**Publisher:**TTC

**Link:**https://www.thegreatcourses.com/courses/learning-statistics-concepts-and-applications-in-r.htmlN/A

24 lectures

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

“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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موضوع: آموزش زبان برنامه نویسی R آموزش های TTC

تگ ها: آموزش آمار آموزش آمار: مفاهیم و اپلیکیشن ها در R فیلم آموزش آمار

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