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Midterm 2 Study Guide

by: Rachael Kroeger

Midterm 2 Study Guide 1350

Marketplace > Ohio State University > Stats > 1350 > Midterm 2 Study Guide
Rachael Kroeger

Elementary Statistics

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Elementary Statistics
Study Guide
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This 1 page Study Guide was uploaded by Rachael Kroeger on Monday May 18, 2015. The Study Guide belongs to 1350 at Ohio State University taught by Strait in Spring 2015. Since its upload, it has received 91 views. For similar materials see Elementary Statistics in Stats at Ohio State University.


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Date Created: 05/18/15
STANDARD SCORE Z SCORE standardizing values puts all observations on the same scale Z observationmeanstd dev zxuo Represents how many std dev away the observation is form mean if then above mean if below mean 6595997 RULE how many std devs the data falls into Cth PERCENTILE value such that c percent of the observations lie below it and rest lie above Ql 25th percentile Q375tquot Median 50th NEGATIVE Z SCORE observation below avg lt50 POSITIVE Z SCORE observation above avg gt50 0 Z SCORE percentile equals 50convert from 2 score TABLE B PROVIDED convert z score SCATTERPLOTS display the relationship between 2 quantitative variables one on x axis on y interested on how they relate to each other use one variable to explainpredict other variable x explanatoryindependent variable y responsedependent variable FORM linear nonlinear no pattern DIRECTION positive negative no association STRENGTH strong moderate weak pattern ASSOCIATION DOES NOT EQUAL CAUSATION CORRELATION number that describes two things about the LINEAR relationship between 2 quantitative variables 1 direction 2 strength CORRELATION r CORRELATION ONLY USEFUL FOR STRAIGHTLINE RELATIONSHIPS 1ltrlt1 sign on r matches scatterplot data association positivenegative Outliers have an impact on r R doesn t change value if you change the units of the x or y variabes R value has no units Absolute value of correlation tells the strength of association 0002 very weak to negligible correlation 0204 weak low 0407 moderate 0709 strong high 0910 very strong LEASTSQUARES REGRESSION quotline of best tquot used to understand relationship between 2 quantitative variables creates equation use to predictexplain one quantitative variable based on other need fairly linear relationship 1 create scatterplot and describe and outliers 2 compute correlation coef cient r 3 obtain equation yabx A intercept value of y when x variable is 0 where the line crosses the y axis B slope amount that the y variable changes when x variable increases by 1 unit larger b steeper line Slope and correlation ALWAYS have same sign R2 percent of variation in the y variable that is explained by the regression line To get R2 value 1 nd correlation r 2 square this r value 3 multiply value by 100 R2 value is always between 0100 Closer it is o 100 the stronger the linear relationship between x and y good PREDICTION plug in value into equation works well when regression line ts data well stong linear patterns best high R2 value PREDICTION using x values within the range of the original x values to predict y EXTRAPOLATION using x values well outside the range of the original x values to predict y BADll OUTLIERs big effect on correlation and regression line think about how removing the outlier will impact the correlation CAUSTAITON x causes y Welldesigned and controlled experiment can show causation but dif cult to show causation Strong association alone is not enough need carefully controlled experiment usually not the entire story causal relationships may not generalize to other settings Can show by strong and consistent association higher doses are associated with stronger responses alleged cause precedes effect alleged cause is plausible Watch for confounding variables CHANCE random BEHAVIOR unpredictable in the short run but regular and predictable pattern in the long run RANDOM DOESN T EQUAL HAPHAZARD RANDOM if individual outcomes are uncertain but there is a regular distribution of outcomes in large number of repetitions order that emerges in the long run PROBABILITY random phenomenon a number between 01 describing the proportion of times that the outcome would occur in a long series of repetition Probability outcome 0 NEVER occurs Probability outcome 1 always occurs LAW OF AVERAGES averages or proportions likely to be more stable when there are more trials while sums or counts are likely to be more variable doesn t happen by compensation for bad run of luck since independent trials have no memory AVERAGESPROPORTIONS as you take more and more trials avgprop tends to be closer to the truth SUMSCOUNTS as you take more and more trials sumscounts tend to differ from them the truth by more and more PERSONAL PROBABILITY not based on data not scienti c just individual s opinion ex quotI am 60 certain that I will say something stupid todayquot PROBABILITY MODEL for a random phenomenon describes all the possible outcomes and says how to assign probabilities to any collection of outcomes Event collection of outcomes ex landing on an even number collection of outcomes 246 RULES FOR PROBABILITY any probability is a number between 0 and 1 all possible outcomes together must have probability 1 must be true for a model to be a probability model probability that an event does not occur is 1 the probability that event does occur Psunny 1Pnotsunny if two events have no outcomes in common the probability that one or the other occurs is the sum of their individual probabilities event1 landing on odd event 2landing on even P landing on odd or even Podd Peven VALID PROB MODEL all of the probs between 0 and 1 all probs add up to 1 SAMPLE DISTRIBUTION choosing random sample form population and calculating statistic like sample proportion sample mean if repeated process and look at distribution probability model Tells us what a sample statistic takes and how often it takes on those values when we look at repeated samples from the population Can be described by shape center and spread or variability Centered where population is centered Less spread out variable than population


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