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Social Case-based Statistics II CSSS 322 Professor: Mark S. Handcock Solutions to Homework 5 Due Thursday, May 16, 2002 Problems to be handed in: 1) In an article on crime in the United States, Newsweek magazine (January 10, 1994) quoted FBI statistics stating that of all blacks slain in 1992, 94% were slain by blacks, and of all whites slain in 1992, 83% were slain by whites. Let Y denote race of victim and X denote race of murderer. a) What conditional distributions do these statistics refer to, those of Y at given levels of X , or those of X at given levels of Y ? Set up a table with race of murderer as rows and race of victim as columns, showing these conditional distributions. Solution(8) : These statistics refer to the conditional distribution of X (race of murderer) at given levels of Y (race of victim). We can represent the data with a contingency table: Murderer (X) Black White Total Black 94% 6% 100% White 17% 83% 100% b) Are X and Y independent random variable or dependent? Explain conceptually what you mean (You need not do a test). Solution(5) : X and Y are dependent, since there is a strong association between race of victim and race of murder. 2) The table below is from the 1991 General Social Survey. White subjects were asked: If your party nominated a (Negro/Black) fro President, would you vote for him or her if he/she were quali ed for the job? and During the last few years, has anyone in your family brought a friend who was a (Negro/Black) home for dinner? Black for President Yes No Don t Know Total Yes 113 6 0 119 Home For Dinner No Don t Know 239 49 13 301 1 0 2 3 Total 353 55 15 423 CSSS 322 Spring 2002 May 21, 2002 Page 1 a) Conduct a 2 test of the hypothesis that these two responses are independent. What is the p -value of the test and your decision. Solution(10) : Data of the question with expected frequencies in parentheses: Black for President Yes No Don t Know Total Yes 113 (99.31) 6 (15.47) 0 (4.22) 119 Home For Dinner No Don t Know 239 (251.19) 49 (39.14) 13 (10.67) 301 1 (2.5) 0 (0.39) 2 (0.11) 3 Total 353 55 15 423 Let fo represent the frequency of observed frequency and fe represent the frequency of expected frequency. Use the information from the table; we then calculate the Chi-Square statistic: (fo fe )2 2 = = 50.49, fe with the degrees of freedom df = (3 1)(3 1) = 4 The p -value of 2 = 50.49 is 4 less than 0.001. There is very strong evidence of an association. b) Some of the expected frequencies are small so the Normal approximation to the binomial may not hold. Hence the 2 test that is based on this approximation might not be valid. It is possible to conduct a small-sample exact test for testing the null hypothesis of independence between the two responses given the marginal totals. This can be done by many statistical software packages and gives a p -value of 0.0000035. Solution(3) : Given that the small-sample exact test for testing the null hypothesis of independence between the two responses given the marginal totals has a p -value of 0.0000035, the test also provides very strong evidence of an association. c) Given the results of the test, interpret the nature of the deviations from the independence assumption. What categories are higher and lower than would be expected if the factors were independent? Solution(4) : The observed frequencies are larger than expected when both responses are Yes or both are No, and less than expected when one is Yes and the other is that No; is, those who have had a black home for dinner are more likely to be willing to vote for a black for president, relative to what is predicted by the hypothesis of independence. d) Using Yes and No categories of each response, estimate the odds ratio. What does it tell us in this case? Solution(5) : The odds ratio = CSSS 322 Spring 2002 113 49 = 3.9 239 6 May 21, 2002 Page 2 The interpretation is that for those who would vote for a black for President, the odds of having invited a Black home for dinner are 3.9 times the odds of an invite for those who would not vote for a Black for President. Extra Credit Problem: 3) According to the U.S. Department of Justice, in 1994 he incarceration rate in the nation s prisons was 646 per 100,000 male residents, 45 per 100,000 female residents, 1471 per 100,000 black residents, and 207 per 100,000 white residents (Bureau of Justice Statistics Bulletin: Prisoners in 1994). a) Find the odds ratio between gender and being incarcerated. Give an interpretation of it. Solution(5) : The probability of incarceration for males is 646/100000 and that of women is 0.00646 45/100000. Hence the odds of incarceration rate for males = (1 0.00646) = 0.0065 and the odds of incarceration rate for females = 0.00045 (1 0.00045) = 0.00045. 0.0065 The odds ratio between gender and whether incarcerated = 0.00045 = 14.4, indicating that males have a much greater (i.e. 14.4 times) odds of being incarcerated than females. This indicates a strong relationship between gender and race in terms of incarceration. b) Find the odds ratio between race and being incarcerated. Give an interpretation of it. Solution(5) : The odds of incarceration rate for blacks = 0.01471 (1 0.01471) = 0.01493 The odds of incar- 0.00207 ceration rate for whites = (1 0.00207) = 0.00207. and whether incarcerated = 0.01493 = 7.2. 0.00207 Hence the odds ratio between race The odds of incarceration for blacks were 7.2 times the odds of whites. c) According to the odds ratio, which has the stronger association with whether incarcerated, gender or race? Solution(2) : Both associations are strong, but association with gender is stronger since the odds ratio is farther from 1 (i.e. 14.4 verses 7.2). d) Conduct a 2 test of independence between the incarceration and race, and incarceration and gender. For these assume that we have samples of 100,000 from each race and gender category. Solution(7) : For this problem we assume that we have populations of 100,000 for each of the CSSS 322 Spring 2002 May 21, 2002 Page 3 groups. Consider rst a comparison of incarceration and gender: Gender Male Female Total Yes Incarceration No 99354 (99654.5) 99955 (99654.5) 199309 646 (345.5) 45 (345.5) 691 The expected frequencies are in parentheses. The test statistic is = 2 (fo fe )2 = 524.53, fe with the degrees of freedom df = (2 1)(2 1) = 1 We have very strong evidence of an association. Next consider a comparison of incarceration and race: Incarceration Race Yes No Black White Total 1471 (839) 207 (99161) 1678 99354 (99161) 99955 (839) 198322 The expected frequencies are in parentheses. The test statistic is 2 = (fo fe )2 = 960.2, fe with the degrees of freedom df = (2 1)(2 1) = 1 We have very strong evidence of an association. Note that the strength of this evidence depends on the size of the populations. Smaller populations leads to smaller test statistics. CSSS 322 Spring 2002 May 21, 2002 Page 4
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hw3.pdf
Path: Washington >> STAT >> 322 Spring, 2008
Description: Case-based Social Statistics II CSSS 322 Professor: Mark S. Handcock Homework 3 Due Thursday, April 25, 2002 Problems to be handed in: 1) In a random sample of 725 selected for interview from a population of 13,916 teachers in Washington, 113 said th...
fin.pdf
Path: Washington >> STAT >> 394 Fall, 2008
Description: ...
AEESP-stat-analysis.pdf
Path: Washington >> STAT >> 486 Fall, 2008
Description: Statistics Statistics for Analysis of Experimental Data Catherine A. Peters Department of Civil and Environmental Engineering Princeton University Princeton, NJ 08544 Statistics is a mathematical tool for quantitative analysis of data, and as such i...
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Path: Washington >> STAT >> 491 Fall, 2008
Description: STAT 491 Group problems 10/3 1. Consider 2a molecules diffusing through a membrane. Let Xn be the number of molecules to the left of the membrane. At each time, one of the 2a molecule is chosen at random and moved to the other side of the membrane ...
sln.hw2.doc
Path: Washington >> STAT >> 491 Fall, 2008
Description: STAT/MATH 491 Solutions to homework 2. 5.4.1 E(Z m Zn) = . Now given that Zm = k, Zn can be thought of as k independent chains of length m n. Thus E(Z n Z m = = = so E(Z m Z n ) = ( ) = . Hence Cov(Z m , Z n ) = = ...
CA.trend.coef.matrix.txt
Path: Washington >> STAT >> 498 Fall, 2008
Description: 060370002,2.93443293273918,-6.60175212411867,1.46086781027834 060371002,3.03280812436641,-6.44671558582038,-1.66919019159562 060371103,2.99947555742709,-6.23861259473043,-1.0092641065844 060371201,2.79750673204645,-6.36486904517982,-0.838880577044036...
CA.lcovar.subset.txt
Path: Washington >> STAT >> 498 Fall, 2008
Description: ID2,LAT,LONG,LANDUSE,PopDens,m_to_a1,m_to_a2,m_to_a3,m_to_commerc,xlamb2,ylamb2 060370002,34.13650,-117.9230,Indust, 9.250915, 7.503247,7.190049,7.660713,6.2324031, -22.4479346, -1.542679 060371002,34.17600,-118.3170,Comm_serv, 9.346770, 7.368975,9.3...
HW506Sol3.pdf
Path: Washington >> STAT >> 506 Spring, 2008
Description: Stat 506, Homework set #3 Due Monday April 21, 2008 From Casella and Berger. 3.3; 3.7; 3.9; 3.20 and 3.23 Solution to Casella and Berger 3.3 Let Xi be the indicator function of the event a car is passing during the i-th second, where we start counti...
hw5.pdf
Path: Washington >> STAT >> 506 Spring, 2008
Description: Computer Environments for Social Scientists CSSS 506 Professor: Mark S. Handcock Solutions to Homework 5 Due Tuesday, March 5, 2002 1) The data frame hills contains the results from the Scottish hill races. The data set is taken from Staudte and Shea...
512 Info.doc
Path: Washington >> STAT >> 512 Fall, 2008
Description: STAT512:STATISTICALINFERENCE AUTUMN2007 Instructor: MichaelPerlman,Dept.ofStatistics,Box354322 Office:B310PadelfordHall(mailboxinB313) Phone:5437735 email:michael@stat.washington.edu Officehours:afterclassorbyappointment MWF10:3011:20,Sieg225. Th10:3...
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Path: Washington >> STAT >> 516 Fall, 2008
Description: Example R Sessionx <- 1:5xy <- 11:15x+yz <- c(10,6,3,5,1)zhelp(seq) seq(from=3,to=7,by=2)seq(3,17)seq(14,2)seq(1,2,.1)help(rep)rep(1,5)rep(1:5,3)temp <- c(2,1,5,9)temp.3 <- rep(temp,3)temp.3rep(c(seq(2,10,2),seq(1,9,2),2)temp.3[3] temp.3[5:7]temp.3[c...
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Path: Washington >> STAT >> 518 Spring, 2008
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Path: Washington >> STAT >> 518 Spring, 2008
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Path: Washington >> STAT >> 518 Spring, 2008
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Path: Washington >> STAT >> 524 Spring, 2008
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CATHEEK STAT 534 HW #1.txt
Path: Washington >> STAT >> 534 Fall, 2008
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Path: Washington >> STAT >> 534 Fall, 2008
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Path: Washington >> STAT >> 535 Fall, 2008
Description: Course Syllabus: BIOSTAT/STAT 535 Statistical Computing Autumn Quarter 2008 Adrian Dobra, Assistant Professor, Statistics, CS&SS and BNHS adobra@u.washington.edu September 30, 2008 Class room The class meets Tuesday and Thursday between 11:30am and ...
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Path: Washington >> STAT >> 535 Fall, 2008
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Path: Washington >> STAT >> 538 Fall, 2008
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Path: Washington >> STAT >> 550 Fall, 2008
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Path: Washington >> STAT >> 560 Fall, 2008
Description: Preliminary Battle Plan CSSS/POLS/STAT 560: Hierarchical Modeling for the Social Sciences Professor: Kevin Quinn, Political Science and CSSS Winter Quarter 2002 Class Room Oce 2:30-4:00 PM Tuesday and Thursday 313 Savery C-14-C Padelford Hall Phone...
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Path: Washington >> STAT >> 560 Fall, 2008
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Path: Washington >> STAT >> 560 Fall, 2008
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Path: Washington >> STAT >> 567 Fall, 2008
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Path: Washington >> STAT >> 567 Fall, 2008
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friends.pdf
Path: Washington >> STAT >> 567 Fall, 2008
Description: Krackhardts Hightech Managers friends network q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q Trace of var1 10 Density of var1 Density 0e+00 3e+05 Iterations 6e+05 5 10 15 20 0.00 20 0.02 0.04 0.06 0 0.08 ...
FigHW5.3.pdf
Path: Washington >> STAT >> 567 Fall, 2008
Description: Linear Quantile Regression 11.5 11.5 Spline Quantile Regression 11.0 10.5 Logearnings 10.0 Logearnings observed quantiles quantile regression lines 9.5 9.5 10.0 10.5 11.0 observed quantiles quantile regression splines 9.0 9.0 70 75 80...
570-Day-2.pdf
Path: Washington >> STAT >> 570 Fall, 2008
Description: Stemming Tokenizing suffixes irrelevant Porter Stemmer, simple and efficient Website: http:/www.tartarus.org/...
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Path: Washington >> STAT >> 573 Fall, 2008
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Path: Washington >> STAT >> 576 Fall, 2008
Description: BIOSTAT/STAT 576 Statistical Methods for Survival Data MW 9:00am - 10:20am, Spring 2007; HST T530 Instructor: Ying Qing Chen Tel: 206.667.7051 Email: yqchen@u.washington.edu Oce hour: Th 2:30pm - 3:30pm; H657 Course Web Site: http:/www.scharp.org/u...
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Path: Washington >> STAT >> 576 Fall, 2008
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579-07au.pdf
Path: Washington >> STAT >> 579 Fall, 2008
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Path: Washington >> STAT >> 579 Fall, 2008
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Path: Washington >> STAT >> 579 Fall, 2008
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581.day1.08.pdf
Path: Washington >> STAT >> 581 Fall, 2008
Description: STATISTICS 581: Advanced Theory of Statistical Inference Fall, 2008 Time: Place: Professor: Oce: Phone: e-mail: Oce Hours: Texts: 10:30 - 11:20 MWF (lecture) MEB 245 Jon A. Wellner B320 Padelford 206-543-6207 jaw@stat.washington.edu 1:30 - 3:30 MWF...
ref.08.pdf
Path: Washington >> STAT >> 581 Fall, 2008
Description: References for Statistics 581, Fall 2008 Analysis: Bartle, R. G., The Elements of Integration. Rudin, W., Principles of Mathematical Analysis. Royden, H. L., Real Analysis. Luenberger, D., Optimization by Vector Space Methods. Probability: Will...
ch2.figs-epsf.pdf
Path: Washington >> STAT >> 581 Fall, 2008
Description: Statistics 581, Chapter 2 Empirical Distribution Function and Empirical Process Figures Wellner; 10/24/2008 1 0.8 0.6 0.4 0.2 0.2 0.4 0.6 0.8 1 Figure 1: Uniform Empirical Distribution Function, n = 50. 1 0.75 0.5 0.25 0.2 -0.25 0.4 0.6...
exam1.06.pdf
Path: Washington >> STAT >> 581 Fall, 2008
Description: Statistics 581, Midterm Exam Wellner; 11/06/2006 This exam is to be taken without any books or notes. 1. (24 points) Dene any three of the following ve terms. (a) A uniformly integrable sequence of random variables. (b) Convergence in rth mean of a...
mt03.pdf
Path: Washington >> STAT >> 582 Fall, 2008
Description: Stat 582 W03 Midterm exam Please give as complete solutions as possible. More paper is available if needed. 1. Let (X,Y) be bivariate normal, mean zero, variance 1, correlation r. Find a minimal sufficient statistic for r. Is it complete? 2. Suppo...
final2.89.pdf
Path: Washington >> STAT >> 582 Fall, 2008
Description: STAT 582 FINAL EXAM 1. Let T (F) = m 2 = ( xdF(x)2 . Find, using the asymptotic theory for statistical functionals, the limiting F distribution of T (F n ) when m F 0. 2. Let (X 1 , Y 1 ), . . . , (X n , Y n ) be independent random variables with ...
gamma.pdf
Path: Washington >> STAT >> 582 Fall, 2008
Description: ...
hw1.sln.doc
Path: Washington >> STAT >> 583 Fall, 2008
Description: STAT583 Sp04 Homework1solution 1. (a)(c) E X i - m = 2 xdF(x) = d 2 2 s (1+ 2e) and (1- e)s + 3es ) = p p 0 E(X - m) 2 = s 2 (1+ 8e) .Standardasymptotictheoryhasthat n ( s2 - s 2 (1+ 8e) N(0,t 2 ) where 2 = E(X - m) 4 - E 2 (X - m) 2 = s 4 (3...
notes1.pdf
Path: Washington >> STAT >> 583 Fall, 2008
Description: STAT 583 SPRING 2008 Lecture Notes 1 Statistical Functionals The Gteux derivative of a statistical functional T(F) is the limit T (F + (G F ) T(F) . d1T(F;G F) = lim If Q( ) = T (F + (G F ) has a McLaurin expansion, we get an expansion (the von...
hw3.sln.pdf
Path: Washington >> STAT >> 583 Fall, 2008
Description: STAT 583 Sp08 Solutions, Homework 3 1. (a) T (F! ) = F + !(G \" F ) so IC(x) = x ! F . (b) By the same calculation as that for the median we get p ! 1(x < F !1 ( p) IC(x) = , x \" F !1 ( p) !1 f (F ( p) d 1 T (F + !(\" x # F) = (c) Using (b) d! 1 ...
HW2.pdf
Path: Washington >> STAT >> 583 Fall, 2008
Description: STAT 583 Sp08 Homework 2 Due April 16. 1. Let F be a cdf on [0,1], and define for ! > 1 T (F) = x\"[0,1] # ( F(x) ! F(x!) $ . (a) Compute the Gateux derivative of T at the uniform distribution U on [0,1]. (b) Show that nR1,n = n(T (Fn ) ! T (U ...
homework.pdf
Path: Washington >> STAT >> 592 Fall, 2008
Description: Homework problems (more problems will be added as we go along) Stat 592, W09 1. For a stationary random field Z(s); s !D \" R 2 , observed at sites s1,.,sn, derive the unbiased linear estimator with the smallest variance. Hint: Use a Lagrange multipli...
Lec1.ppt
Path: Washington >> STAT >> 592 Fall, 2008
Description: NRCSE SpatialStatisticalMethods peter@stat.washington.edu www.stat.washington.edu/peter/592 STAT592A(UW)526(UBCV) 8904(SFU) Coursecontent 1.Kriging 1.Gaussianregression 2.Simplekriging 3.Ordinaryanduniversalkriging 4.Effectofestimatedcovariance 5....
syllabus.pdf
Path: Washington >> STAT >> 593 Fall, 2008
Description: Course Syllabus: STAT 593 Modern Topics in Discrete Multivariate Analysis Spring Quarter 2008 Time and Location When: 10:30am-11:50am Tuesday and Thursday Where: TBA Instructor Adrian Dobra Oce: Padelford Hall B-303 E-mail: adobra@u.washington.edu ...
LECT 14.ppt
Path: Washington >> HUM >> 202 Fall, 2008
Description: Lecture 14: October 27, 2006 Questions Reading Lyrical Ballads (1798), published Anonymously; 3 poems by Coleridge; 20 poems by Wordsworth Preface added in 1800 2nd edition Lyrical Ballads: not just an experiment but a poeti...
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Path: Washington >> HUM >> 204 Fall, 2008
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Path: Washington >> HUM >> 207 Winter, 2008
Description: Molecular and Cellular Endocrinology 161 (2000) 117 120 www.elsevier.com/locate/mce Spermatogonial transplantation an update for the millennium Lonnie D. Russella *, Michael D. Griswoldb a Department of Physiology, School of Medicine, Southern Il...
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Path: Washington >> HUM >> 208 Fall, 2008
Description: HUMANITIES 208: VIOLENCE, MYTH, AND MEMORY (SPRING 2008) Tuesday and Thursday 1:00-2:20, Johnson Hall 102 Francisco Benitez (Comp Lit) and Laurie Sears (History) TAs: Cheryll Alipio, Katrina Hagen, William Mitchell \"Violence, Myth, and Memory\" is bui...
lect36_overheads.pdf
Path: Washington >> SWED >> 101 Fall, 2008
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JFQA-402-JPPW-Appendices.pdf
Path: Washington >> T C >> 402 Winter, 2008
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TC 403 Final.pdf
Path: Washington >> T C >> 403 Fall, 2008
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Path: Washington >> T C >> 493 Fall, 2008
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Path: Washington >> T C >> 505 Fall, 2008
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twodimensional.pdf
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intro.pdf
Path: Washington >> T C >> 509 Fall, 2008
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midterm_soln.pdf
Path: Washington >> T C >> 509 Fall, 2008
Description: GFD I: Winter 2007 Midterm Solutions Professor: Chris Bretherton TA: Tom Connolly \\) As A.\' ( ynOt/e g iawardCg- n\"a ir\",{ ina f r{ r,\\6rI V c\\.,r P *e*^p *ropi cc,t {cto nP- r {n 3ce t,( tt 17o r* lo t% scr rq- Av-ops {r\" ^ l o \\ o ,*b ...
hw7_soln.pdf
Path: Washington >> T C >> 509 Fall, 2008
Description: GFDI f HW io^t Sotto{ P.of, Ch.i e hn the\"r{o^ TA\' J[vu\"\'G^nolt1 f)\". No\',-\\incar SWt PV Conrrvr^4ion %:4) D+v _ .P/ )+ +- H *{-zv (,\"tlr, Ass,.^,- 5/r , , \\/3\'rth, q, 1-tr.) \'(\'i-r.)+H {t1)[r -efo,\"J TtlTm-ll1 x (+iir:Lr H T(Ti l-l 3=bll...
ch4.pdf
Path: Washington >> T C >> 516 Fall, 2008
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ps4.pdf
Path: Washington >> T C >> 521 Winter, 2008
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ps7.pdf
Path: Washington >> T C >> 521 Winter, 2008
Description: ...
sol.ps3.pdf
Path: Washington >> T C >> 521 Winter, 2008
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1970_statewide-television-address-on-citizen-unrest.pdf
Path: Washington >> T C >> 598 Fall, 2008
Description: a) \\<\\:J \' .\\t \\ rf -: \'t .t\\, a : A O \\ \\ l R1 \\: q : F dl tr- (t) r-,\\i \'\\\'x A .i I 5 ;: H z f r\'l F (h F \'6; ar Y H ()Fr q aa frl Z F r\') 7 3 iJa -{ \'r1 a EK ,ii +) F v 6)x \\J e Y H ^ .H 14 F] (I a5 A 6 z ^ r- - z...
1972_the-day-state-services-were-suspended.pdf
Path: Washington >> T C >> 598 Fall, 2008
Description: The Dav State Services \\WereSuspende d by Governor Dan Evans What if 24 hours? State services \\tere suspended for The federal government has been called local governments have been called omnipotent, and of American politics Ehe \"dark contine...
Porter1976.pdf
Path: Washington >> THAI >> 302 Fall, 2008
Description: ...
mt2_sol.pdf
Path: Washington >> IND E >> 101 Fall, 2008
Description: Name: _Section/TA Name: _ Atmospheric Science 101, Spring 2003 Midterm 2 Thursday 22 May 2003 Version A Multiple Choice (2 points each) Choose the best answer and mark it on a Scantron sheet. 1. Choose the words which best complete the following sent...
