A resource for learning about probability and statistics. The text is motivated by real data and is integrated with interactive features such as applets, videos, and example prompts.
Video lectures covering all topics in a psychology introductory statistics course.
I have designed and presented the content within StatsforMedics specifically for use by undergraduate medical students who are considering use of statistics for short-term research projects. However, this is with the understanding that students from allied health sciences may also benefit from engaging with the site and its sister site, Statistics CALs. Also, I am currently exploring use of selected content for outreach work in pre-university sectors.
Stebbins is a game about evolution. Students collect data as predators “eating” colored circles on a colored background, being careful to avoid the poisonous ones. Data analysis reveals how the population changes color over time, and can be used to illuminate a common misconception that individuals change in response to predation. Stebbins is modeled on a non-digital game-like simulation of natural selection created by evolutionary biologist G. Ledyard Stebbins.
In Stella, students act as astronomers, studying stars in a “patch” of sky in our own galaxy. Using simulated data from spectroscopy and other real-world instrumentation, students learn to determine star positions, radial velocity, proper motion, and ultimately, degree of parallax. As students establish their expertise in each area, they earn “badges” that allow them greater and easier access to the data. The Teacher Guide includes background on stellar spectroscopy (the brightness of a star), photometry (the breakdown of light from a star), and astrometry (measuring the positions of stars).
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 activity was inspired by the "Pet Rock" project of Daryl Henry. I developed this activity to be a capstone experience for our students. During the fall 4th year field trip, students are responsible for leading their field stop/project, and for collecting samples and measurements while at their stop. Students then analyze their samples/measurements as their term projects in the fall course. In the winter course the class compiles these field trip projects into their classes' field guide. Key Words: Field guide, tectonics, capstone
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We've talked a lot about modeling data and making inferences about it, but today we're going to look towards the future at how machine learning is being used to build models to predict future outcomes. We'll discuss three popular types of supervised machine learning models: Logistic Regression, Linear discriminant Analysis (or LDA) and K Nearest Neighbors (or KNN).
1 – Sampling2 – Data3 – Numerically Summarizing Data4 – Linear Regression and Correlation5 – Probability Topics6 – Random Variables7 – The Normal Distribution8 – The Central Limit Theorem9 – Confidence Interval10 – Hypothesis Testing with One Sample11 – Hypothesis Testing with Two Samples12 – The Chi-Square Distribution13 – F Distribution and One-Way ANOVA
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.
An introduction and examples of how to use Survival analysis and Life event analysis. This is about statistical methods for analyzing longitudinal data on the occurrence of events. Events may include death, injury, marriage, getting a job (binary variables).
In these open-ended but simple activities, students use basic mathematics and descriptive statistics to analyze campus sustainability efforts.
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Syllabus for the course "CSC 21700 - Probability and Statistics for Computer Science" delivered at the City College of New York in Spring 2019 by Evan Agovino as part of the Tech-in-Residence Corps program.
C'est une formation en ligne qui vise à aider les participants à réaliser une Analyse en composante Principale (ACP). Le niveau intermédiaire de cette formation porte sur l'utilisation des bibliothèques FactoMineR et factoextra pour analyser et visualiser l'ACP des variables puis des individus sur un exemple de données iris. Le public cible: étudiants en master de recherche ou professionnel, doctorants, docteurs, enseignants, chercheurs, ingénieurs, médecins, autres.
This is a link to the main TANGO Stat Ed website
This applet allows the user to adjust the degrees of freedom of the T Distribution with a slider or manual input. The applet allows the user to fix the x and or y axes. The user immediately sees how this affects the shape of the graph.
The applet in this section allows you to see how the T distribution is related to the Standard Normal distribution by calculating probabilities. The T distribution is primarily used to make inferences on a Normal mean when the variance is unknown.
Today we're going to walk through a couple of statistical approaches to answer the question: "is coffee from the local cafe, Caf-fiend, better than that other cafe, The Blend Den?" We'll build a two sample t-test which will tell us how many standard errors away from the mean our observed difference is in our tasting experiment, and then we'll introduce a matched pair t-tests which allow us to remove variation in the experiment. All of these approaches rely on the test statistic framework we introduced last episode.
This is an activity that uses the spreadsheet program Excel to explore the origins of subsidence in New Orleans. There are two versions. The first is a traditional Spreadsheets Across the Curriculum (SSAC) module that couples a PowerPoint presentation with an embedded Excel spreadsheet where students construct a spreadsheet, and then submit the Excel file for grading. The second is a macro-enabled Excel spreadsheet that provides automatic feedback to answers and calculates the score. Upon completion the students are given a code that encrypts their spreadsheet score and then take a follow-up quiz that probes their understanding.
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Landscape evolution provides a convenient framework for understanding geologic time and rates because students can observe how processes like erosion and deposition shape their surroundings, even in urban settings. In order to describe landscapes qualitatively and quantitatively, students build 3-D sandbox models based on topographic maps and design and stage a "virtual adventure race." Sandbox landscapes are used to illustrate erosional processes, the role of water in sediment transport, relief change, and how erosion exhumes rocks from depth, while local examples are used to discuss landscapes as transient or steady over different time- and length scales. To convince students that the observed processes act over millions of years to shape Earth's surface, quantitative dating tools are introduced. Dice experiments illustrate radioactive decay and the shape of the age equation curve, and 14C dating, geochronology and thermochronology are introduced as "stopwatches" that start when a plant dies, a crystal forms, or a rock nears the surface and cools to a certain temperature.
The sandbox model and thermochronometer "stopwatches" are combined to measure erosion rates at a point, uniform and spatially variable erosion, and rates of landscape change. Ultimately, model rates (cm/hour) calculated from stopwatch times on the order of seconds can be related to geologic rates (km/My) calculated from real million-year-old samples. SEE POSTER for detailed descriptions of each activity in Parts 1-4 (complete with specific Learning Goals, Context, Materials, Activity Summary, Evaluation, and adaptation to challenge students in grades 9-16).
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