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Math 203_Lecture 1

Math 203_Lecture 1 - Principles of Statistics 1 Math 203...

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Principles of Statistics 1 Math 203 Abbas Khalili Department of Mathematics and Statistics McGill University May 02, 2011 Principles of Statistics 1 Math 203 – p. 1/5
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Outline Course Syllabus Lecture 1 Principles of Statistics 1 Math 203 – p. 2/5
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What “statistics” is not Statistics is Not: Mathematics Although mathematics lies at its core, statistics as a discipline involves several essential components beyond mathematics. Just playing with numbers Formula memorization Not useful Principles of Statistics 1 Math 203 – p. 3/5
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What is statistics? Statistics is: The science of doing other sciences by: collecting, summarizing, and analyzing data; drawing conclusions and making decisions. The range of applications of statistics is vast and is growing: astronomy, biology, economy, engineering, medicine, social sciences. Principles of Statistics 1 Math 203 – p. 4/5
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Statistics A quote from The New York Times; August 15, 2009 : “I keep saying that the sexy job in the next ten years will be statisticians,” said Hal Varian, chief economics at Google . “And I’m not kidding. ” Principles of Statistics 1 Math 203 – p. 5/5
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Example: in biology DNA microarray technology provides biologists with the ability to measure the expression levels of tens of thousands of genes in a single experiment. Of interest is to identify genes that differ in expression across, say, cancer and normal samples (cells). The identification provides insight into the genetic mechanisms underlying biological processes. Principles of Statistics 1 Math 203 – p. 6/5
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Microarray technology Talking Glossary of Genetics at www.genome.gov Principles of Statistics 1 Math 203 – p. 7/5
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Analyzing gene expression data Data from such experiments are noisy, and very complex to analyze and interpret. New difficulties for statistician, but also opens new opportunities ! For example, multiple testing problem in which tens of thousands of hypothesis are to be tested simultaneously. Principles of Statistics 1 Math 203 – p. 8/5
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Types of statistics that we often do Descriptive statistics : Uses numerical and graphical techniques for: data summary (mean, variance, correlation, ...); data visualization (histogram, boxplot, piechart,...). Inferential statistics : Uses sample data for estimation, prediction, and decision making about a larger data set (population). Principles of Statistics 1 Math 203 – p. 9/5
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Example: Boston housing data Boston housing data : it concerns the house values in suburbs of Boston. The data contains 506 observations on: the median value of owner-occupied homes in 1000’s, (MEDV) and 13 factors (e.g. crime rate, pupil-teacher ratio, lower status population, number of rooms, ...) that may have effects on the house value. Principles of Statistics 1 Math 203 – p. 10/5
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Example: Boston housing data Descriptive statistics : for instance histogram of MEDV MEDV Frequency 10 20 30 40 50 0 50 100 150 200 it has been found that the most significant factors affecting the house values are: crime rate, pupil-teacher ratio, lower status population, and number of rooms.
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