2 Probability Theory and Classical Statistics

2 Probability Theory and Classical Statistics Statistical inference rests on probability theory, and so an in-depth under-standing of the basics of probability theory is necessary for acquiring a con-

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Chapter 14 Within-Subjects Designs - CMU Statistics

Chapter 14 Within-Subjects Designs ... although often the term repeated measures analysis is used in a narrower sense to indicate the speci c set of analyses discussed

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Chapter 9 Simple Linear Regression

Chapter 9 Simple Linear Regression An analysis appropriate for a quantitative outcome and a single quantitative ex-planatory variable. 9.1 …

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Lecture Notes 9 Asymptotic Theory (Chapter 9)

Lecture Notes 9 Asymptotic Theory (Chapter 9) In these notes we look at the large sample properties of estimators, especially the maxi-mum likelihood estimator.

Ryan Tibshirani Data Mining: 36-462/36-662 January 22 2013

Ryan Tibshirani Data Mining: 36-462/36-662 January 22 2013 Optional reading: ESL 14.10 1. Information retrieval with the web Last time:information retrieval, learned how to compute similarity scores (distances) of documents to a given query string But what if …

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Ryan Tibshirani Data Mining: 36-462/36-662 April 25 2013

Boosting Boosting1 is similar to bagging in that we combine the results of several classi cation trees. However, boosting does something fundamentally di erent, and can work a lot better As usual, we start with training data (x

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Chapter 8 Threats to Your Experiment - CMU Statistics

This chapter discusses possible complaints about internal validity, external validity, construct validity, Type 1 error, and power. We are using \threats" to mean things that will reduce the impact of

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Advanced Data Analysis from an Elementary Point of View

Advanced Data Analysis from an Elementary Point of View Cosma Rohilla Shalizi

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Finding Informative Features - CMU Statistics

Similarly, our uncertainty about the class C, in the absence of any other information, is just the entropy of C: H[C] = X c Pr(C= c)log 2 Pr(C= c) Now suppose we observe the value of the feature X.

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Degrees of Freedom and Model Search - CMU Statistics

Degrees of Freedom and Model Search Ryan J. Tibshirani Abstract Degrees of freedom is a fundamental concept in statistical modeling, as it provides a quan-titative description of the amount of tting performed by a given procedure. But, despite this

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Using EXCEL for Statistical Analysis - University of Phoenix

test measures the di erence between the means of two groups, an ANOVA tests the di erence between the means of two or more groups A one-way ANOVA, or single factor ANOVA as mentioned in EXCEL, tests di erences between groups that are only classi ed on one independent variable which is called the treatments.

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Using SPSS, Chapter 9: Hypothesis Testing - Two Samples

test, we would reject the null hypothesis that the mean di erence is zero. Using the con dence interval approach, we are 95% con dent that the mean di erence is between 21 and 43. If you want to test for a mean di erence greater than zero, H 1: 1 2 > ;

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Goodness of Fit in Logistic Regression

(residual) deviance of a model is the di erence between the minus twice the log likelihood of that model and that of the saturated model that ts each group with its own proportion. So we could consider the deviance of the given model as a likelihood ratio test of whether the given model is satisfactory; that is, whether it can be

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Permutation tests - University of Washington

In this case we know from theory the distribution of a di erence in means and we could just do a t-test. We can compare the t-test results to the results of a permutation test on the mean di erence. Means: t-test > t.test(null.y~carrier, var.equal=TRUE) …

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1 The basics of panel data - University of California ...

treatment group dummy variable in the di erence-in-di erences regression speci cation. Just like the treatment group dummy variable controls for baseline di erences between the control and treatment groups, the city xed e ects (i.e. city dummy variables) control for baseline di erences between cities.

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Expected Utility Theory - Columbia University

Because the di⁄erence in life outcomes between $0 and $499,999 is massive Get to eat, buy clothes, etc Whereas the di⁄erence between $499,999 and $1,000,000 is relatively small A third pair of silk pyjamas Thus, by keeping the lottery, the pauper risks losing an awful lot ($0 vs $499,999) against gaining relatively little ($499,999 vs ...

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CUPL Programmer’s Reference Guide

Note the di erence between index variables with leading zeroes; the variable D07 is not the same as D7. Examples of some invalid indexed variable names are as follows: D0F index number is not decimal a36 index number out of range These are valid variable names, but they are not considered indexed. 1.1.3 Reserved Words and Symbols

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Multinomial Response Models - Princeton University

the single logistic regression equation is a contrast between successes and failures. If J= 2 the multinomial logit model reduces to the usual logistic regression model. Note that we need only J 1 equations to describe a variable with J response categories and that it really makes no di erence …

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The Z-test - University of Washington

The z-test is a hypothesis test to determine if a single observed mean is signi cantly di erent (or greater or less than) the mean under the null hypothesis, hypwhen you know the standard deviation of the population. Here’s where the z-test sits on our ow chart. Test for = 0 Ch 17.2 Test for 1 = 2 Ch 17.4 2 test frequency Ch 19.5 2 test ...

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