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# Fundamentalsof Crime Mapping 8

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Fundamentals of crime mapping chapter 8

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### Fundamentalsof Crime Mapping 8

1. 1. Understand the difference between qualitative and  quantitative data. Define and explain levels of measurement including  nominal, ordinal, interval, and ratio. Understand the difference between discrete and continuous  variables. Understand descriptive statistics, including typical measures  of central tendency and dispersion. Understand inferential statistics, including typical tests of  significance and measures of association. Understand what a regression model is and how it works.  Understand the limitations of statistics and how their  improper application can yield misleading results. Define and explain classification in crime mapping and be  able to identify strengths and weaknesses of each method.
2. 2. Qualitative  ◦ Yields narrative-oriented information  Park, Blue, Yes, Tall, Short, etc Quantitative  ◦ Produces number-oriented information Key Factors or ―Variables‖ 
3. 3. Ratio  ◦ Highest level ◦ Can be reclassified to any of the other levels ◦ - ∞ to + ∞ Interval  ◦ Precise value of a measure is known and thus can also be ranked ◦ 1,2,3,4,5,6,7,8,9,10 Ordinal  ◦ Rank order nominal data and order can be important ◦ Officer, Sergeant, Lt, Commander, Majo r, Chief Nominal  ◦ Male, Female
4. 4. Nominal  ◦ Dichotomous  Caucasian African American  Non-Caucasian  Caucasian  Hispanic  Native American  Asian  Other  Must be mutually exclusive and exhaustive
5. 5. Traits, concepts, and ideas in criminal justice can be difficult to Ordinal operationalize, or  measure. ◦ Categorical or numerical data that can be ranked, but the precise value is not known  Likert scale example I feel safe walking in my neighborhood alone at night 1 -Strongly agree 2 – Agree What is your annual household 3 – Neutral income? 4 – Disagree 1. Less than \$20,000 5 - Strongly disagree 2. Between \$20,000 and \$40,000 6 - Don’t know 3. Between \$40,001 and \$60,000 4. Between \$60,001 and \$80,000 5. More than \$80,000
6. 6. Validity  ◦ A variable accurately reflects the trait or concept it is measuring Reliability  ◦ The measure is representative consistently across people, places, and time
7. 7. Interval  ◦ What is your annual household income? __________________  Ranking possible and precise value known  112 burglaries occurred in beat 32
8. 8. Ratio  ◦ Treated the same as interval data  112.23 burglaries occurred on average in beat 32  Can we have .23 of a burglary?
9. 9. \$16095.32 \$16095.00 \$0 - \$25,000 Below \$35,000 \$17262.67 \$17262.00 \$25,001 - \$35,000 Over \$35,000 \$24262.78 \$24262.00 \$35,001 - \$45,000 \$26095.32 \$26095.00 \$45,001 - \$55,000 \$27262.67 \$27262.00 \$55,001 - \$65,000 \$32262.78 \$32262.00 Over \$65,000 \$33095.32 \$33095.00 \$35262.67 \$35262.00 \$36262.78 \$36262.00 \$36095.32 \$36095.00 \$40262.67 \$40262.00 \$41262.78 \$41262.00 \$52095.32 \$52095.00 \$55262.67 \$55262.00 \$68262.78 \$68262.00
10. 10. Discrete Continuous   ◦ Variables that cannot be Can be subdivided—  subdivided theoretically they can be subdivided an  The number of persons living in a household is a infinite number of discrete variable. For times. example, there cannot be  Time for example 2.3 persons living in a  Days, Hrs, Mins, Secs, household. There can be 2, Nanosecs, etc. or there can be 3, but not 2.3.
11. 11. Rates Ratios   ◦ Violent crimes per Violent Crimes ―per‖  100,000 population Property crime  Violent Crimes /  Violent crimes = 10 (Population/100000) =  Property crimes = 300 Rate  PC/VC (300/10)=30  For every one violent crime, there are 30 property crimes
12. 12. Percent Change  ◦ For comparing time periods ((New-Old)/Old) *100  2009 property crimes =2567  2008 property crimes = 2655  Percent change=   (2567-2655)/2655  or -0.033 * 100 = -3.3%
13. 13. Measures of Central  25 Tendency 55 ◦ Mean or Average 56 65  Average of a distribution of Median = 82-72 72 values = 10/2 82 = 72+5 ◦ Mode 82 84  Most often found value in a 90 distribution 97 ◦ Median  The middle value in a distribution
14. 14. Bi-Modal  25 55 55 65 Median = 82-72 72 = 10/2 82 = 72+5 82 84 90 97
15. 15. Mean  Positive or Right Skewed ◦ Should not be used when distribution is greatly ―skewed‖  As with most crime data ◦ Use Median where it Almost normal makes sense instead Negative or Left Skewed
16. 16. Measures of Variance or  Dispersion 25 ◦ Range 55 55  The distance between the 1st Quartile = 57.5 65 lowest and highest score 72 ◦ Interquartile range 26 82  The distance between the 82 3rd Quartile = 83.5 25th and 75th percentile 84 ◦ Variance 90  The average squared 97 distance of each score in a distribution from the mean of the distribution ◦ Standard deviation  The average distance of each score from the mean
17. 17. Measures of Variance or  Dispersion ◦ Range  The distance between the lowest and highest score ◦ Interquartile range  The distance between the 25th and 75th percentile ◦ Variance  The average squared distance of each score in a distribution from the mean of the distribution ◦ Standard deviation  The average distance of each score from the mean
18. 18. Sample Analyzed and  ―infer‖ information to the population ◦ Probability theory  The number of times any given outcome will occur if the event is repeated many times.
19. 19. Bell-Shaped or Normal  Curve Mode & Median same as Mean
20. 20. Histogram  ◦ Normal Average 13.6 Median 10 Mode 1 ◦ Skewed Average 20 Average 26.20 Median 20 Median 30 Mode 20 Mode 40
21. 21. What variables are available?  What is the overall n?  What is the unit of analysis?  What do I want to know about the variable(s)?  What is the level of measurement of the  variable(s)? Are the variables discrete or continuous?  How many groups will be compared in the  analysis? Am I interested in just describing the data or  finding inferences within it?
22. 22. Independent variable  ◦ The variable that analysts are trying to explain  (in crime mapping, the dependent variable is often some crime measure). Dependent variable  ◦ Variables that produce a change in our dependent variable
23. 23. X Casual relationship  Intervening variable ◦ Antecedent variable Multicollinearity ◦ Contingent variable ◦ Z Y Multicollinearity ◦  When X, Y, and Z have overlapping measures of the same concept ◦ Spurious relationships  When X and Y have no direct relationship but are both affected by Z
24. 24. Chi-square  T-tests  Z-tests  ANOVA  ◦ Essentially, they work by determining whether or not variable distributions or differences between groups or areas would be expected based on random chance
25. 25. Lambda  Gamma  Kendall’s tau statistics  Spearman’s rho  Pearson’s correlation coefficient  ◦ To determine the strength and direction of a relationship between two variables ◦ Values between -1 and +1 ◦ Inverse/negative or positive relationships possible Variable 2 Variable 2 Variable 1 Variable 1
26. 26. Spatial Autocorrelation  ◦ Moran’s I  A value between 0 and 1 indicates positive spatial autocorrelation (or clustering).  A value between 1 and 0 indicates negative spatial autocorrelation (random distribution). ◦ Geary’s C  Values under 1 signify positive spatial autocorrelation  Values over 1 designate negative spatial autocorrelation
27. 27. Linear relationship  ◦ (OLS) Ordinary least-squares  Y =a + b1 X1 + b2 X2 + b3 X3 … ◦ Units of analysis  Must be the same
28. 28. Nominal (categories), Ordinal, Interval and Ratio  (Quantities) can be used with different methods Fills and outlines  Nominal data example Ratio Data Example
29. 29. Category data  symbology comes next It displays data  by unique values of a field, or multiple fields Nominal, ordinal,  ratio or interval data
30. 30. Next, comes the  quantities symbology method  It uses a number field in the table to display data by classified values  Ratio and interval data
31. 31. Six different ways to classify data, with an  added manual method for infinite freedom
32. 32. Equal Interval  Defined Interval  Quantile  Natural Breaks  Geometrical Interval  Standard Deviation 
33. 33. Categorical (Qualitative)  Grouping based on some quality ◦ Labels or categories ◦ E.g.; Sex = Male or Female ◦ Nominal or Ordinal ◦  Nominal the order is not important  E.g.: Sex = male or female  Ordinal the order is important  E.g.; Rank = Officer, Sergeant, Lieutenant, etc ◦ Can be binary or non-binary  Binary = only two values (male or female)  Non-Binary = More than two (red, blonde, brunette, etc)
34. 34. Measurement (Quantitative)  ◦ Grouping based on some quantity or value ◦ Always numbers ◦ Discrete or continuous  Discrete = only certain values are possible and data could have gaps (1, 2, 3, or 4)  Continuous = Any value along some interval (any value between 1 and 4 (ie: 3.24211) ◦ Interval or ratio  In interval data the interval between values is important (ie; temperature of 30 compared to 110 means something)  Ratio data is the best, and the ―0‖ value can be informative (ie; a grid can have 0 crimes, or any value up to infinity)
35. 35. http://www.socialresearchmethods.net/kb  /index.php
36. 36. Number of Equal Interval (ratio, Interval)  classes desired ◦ The range between the classifications is thedetermines interval same Take the high value-low value and for each of the 5 classes, the value is 199.61
37. 37. Defined Interval (ratio, interval)  ◦ Similar to the equal interval, but here, we define what the interval will be and thus establish the classes In this case the interval was set to 150, and so the number of classes is determined by the interval
38. 38. Quantile (ratio, interval)  ◦ A percentage of the values in the class falling with the range. Each class contains an equal number of features. Each of the 10 classes has the same number of features within each class, or makes up 10% of the total records
39. 39. Natural Breaks (ratio, interval)  ◦ Breaks the data where there are natural holes between values Use test exam score example
40. 40. Geometrical Interval (ratio, interval)  ◦ This is a classification scheme where the class breaks are based on class intervals that have a geometrical series. This ensures that each class range has approximately the same number of values with each class and that the change between intervals is fairly consistent. The interval is determined by a geometric equation (large and small changes depending on breaks in data)
41. 41. Standard Deviation (ratio, interval)  ◦ Classes are determined by mean and standard deviation of values. Can display by 1, ½, ¼ standard deviations as needed
42. 42. Getting to know your data, and the factors that  influence crime can help analysts create more useful maps and analysis products and do problem solving Handling data properly will keep your from making  incorrect assumptions and coming to unrealistic conclusions Remember the wheel of science 