Statistical hypothesis testing | Logic and statistics

Dichotomous thinking

In statistics, dichotomous thinking or binary thinking is the process of seeing a discontinuity in the possible values that a p-value can take during null hypothesis significance testing: it is either above the significance threshold (usually 0.05) or below. When applying dichotomous thinking, a first p-value of 0.0499 will be interpreted the same as a p-value of 0.0001 (the null hypothesis is rejected) while a second p-value of 0.0501 will be interpreted the same as a p-value of 0.7 (the null hypothesis is accepted). The fact that first and second p-values are mathematically very close is thus completely disregarded and values of p are not considered as continuous but are interpreted dichotomously with respect to the significance threshold. A common measure of dichotomous thinking is the cliff effect. A reason to avoid dichotomous thinking is that p-values and other statistics naturally change from study to study due to random variation alone; decisions about refutation or support of a scientific hypothesis based on a result from a single study are therefore not reliable. Dichotomous thinking is very often associated with p-value reading but it can also happen with other statistical tools such as interval estimates. (Wikipedia).

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Dihedral group example

In this veideo we continue our look in to the dihedral groups, specifically, the dihedral group with six elements. We note that two of the permutation in the group are special in that they commute with all the other elements in the group. In the next video I'll show you that these two el

From playlist Abstract algebra

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Introduction to Solving Linear Diophantine Equations Using Congruence

This video defines a linear Diophantine equation and explains how to solve a linear Diophantine equation using congruence. mathispower4u.com

From playlist Additional Topics: Generating Functions and Intro to Number Theory (Discrete Math)

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Dihedral Group (Abstract Algebra)

The Dihedral Group is a classic finite group from abstract algebra. It is a non abelian groups (non commutative), and it is the group of symmetries of a regular polygon. This group is easy to work with computationally, and provides a great example of one connection between groups and geo

From playlist Abstract Algebra

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Theory of numbers: Linear Diophantine equations

This lecture is part of an online undergraduate course on the theory of numbers. We show how to use Euclid's algorithm to solve linear Diophantine equations. As a variation, we discuss the problem of solving equations in non-negative integers. We also show how to solve systems of linear D

From playlist Theory of numbers

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Abstract Algebra | The dihedral group

We present the group of symmetries of a regular n-gon, that is the dihedral group D_n. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/

From playlist Abstract Algebra

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Dichotomous Search

Dichotomous Search is an improved version of Ternary Search. This video describes the motivation and algorithm followed by a visualized example. Code can be found on GitHub https://www.github.com/osveliz/numerical-veliz *Correction* The numerical example used epsilon = 10^(-6) not 10^(-7)

From playlist Numerical Methods

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Intro to Number Theory and The Divisibility Relation

This video introduces the divisibility relation and provided several examples. mathispower4u.com

From playlist Additional Topics: Generating Functions and Intro to Number Theory (Discrete Math)

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R - Item Response Theory Analysis Lecture

Lecturer: Dr. Erin M. Buchanan Missouri State University Summer 2016 This lecture covers Item Factor Analysis and Item Response Theory from the Beaujean SEM in R book. IRT information also pulled from StatsCamp materials taught by William Skorupski (highly recommend his class!). Both dic

From playlist Structural Equation Modeling

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Josh Bongard - A xither of xenobots: demolishing dichotomous thinking with synthetic proto-organisms

Recorded 17 February 2022. Josh Bongard of the University of Vermont presents "A xither of xenobots: demolishing dichotomous thinking with synthetic proto-organisms" at IPAM's Mathematics of Collective Intelligence Workshop. Learn more online at: http://www.ipam.ucla.edu/programs/workshops

From playlist Workshop: Mathematics of Collective Intelligence - Feb. 15 - 19, 2022.

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Number Theory | Linear Diophantine Equations

We explore the solvability of the linear Diophantine equation ax+by=c

From playlist Divisibility and the Euclidean Algorithm

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Jamovi 1.2/1.6 Tutorial: Statkat Module (Episode 21)

In this Jamovi tutorial, I go how to use the additional module from the package library called Statkat. It helps you choose which analysis test to complete based on the type of variables you have. It's uses are limited to basic tests and cannot suggest higher-level tests like hierarchical

From playlist Jamovi Tutorials

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JASP 0.14 Tutorial: Logistic Regression (Episode 28)

In this JASP tutorial, I go through a quick example of a binomial/dichotomous outcome dependent variable that requires logistic regression, not linear regression! Discussion of the plots, options, and output is included. JASP: https://jasp-stats.org NOTE: This tutorial uses the new previ

From playlist JASP Tutorials

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Introduction to Probability and Statistics 131B. Lecture 03.

UCI Math 131B: Introduction to Probability and Statistics (Summer 2013) Lec 03. Introduction to Probability and Statistics View the complete course: http://ocw.uci.edu/courses/math_131b_introduction_to_probability_and_statistics.html Instructor: Michael C. Cranston, Ph.D. License: Creativ

From playlist Introduction to Probability and Statistics 131B

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Fibonacci Search

Fibonacci search scheme for finding the minimum of a function discovered by J. Kiefer and S. M. Johnson. This interval-based numerical method improves on Ternary Search and Dichotomous Search be reusing interval points based on ratios from the Fibonacci Sequence. Code can be found on GitHu

From playlist Numerical Methods

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R - Item Response Theory Example

Lecturer: Dr. Erin M. Buchanan Missouri State University Summer 2016 This video covers ltm(), tpm(), and mirt() on how to perform a 2PL/3PL on dichotomous data and a generalized partial credit model for polytomous data. Lecture materials and assignment available at: https://statisticso

From playlist Structural Equation Modeling

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Discovering Variables – Combining Numbers for More Powerful Statistics (1-4)

Combining numbers creates variables – values that can vary or take on more than one value. If a value can be measured among a group and that value will be different for at least some of the group members, then you are measuring a variable. You will learn about qualitative (categorical) and

From playlist WK1 Numbers and Variables - Online Statistics for the Flipped Classroom

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Cronbach's α and McDonald’s ω reliability coefficients in Jamovi | Theory and practice

This video is bout Cronbach's α and McDonald’s ω in Jamovi. Useful links: Jamovi: https://www.jamovi.org/download.html Two book chapters: https://www.routledge.com/Quantitative-Data-Analysis-for-Language-Assessment-Volume-I-Fundamental/Aryadoust-Raquel/p/book/9780367671396 Paper by Haye

From playlist Jamovi software

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Introduction to the Distributive Property

This video explains the distributive property and provides examples on how to use the distributive property. http://mathispower4u.yolasite.com/

From playlist The Distributive Property and Simplifying Algebraic Expressions

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P-value | Statistics | Statistical hypothesis testing