# Posts Tagged ‘ statistics ’

## Mathematical and Applied Statistics Lesson of the Day – The Motivation and Intuition Behind Markov’s Inequality

$Mathematical and Applied Statistics Lesson of the Day – The Motivation and Intuition Behind Markov’s Inequality$

Markov’s inequality may seem like a rather arbitrary pair of mathematical expressions that are coincidentally related to each other by an inequality sign: where . However, there is a practical motivation behind Markov’s inequality, and it can be posed in the form of a simple question: How often is the random variable “far” away from […]

August 26, 2014
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What is the Gauss-Markov theorem? From “The Cambridge Dictionary of Statistics” B. S. Everitt, 2nd Edition: A theorem that proves that if the error terms in a multiple regression have the same variance and are uncorrelated, then the estimators of the parameters in the model produced by least squares estimation are better (in the sense […] Related posts: What is meant by regression modeling? Skimming statistics papers for the ideas…

## The Chi-Squared Test of Independence – An Example in Both R and SAS

$The Chi-Squared Test of Independence – An Example in Both R and SAS$

Introduction The chi-squared test of independence is one of the most basic and common hypothesis tests in the statistical analysis of categorical data.  Given 2 categorical random variables, and , the chi-squared test of independence determines whether or not there exists a statistical dependence between them.  Formally, it is a hypothesis test with the following null and […]

## Recent Articles

August 20, 2014
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I have uploaded a few papers I have written and presented at some national conferences over the past several years.  Currently, all the articles relate to election research.

## GEFCom 2014 energy forecasting competition is underway

August 18, 2014
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GEFCom 2014 is the most advanced energy forecasting competition ever organized, both in terms of the data involved, and in terms of the way the forecasts will be evaluated. So everyone interested in energy forecasting should head over to the competitio...

## Are P Values Error Probabilities? or, “It’s the methods, stupid!” (2nd install)

August 18, 2014
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Despite the fact that Fisherians and Neyman-Pearsonians alike regard observed significance levels, or P values, as error probabilities, we occasionally hear allegations (typically from those who are neither Fisherian nor N-P theorists) that P values are actually not error probabilities. The denials tend to go hand in hand with allegations that P values exaggerate evidence against […]

## Teaching random variables and distributions

August 18, 2014
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Why do we teach about random variables, and why is it so difficult to understand? Probability and statistics go together pretty well and basic probability is included in most introductory statistics courses. Often maths teachers prefer the probability section as … Continue reading →

## Mathematical Statistics Lesson of the Day – Markov’s Inequality

$Mathematical Statistics Lesson of the Day – Markov’s Inequality$

Markov’s inequality is an elegant and very useful inequality that relates the probability of an event concerning a non-negative random variable, , with the expected value of .  It states that where . I find Markov’s inequality to be beautiful for 2 reasons: It applies to both continuous and discrete random variables. It applies to any non-negative […]

## STEM forums

August 15, 2014
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“I can calculate the movement of stars, but not the madness of men.” Isaac Newton When visiting the exhibition hall at JSM 2014, I spoke with people from STEM forums on the Springer booth. The concept of STEM (why STEM? Nothing to do with STAN! Nor directly with Biology. It stands as the accronym for Science, Technology, […]

## Intuition and Data at KeenCON

August 14, 2014
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I will be giving a talk “Bayesian statistics as a way to integrate intuition and data” at KeenCon, September 11, 2014 in San Francisco. Update: Use promo code KeenCon-JohnCook to get 75% off registration.