This 7-minute video lesson provides an introduction to the idea that one can find a line that minimizes the squared distances to the points. [Statistics playlist: Lesson 62 of 85]
This 15-minute video lesson looks at the Standard Error of the Mean (a.k.a. the standard deviation of the sampling distribution of the sample mean!). [Statistics playlist: Lesson 38 of 85]
This 12-minute video lesson looks at the T-Statistic Confidence Interval (for small sample sizes). [Statistics playlist: Lesson 52 of 85]
This 3-minute video lesson discusses Type I Errors. [Statistics playlist: Lesson 50 of 85]
This 11-minute video lesson discusses variance of differences of random variables. [Statistics playlist: Lesson 54 of 85]
This 12-minute video lesson explains variance of a population. [Statistics playlist: Lesson 13 of 85]
This 7-minute video lesson compares Z-statistics and T-statistics. [Statistics playlist: Lesson 49 of 85]
A whirl-wind tour of the statistics used in behavioral science research, covering topics including: data visualization, building your own null-hypothesis distribution through permutation, useful parametric distributions, the generalized linear model, and model-based analyses more generally. Familiarity with MATLABA, Octave, or R will be useful, prior experience with statistics will be helpful but is not essential. This course is intended to be a ground-up sketch of a coherent, alternative perspective to the "null-hypothesis significance testing" method for behavioral research (but don't worry if you don't know what this means).
This 8-minute video lesson takes some problems from CK12.org to provide Z-score practice. [Statistics playlist: Lesson 31 of 85]
This course is a broad treatment of statistics, concentrating on specific statistical techniques used in science and industry. Topics include: hypothesis testing and estimation, confidence intervals, chi-square tests, nonparametric statistics, analysis of variance, regression, correlation, decision theory, and Bayesian statistics.
The lectures are at a beginning graduate level and assume only basic familiarity with Functional Analysis and Probability Theory. Topics covered include: Random variables in Banach spaces: Gaussian random variables, contraction principles, Kahane-Khintchine inequality, Anderson’s inequality. Stochastic integration in Banach spaces I: γ-Radonifying operators, γ-boundedness, Brownian motion, Wiener stochastic integral. Stochastic evolution equations I: Linear stochastic evolution equations: existence and uniqueness, Hölder regularity. Stochastic integral in Banach spaces II: UMD spaces, decoupling inequalities, Itô stochastic integral. Stochastic evolution equations II: Nonlinear stochastic evolution equations: existence and uniqueness, Hölder regularity.
This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important aspects of the task and its potential use.
In order to promote students’ conceptual understanding and learning experience in introductory statistics, a technology task, which focuses on the probability distribution in which means are defined, was created using TinkerPlots, an exploratory data analysis and modeling software. The targeted audiences range from senior high school grade levels to college freshmen who are starting their introductory course in statistics. Students will be guided to explore and discover the movement behaviors of means of a set of numbers randomly generated from a fixed range of values characterized by a predetermined probability distribution. The cognitive, mathematical, technological and pedagogical natures of the task, as well as its association with the statistics education framework based on the Guidelines for Assessment and Instruction in Statistics Education (GAISE) by the American Statistical Association, will be elaborated. A brief discussion on what cognitive design principles this task satisfies will also be provided at the end.
In this task students are asked to describe the data represented in a scatter plot.
This course covers topics such as sums of independent random variables, central limit phenomena, infinitely divisible laws, Levy processes, Brownian motion, conditioning, and martingales.
The book is appropriately comprehensive, covering the basics as well as interesting and important applications of Bayesian methods.
Think Stats is an introduction to Probability and Statistics for Python programmers.
*Think Stats emphasizes simple techniques you can use to explore real data sets and answer interesting questions. The book presents a case study using data from the National Institutes of Health. Readers are encouraged to work on a project with real datasets.
*If you have basic skills in Python, you can use them to learn concepts in probability and statistics. Think Stats is based on a Python library for probability distributions (PMFs and CDFs). Many of the exercises use short programs to run experiments and help readers develop understanding.
This graduate-level course focuses on one-dimensional nonparametric statistics developed mainly from around 1945 and deals with order statistics and ranks, allowing very general distributions. For multidimensional nonparametric statistics, an early approach was to choose a fixed coordinate system and work with order statistics and ranks in each coordinate. A more modern method, to be followed in this course, is to look for rotationally or affine invariant procedures. These can be based on empirical processes as in computer learning theory. Robustness, which developed mainly from around 1964, provides methods that are resistant to errors or outliers in the data, which can be arbitrarily large. Nonparametric methods tend to be robust.
The main goal of this course is to study the generalization ability of a number of popular machine learning algorithms such as boosting, support vector machines and neural networks. Topics include Vapnik-Chervonenkis theory, concentration inequalities in product spaces, and other elements of empirical process theory.
The purpose of this task is to provide students with the opportunity to determine experimental probabilities by collecting data.