistical measures, concepts, and techniques: how and when to use them, what they mean, and how to recognize when arguments or conclusions based on statistical data are suspect or wrong.

Learning Statistics will especially benefit those who want to go beyond a beginner level and get a deeper, fuller understanding of the discipline. And for anyone who learned statistics many years ago, this course gives an updated experience of what is going on in the field today and how user access to the R programming language is transforming the everyday practice of statistics.

The special advantages of this video-only course include:

  • Statistics concepts combined with R examples: Viewers get a two-for-one combination of thorough grounding in statistical concepts with ground-up demonstrations of how problems are solved with the R programming languge
  • A guided tour of R in action: Viewers get a gentle introduction to R in use—from how to download R and RStudio, to importing and exporting data, writing code, and generating plots. All examples in the course are conducted in R.
  • Enhanced graphics: On-screen graphics are based on outputs from RStudio, but with frequent enhancements to make the visuals even easier to read and understand.
  • Large screen or handheld: The presentation has been optimized for everything from TVs and computers to mobile devices, meaning you can watch it on a handheld device with the same comfort and clarity as on a television screen.
  • Links to the R community: When you finish these lectures, you are not on your own. Professor Williams helps you join the worldwide community of R users, who have been advising the novice and expert alike for two decades.

Professor Williams has organized the course so that it can be taken straight through, proceeding from elementary descriptive statistics to standard and advanced techniques in statistical inference. Those with a background in other statistics software may also find the progression very helpful, while students seeking help in specific areas can jump in and out at any point throughout the course.

Discover a Powerful Set of Statistical Tools

Learning Statistics begins with an overview of the field, including how to calculate and display summaries of data. Professor Williams then introduces R and discusses its advantages over other statistical analysis packages. Unlike many such products, which are costly to purchase and upgrade, R and RStudio are entirely free. Before the end of Lecture 2, you are up and running R code.

The next six lectures cover descriptive statistics and probability, in which you learn to draw conclusions from a given sample of data by using visual aids such as histograms, scatterplots, and box plots. Employing concepts such as the normal distribution, central limit theorem, and correlation, you explore a variety of probability distributions and graphical analysis techniques. You are introduced to the formulas for these operations as well as the simple R commands that run them automatically.

Starting in Lecture 8, you explore the remarkable power of statistics to make inferences about an entire population, based on a small sample. You discover how to frame a hypothesis, build a model, and deduce propositions from the resulting data. You study simple linear regression, multiple linear regression, ANOVA (analysis of variance), and other cornerstone techniques, while also using R to run simulations of many different scenarios from the R Datasets Package.

In the last third of the course, you learn how statisticians go beyond what beginners are often taught, developing branches of applied statistics that have spun off to form their own immensely productive specialties. These include:

  • Experimental design: While there are many techniques for analyzing data you already have, even more powerful is designing an experiment to decide how data is collected from the start. Consider such elements of good design as blocking, randomization, and replication to ensure that your experiment produces sound statistical results.
  • Spatial statistics: Maps have always been information-rich artifacts, but they are now more useful than ever thanks to the advent of GPS-enabled data-gathering devices and powerful computers, combined with a panoply of statistical tools for treating spatial autocorrelation as a rich new source of information.
  • Time series analysis: Just as fascinating as spatial data is information collected sequentially over time—in finance, meteorology, biology, agriculture, and other fields. One of the most important goals of time series analysis is forecasting, which extracts short- and longer-term patterns in the data.
  • Bayesian inference: Textbook statistics is often based on a “frequentist” paradigm, in which sampling is theoretically unlimited. But for many real-life situations, your information is almost always incomplete, and likely to be revised. This is the forte of Bayesian inference.

You close the course with a lecture on how to customize R to select and combine information in whatever way you want, so that R best serves your own needs.

Dr. Williams has made it her life’s work to get students, parents, educators, and the community at large excited about mathematics and especially statistics, which she describes as “a powerful framework for THINKING—for reaching insights and solving problems.” As witnessed by her TED Talk, which has been viewed over one million times, Dr. Williams has a gift for demystifying statistics and making it relevant to everyone—because whenever you hear a statistical argument that directly affects your health, livelihood, autonomy, or your firmly held beliefs, you should say, “Show me the data, so I can decide for myself.” With this course, you will be able to do exactly that.

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24 lectures
 |  Average 29 minutes each
  • 1
    How to Summarize Data with Statistics
    Confront how ALL data has uncertainty, and why statistics is a powerful tool for reaching insights and solving problems. Begin by describing and summarizing data with the help of concepts such as the mean, median, variance, and standard deviation. Learn common statistical notation and graphing techniques, and get a preview of the programming language R, which will be used throughout the course. x
  • 2
    Exploratory Data Visualization in R
    Dip into R, which is a popular open-source programming language for use in statistics and data science. Consider the advantages of R over spreadsheets. Walk through the installation of R, installation of a companion IDE (integrated development environment) RStudio, and how to download specialized data packages from within RStudio. Then, try out simple operations, learning how to import data, save your work, and generate different plots. x
  • 3
    Sampling and Probability
    Study sampling and probability, which are key aspects of how statistics handles the uncertainty inherent in all data. See how sampling aims for genuine randomness in the gathering of data, and probability provides the tools for calculating the likelihood of a given event based on that data. Solve a range of problems in probability, including a case of medical diagnosis that involves the application of Bayes' theorem. x
  • 4
    Discrete Distributions
    There's more than one way to be truly random! Delve deeper into probability by surveying several discrete probability distributions—those defined by discrete variables. Examples include Bernoulli, binomial, geometric, negative binomial, and Poisson distributions—each tailored to answer a specific question. Get your feet wet by analyzing several sets of data using these tools. x
  • 5
    Continuous and Normal Distributions
    Focus on the normal distribution, which is the most celebrated type of continuous probability distribution. Characterized by a bell-shaped curve that is symmetrical around the mean, the normal distribution shows up in a wide range of phenomena. Use R to find percentiles, probabilities, and other properties connected with this ubiquitous data pattern. x
  • 6
    Covariance and Correlation
    When are two variables correlated? Learn how to measure covariance, which is the association between two random variables. Then use covariance to obtain a dimensionless number called the correlation coefficient. Using an R data set, plot correlation values for several variables, including the physical measurements of a sample population. x
  • 7
    Validating Statistical Assumptions
    Graphical data analysis was once cumbersome and time-consuming, but that has changed with programming tools such as R. Analyze the classic Iris Flower Data Set—the standard for testing statistical classification techniques. See if you can detect a pattern in sepal and petal dimensions for different species of irises by using scatterplots, histograms, box plots, and other graphical tools. x
  • 8
    Sample Size and Sampling Distributions
    It’s rarely possible to collect all the data from a population. Learn how to get a lot from a little by “bootstrapping,” a technique that lets you improve an estimate by resampling the same data set over and over. It sounds like magic, but it works! Test tools such as the Q-Q plot and the Shapiro-Wilk test, and learn how to apply the central limit theorem. x
  • 9
    Point Estimates and Standard Error
    Take your understanding of descriptive techniques to the next level, as you begin your study of statistical inference, learning how to extract information from sample data. In this lecture, focus on the point estimate—a single number that provides a sensible value for a given parameter. Consider how to obtain an unbiased estimator, and discover how to calculate the standard error for this estimate. x
  • 10
    Interval Estimates and Confidence Intervals
    Move beyond point estimates to consider the confidence interval, which provides a range of possible values. See how this tool gives an accurate estimate for a large population by sampling a relatively small subset of individuals. Then learn about the choice of confidence level, which is often specified as 95%. Investigate what happens when you adjust the confidence level up or down. x
  • 11
    Hypothesis Testing: 1 Sample
    Having learned to estimate a given population parameter from sample data, now go the other direction, starting with a hypothesized parameter for a population and determining whether we think a given sample could have come from that population. Practice this important technique, called hypothesis testing, with a single parameter, such as whether a lifestyle change reduces cholesterol. Discover the power of the p-value in gauging the significance of your result. x
  • 12
    Hypothesis Testing: 2 Samples, Paired Test
    Extend the method of hypothesis testing to see whether data from two different samples could have come from the same population—for example, chickens on different feed types or an ice skater’s speed in two contrasting maneuvers. Using R, learn how to choose the right tool to differentiate between independent and dependent samples. One such tool is the matched pairs t-test. x
  • 13
    Linear Regression Models and Assumptions
    Step into fully modeling the relationship between data with the most common technique for this purpose: linear regression. Using R and data on the growth of wheat under differing amounts of rainfall, test different models against criteria for determining their validity. Cover common pitfalls when fitting a linear model to data. x
  • 14
    Regression Predictions, Confidence Intervals
    What do you do if your data doesn't follow linear model assumptions? Learn how to transform the data to eliminate increasing or decreasing variance (called heteroscedasticity), thereby satisfying the assumptions of normality, independence, and linearity. One of your test cases uses the R data set for miles per gallon versus weight in 1973-74 model automobiles. x
  • 15
    Multiple Linear Regression
    Multiple linear regression lets you deal with data that has multiple predictors. Begin with an R data set on diabetes in Pima Indian women that has an array of potential predictors. Evaluate these predictors for significance. Then turn to data where you fit a multiple regression model by adding explanatory variables one by one. Learn to avoid overfitting, which happens when too many explanatory variables are included. x
  • 16
    Analysis of Variance: Comparing 3 Means
    Delve into ANOVA, short for analysis of variance, which is used for comparing three or more group means for statistical significance. ANOVA answers three questions: Do categories have an effect? How is the effect different across categories? Is this significant? Learn to apply the F-test and Tukey's honest significant difference (HSD) test. x
  • 17
    Analysis of Covariance and Multiple ANOVA
    You can combine features of regression and ANOVA to perform what is called analysis of covariance, or ANCOVA. And that's not all: Just as you can extend simple linear regression to multiple linear regression, you can also extend ANOVA to multiple ANOVA, known as MANOVA, or multivariate analysis of variance. Learn when to apply each of these techniques. x
  • 18
    Statistical Design of Experiments
    While a creative statistical analysis can sometime salvage a poorly designed experiment, gain an understanding of how experiments can be designed in from the outset to collect far more reliable statistical data. Consider the role of randomization, replication, blocking, and other criteria, along with the use of ANOVA to analyze the results. Work several examples in R. x
  • 19
    Regression Trees and Classification Trees
    Delve into decision trees, which are graphs that use a branching method to determine all possible outcomes of a decision. Trees for continuous outcomes are called regression trees, while those for categorical outcomes are called classification trees. Learn how and when to use each, producing inferences that are easily understood by non-statisticians. x
  • 20
    Polynomial and Logistic Regression
    What can be done with data when transformations and tree algorithms don't work? One approach is polynomial regression, a form of regression analysis in which the relationship between the independent and dependent variables is modelled as the power of a polynomial. Step functions fit smaller, local models instead of one global model. Or, if we have binary data, there is logistic regression, in which the response variable has categorical values such as true/false or 0/1. x
  • 21
    Spatial Statistics
    Spatial analysis is a set of statistical tools used to find additional order and patterns in spatial phenomena. Drawing on libraries for spatial analysis in R, use a type of graph called a semivariogram to plot the spatial autocorrelation of the measured sample points. Try your hand at data sets involving the geographic incidence of various medical conditions. x
  • 22
    Time Series Analysis
    Time series analysis provides a way to model response data that is correlated with itself, from one point in time to the next, such as daily stock prices or weather history. After disentangling seasonal changes from longer-term patterns, consider methods that can model a dependency on time, collectively known as ARIMA (autoregressive integrated moving average) models. x
  • 23
    Prior Information and Bayesian Inference
    Turn to an entirely different approach for doing statistical inference: Bayesian statistics, which assumes a known prior probability and updates the probability based on the accumulation of additional data. Unlike the frequentist approach, the Bayesian method does not depend on an infinite number of hypothetical repetitions. Explore the flexibility of Bayesian analysis. x
  • 24
    Statistics Your Way with Custom Functions
    Close the course by learning how to write custom functions for your R programs, streamlining operations, enhancing graphics, and putting R to work in a host of other ways. Professor Williams also supplies tips on downloading and exporting data, and making use of the rich resources for R—a truly powerful tool for understanding and interpreting data in whatever way you see fit. x

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  • 408-page printed course guidebook
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Course Guidebook Details:
  • 408-page printed course guidebook
  • Charts, data, and graphics
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Your professor

Talithia Williams

About Your Professor

Talithia Williams, Ph.D.
Harvey Mudd College
Talithia Williams is an Associate Professor of Mathematics and the Associate Dean for Research and Experiential Learning at Harvey Mudd College. She earned her bachelor’s degree in Mathematics from Spelman College, a master’s degree in mathematics from Howard University and her Ph.D. in Statistics from Rice University. Her professional experiences include research appointments at NASA’s Jet Propulsion Laboratory,...
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Learning Statistics: Concepts and Applications in R is rated 3.9 out of 5 by 49.
Rated 3 out of 5 by from annoying error that breaks reasoning chain in lecture 3 (page 47 of guide) the lecturer's words do no match the mathematical statement for independent events. She said "if a and b are independent, the probability of their union is the product of their probabilities", which is wrong. The math expression shown reads "probability of inersection of a and b equals product of their probabilities". I like the course a lot, as a review. It may be difficult as a standalone course for complete beginner due to errors.
Date published: 2020-11-22
Rated 5 out of 5 by from The title of the course is well thought out. Great Course well presented by the Professor - She knows her subject and I have enjoyed listening to her lectures.
Date published: 2020-11-08
Rated 4 out of 5 by from A good tour of a challenging subject As a retired engineer who has dodged around statistical inference in many applications, but has had no formal training in the subject, I found this to be a good survey of population parameter estimators, basic regression, analysis of variance/covariance, and time series analysis. Prof. Williams also provides a quick introduction to a few topics that I have never encountered: regression trees and spatial statistics. Altogether, it is a fine tour of the subject, but not meant as a substitute for a textbook. Back in 1965, I was a 17-year-old research assistant to a clinical psychologist. I recall working up experimental data for an Analysis of Variance (ANOVA) without any real understanding of what I was doing. I remember long nights calculating sums of squares on an electromechanical Monroe “Monroematic” Model 88N-213 calculator which made satisfying clunk & whir sounds when dividing. Years later, I became involved in sensitivity test statistics, e.g. the 1948 Dixon and Mood Bruceton protocol, for electro-explosive devices (EEDs), and the calculation of statistical tolerance intervals for population parameter estimates. I am still bothered by some of the shortcuts that the automotive inflatable restraints industry has taken with this particular method. Prof. Williams course provides a nice supplement to the collection of books on statistical methods that I have assembled over the years and am now wondering what to do with. It was good that she cited the important statistical methods developed by Sir Ronald Aylmer Fisher FRS (1890-1962) who is being maligned these days for his studies of racial differences. HWF, Mesa AZ.
Date published: 2020-09-26
Rated 1 out of 5 by from Dated and confusing Definition of the course is confusing. The looming question is whether this is a course statistics or R. Both the first and second lectures contain a section “Introduction to R.” The major issue is that there are assumptions in various places that the learner already understands the concept or the distribution of data points behind it. A clear introduction of the concept prior to jumping into how to accomplish the task in R. Knocking other products and do so multiple times would lead one to conclude that the instructor had stock in R were it not for the fact that it is a free product. The course is also out of date relative to the current versions of R and RStudio that one downloads. To follow the steps and instructions one would need to know the version that was being used at the time of writing the course work. For instance, the instructions are to execute “install.packages(“datasets”). Such will corrupt the current version of RStudio as it is part of the standard data sets and is loaded on install of RStudio. After attempting to install “datasets” my installation was corrupted and I was forced to delete and reinstall both R and RStudio. The book wastes space. In the old faithful example, there are four pages dedicated to the data that is loaded via the dataset invocation. I’m fairly certain that the average learner is not going to even browse that list. A small, emphasis on small, sample would suffice. The lecture transcript is totally worthless as the lecture transcript is intersperses into a copy of the Guidebook. The lecture transcript is over 600 pages, over 400 of which are the Guidebook. In addition, the lecture transcript is single spaced on the same size printed page as the Guidebook in a font point size that makes it impossible to take notes or highlight for later review. To be of any value the transcript should be printable on 8.5x11 paper with margins sufficient to make notations or point for further review. I must add that these observations are from the viewpoint of an adjunct professors’ position that considered it a necessity that the students know the applicable definitions and terms prior to launching into the course material. In short, understanding that “We are going from point A to point B and you need to understand these definitions and terms.” As it is, “We are going to leave point A, somewhere along the way we will encounter terms and definitions, hopefully before we use them, and we will hopefully arrive at point B. We may visit point C first.” In general, if one learns statistics or R from this course, it will be in spite of the course, not because of it.
Date published: 2020-08-31
Rated 4 out of 5 by from Engaging Lectures, Great Graphics, R Not Helpful Professor Williams' "Learning Statistics" is a nice supplement to Michael Starbird's "Meaning from Data: Statistics Made Clear" (also from The Great Courses) in that it is more technical, covers a wider range of statistical techniques, and very ably shows the analyst how to progress through the sequence of statistical output to improve the analysis and the results; in contrast, Professor Starbird's course does a marvelous job in capturing the insights of statistics in an intuitive and easily understood manner. It also should be noted that Professor Williams' course is about 25% programming and 75% statistical analysis which shouldn't surprise anyone since the title of the course mentions "Concepts and Applications in R" which is a free programming language that is said to be "transforming how statistics is done around the world." Professor Williams is an amiable lecturer who provides personal anecdotes to enliven her lectures. As mentioned, the course is pitched at a higher level than Starbird's course; she provides much of the underlying mathematics and shows the statistical output in all its complexity and ambiguity. I found the course particularly helpful in her analysis of the stages of output, with its p values, F-statistics and R-squareds, and how we use this output to interpret our interim analyses and then improve upon our models by dropping variables, changing the analysis from linear to non-linerar, etc. I particularly enjoyed her lectures on multiple regression and logistic regression. Logistic regression brought back memories from many years ago when I was involved in an economics research project where our "binary" dependent variable was whether a bank was a member of the Federal Reserve System or not. I think I now understand more how logistic regression works than I did back then when we had our programmers make the calculations. I also thought her lecture on "Bayesian Inference" was very insightful as she used a baseball player's batting average to show how we can continually update our beliefs , e.g., the player's batting average, by observing new data. On the critical side, while I'm familiar with decision trees, her discussion of related regression trees was not at all clear to me, and although I downloaded the R programming language, I didn't use it very much since at this stage of my life I don't have the time to overcome what Professor Williams herself says is a "steep learning curve." Finally, although she mentions the issue of "over-fitting" once or twice, I believe this should be emphasized in a statistics course. In this day of big data and easy computation, some computer scientists encourage "data mining" where we just explore the data for quantitative relationships with no guiding theory or hypothesis. I would venture to say that the social science journals are full of papers where the supporting research ran 300 or so regressions and published the 10 best with a post hoc theory.
Date published: 2020-08-17
Rated 4 out of 5 by from Excellent presentation, intrusive camera movement This is a very rewarding and informative course. Professor Williams adopts a friendly informality that never interferes with clarity and precision. Sadly, her excellent presentation is sabotaged by poor video direction. The angle changes every twenty seconds, which is both intrusive and distracting. A good lecture doesn't need such gimmicks.
Date published: 2020-06-18
Rated 5 out of 5 by from Excellent I took statistics many years ago and wanted to take a refresher on the latest concepts and techniques. Professor Williams is an excellent teacher that delivers and also challenges the student. I like the use of R to support my learning efforts. The course leaves me with the skills to perform my own engineering studies as well as investigating studies presented to me. I highly endorse this course.
Date published: 2020-06-04
Rated 5 out of 5 by from Enjoyable Excellent teacher who adapted the subject to the real world.
Date published: 2020-05-26
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