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Horvitz-Thompson estimation
Horvitz-Thompson estimation

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Tools - Hypothesis Tests

an1 - Andrew.cmu.edu
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... • Recall, b0 and b1 are the estimates of the slope β1 and intercept β0 of population regression line. • We can shows that b0 and b1 are the unbiased estimates of β1 and β0 and furthermore that b0 and b1 are Normally distributed with means β1 and β0 and standard deviation that can be estimated from t ...
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... Some Review • But often we’re not interested in single numbers - we’ve collected a sample and computed a mean • That mean comes from a population of sample means (you just happened to pick one of them) • The mean of the distribution of sample means is the mean of the population • The standard devia ...
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... distributed data values, approximately 68% of the distribution falls within ± 1 SD of the mean, 95% of the distribution falls within ± 2 SDs of the mean, and 99.7% of the distribution falls within ± 3 SDs of the mean. If our 10 scores were evenly distributed, with a M of 83.1 and SD of 8.39, this me ...
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... • Using this approximation results in narrower confidence intervals and smaller p-values than the conservative approach mentioned before ...
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Chapter 7

... These situations produce two samples that are not independent — they are related to each other. The members of one sample are identical to, or matched (paired) with, the members of the other sample. Example: Pre-test and post-test studies look at data collected on the same sample elements before and ...
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How I teach the interaction between contingency tables and tree

... We are often confronted with tables of summarised data by the media, census releases, etc. It is crucial to know how to draw meaningful conclusions from these tables, and knowledge of conditional probability can be very useful in this regard. We will investigate how the probability laws and concepts ...
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AP Statistics Learning Targets for Unit 8 Inference on Two Samples

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Scalable and Numerically Stable Descriptive Statistics in SystemML
Scalable and Numerically Stable Descriptive Statistics in SystemML

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Foundations of statistics

Foundations of statistics is the usual name for the epistemological debate in statistics over how one should conduct inductive inference from data. Among the issues considered in statistical inference are the question of Bayesian inference versus frequentist inference, the distinction between Fisher's ""significance testing"" and Neyman-Pearson ""hypothesis testing"", and whether the likelihood principle should be followed. Some of these issues have been debated for up to 200 years without resolution.Bandyopadhyay & Forster describe four statistical paradigms: ""(1) classical statistics or error statistics, (ii) Bayesian statistics, (iii) likelihood-based statistics, and (iv) the Akaikean-Information Criterion-based statistics"".Savage's text Foundations of Statistics has been cited over 10000 times on Google Scholar. It tells the following.It is unanimously agreed that statistics depends somehow on probability. But, as to what probability is and how it is connected with statistics, there has seldom been such complete disagreement and breakdown of communication since the Tower of Babel. Doubtless, much of the disagreement is merely terminological and would disappear under sufficiently sharp analysis.
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