UK Police Forces: Crime Analysis, Detection Rates, and Public Perception Monitoring, Exams of Statistics

Download UK Police Forces: Crime Analysis, Detection Rates, and Public Perception Monitoring and more Exams Statistics in PDF only on Docsity! M. PHIL. IN STATISTICAL SCIENCE Monday 7 June to Thursday 10 June 2004 APPLIED STATISTICS Attempt THREE questions. There are four questions in total. The questions carry equal weight. This is an ‘Open Book’ examination, involving the use of the Statistical Laboratory’s network of workstations. Candidates will receive this paper at 9.00am on Monday 7 June, and must hand in their scripts to the Chairman of Examiners by 1.00pm on Thursday 10 June. The data sets will be emailed to candidates on Monday 7 June. (The Statistical Laboratory Computer Officer and an Examiner will normally be available for consultation if required between 9.00am and 4.30pm on these four days.) Each candidate should submit his/her script with a signed statement that the work has been carried out without any collaboration with others. The scripts may be handwritten. Candidates are requested to submit at most 25 pages in total. They are advised that the total work set should take between 4 and 6 hours. 2 1 The Independent, on February 20, 2003, gave the following data on Police Perfor- mance Monitoring, for the 43 police forces of England and Wales. The 6 columns of the table are, respectively Burg = number of Burglaries for every 1000 households Vehc = Vehicle crimes for every 1000 residents Robb = Robberies for every 1000 residents Offdet = percentage of offences detected HiDis = percentage of residents perceiving disorder as high GoodJob = percentage of residents thinking police do a good job (i) Summarise the data with appropriate graphs, tables and a paragraph of text. (ii) How does HiDis depend on the first 4 variables Burg, . . . , Offdet? How does GoodJob depend on these first 4 variables? Illustrate the use of the stepAIC( ) function in your solution. (iii) What is the sample correlation matrix for the 6 variables? What is the partial correlation of HiDis and GoodJob, conditional on the remaining 4 variables? APPLIED STATISTICS 5 3 You see in the Table below an extract from the Metropolitan Police Statistics for offences in the category “Violence against the Person” for each of the 33 Metropolitan boroughs, for September 2003 and October 2003. The Metropolitan Police Service, Offences by Borough www.met.police.uk/crimestatistics/stat Violence against the person ........................................................... September 2003 Murder GBH ABH ComAss OffW Har OViol VAP.Tot Westminster 0 12 159 316 82 117 47 733 Camden 1 21 147 196 33 88 29 515 Islington 1 10 124 227 40 116 40 558 Hackney 0 27 132 232 38 89 53 571 Tower_Ham 1 12 70 298 37 136 34 588 Greenwich 2 10 122 283 19 115 34 585 Lewisham 3 16 85 246 24 69 54 497 Southwark 2 26 165 322 32 146 67 760 Lambeth 2 31 190 325 55 155 51 809 Wandsworth 0 19 90 236 23 90 17 475 Hamm&Fulham 0 8 91 141 20 78 20 358 Kens&Chelsea 0 6 88 115 10 49 8 276 Walt_Forest 0 15 90 259 25 115 23 527 Redbridge 0 8 37 221 15 76 32 389 Havering 0 5 39 207 11 44 14 320 Bark&Dagenham 0 10 50 194 14 44 14 326 Newham 1 13 101 383 34 128 42 702 Bexley 0 2 64 175 6 72 31 350 Bromley 0 7 67 217 12 82 30 415 Croydon 0 21 146 333 21 133 40 694 Sutton 0 5 24 162 4 49 4 248 Merton 0 6 76 126 17 73 14 312 Kingston_u_T 1 5 41 180 3 36 6 272 Richmond_u_T 0 1 32 112 9 41 11 206 Hounslow 0 11 139 264 20 124 59 617 Hillingdon 0 10 92 178 16 64 25 385 Ealing 0 16 142 317 13 94 48 630 Brent 2 16 77 372 18 86 52 623 Harrow 1 7 68 126 9 31 17 259 Barnet 0 9 93 216 20 85 33 456 Haringey 1 14 162 133 31 52 39 432 Enfield 0 15 91 180 18 46 35 385 H/R_Airport 0 0 5 14 5 5 1 30 Total 18 394 3099 7306 734 2728 1024 15303 APPLIED STATISTICS [TURN OVER 6 October 2003 Murder GBH ABH ComAss OffW Har OViol VAP.Tot Westminster 0 21 180 307 87 148 46 789 Camden 0 29 130 225 35 110 37 566 Islington 1 18 106 223 38 124 42 552 Hackney 5 22 148 277 44 80 53 629 Tower_Ham 1 22 60 331 29 153 38 634 Greenwich 1 6 106 262 12 111 34 532 Lewisham 0 11 93 273 30 98 54 559 Southwark 1 21 158 313 55 116 64 728 Lambeth 1 25 209 295 52 123 72 777 Wandsworth 0 11 91 180 27 95 26 430 Hamm&Fulham 1 10 73 139 21 80 20 344 Kens&Chelsea 0 4 73 94 15 42 11 239 Walt_Forest 2 15 80 205 26 103 18 449 Redbridge 1 2 63 179 14 67 24 350 Havering 0 9 48 184 12 39 14 306 Bark&Dagenham 0 7 91 225 32 78 20 453 Newham 1 17 109 386 25 109 40 687 Bexley 0 7 69 145 11 70 23 325 Bromley 0 6 70 201 17 119 20 433 Croydon 1 24 134 270 29 113 30 601 Sutton 0 3 28 147 25 49 3 255 Merton 0 1 63 149 17 66 19 315 Kingston_u_T 0 5 64 156 11 51 15 302 Richmond_u_T 0 8 31 95 6 32 11 183 Hounslow 1 7 125 272 12 147 32 596 Hillingdon 0 8 82 205 15 78 29 417 Ealing 0 17 121 273 19 91 30 551 Brent 1 16 77 409 48 100 53 704 Harrow 0 5 49 115 17 21 13 220 Barnet 0 10 94 191 11 104 30 440 Haringey 1 20 110 137 46 73 35 422 Enfield 2 11 112 181 18 49 32 405 H/R_Airport 0 1 1 8 9 3 0 22 Total 21 399 3048 7052 865 2842 988 15215 Key: Murder = Murder, GBH = Grievous Bodily Harm, ABH = Aggravated Bodily Harm, ComAss = Common Assault, Har = Harassment, OViol= Other Violence, VAP.Tot = Violence against the person, total. APPLIED STATISTICS 7 (i) Summarise the data with appropriate graphs, and a paragraph of text. This summary should include informal comparisons of the crime statistics for September with those of October. (ii) Let ySept be the “VAP.Tot” figures for September 2003, and let yOct be the corresponding figures for October 2003. Use appropriate non-parametric methods to see whether (a) ySept are different from yOct; (b) ySept are related to yOct. (iii) Now let (y1j) be ySept, and let (y2j) be yOct. Let (CA1j) be the number of Common Assaults for September, and let (CA2j) be the corresponding number for October. (Here j = 1, . . . , 33, corresponding to the 33 boroughs) Let E(CAij/yij) = πij , for i = 1, 2 and j = 1, . . . , 33. (a) Test the hypothesis H0 : π1j = π1 for all j. (b) Fit the model g(πij) = µ + αi + βj , for i = 1, 2 and j = 1, . . . , 33. where g( ) is the usual logit link. Can you identify one particular Borough whose removal makes this model fit quite well? How would you interpret the model to a layman? APPLIED STATISTICS [TURN OVER