Review Terms from Day 1 Descriptive Statistics

Review I Variable = any trait that can change values from case to case. Must be: Exhaustive: variables should consist of all possible values/attributes Mutually Exclusive: no case should be able to have 2 attributes simultaneously Attribute = specific value on a variable The variable “sex” has two attributes (female and male) Independent (X) and Dependent (Y) variables X (poverty)  Y (child abuse)

Review II Levels of Measurement Nominal Only ME&E (categories cannot be ordered) Sex, type of religion, city of residence, etc. Ordinal Ability to rank categories (attributes) Anything using Likert type questions (e.g., sa, a, d, sd) Interval/ratio Equal distance between categories of variable Age in years, months living in current house, number of siblings, population of Duluth… This level permits all mathematical operations (e.g., someone who is 34 is twice as old as one 17)

3 Levels of Measurement Classification: Exclusive/Exhaustive Rank OrderEqual Interval NOMINALX ORDINALXX INTERVAL- RATIO XXX

Review III Sort of Statistics Descriptive Statistics Data reduction (Univariate) Measures of Association (Bivariate) Inferential Statistics Are relationships found in sample likely true in population? Trick is finding correct statistic for particular data (level of measurement issues)

Basic Descriptive Statistics All about data reduction and simplification Organizing, graphing, describing…quantitative information Researchers often use descriptive statistics to describe sample prior to more complex statistics Proportions/percentages Ratios and Rates Percentage change Frequency distributions Cumulative frequency/percentage Charts/Graphs

Data Reduction Unavoidably: Information is lost Example: Study of textbooks 2 hypotheses: Textbook prices are rising faster than inflation. Textbooks are getting bigger (& heavier!) with time Still, useful & necessary: To make sense of data & To answer questions/test hypotheses

Descriptive Statistics Percentages & proportions: Most common ways to standardize raw data Provide a frame of reference for reporting results Easier to read than frequencies Formulas Proportion(p) = (f/N) Percentage (%) = (f/N) x 100

Descriptive Statistics Example: Prisoners Under Sentence of Death, by Region, 2006 Regionf Northeast236 Midwest276 South1,750 West924 Total3,186

Descriptive Statistics Example: Prisoners Under Sentence of Death, by Region, 2006 Regionfp% Northeast Midwest South1, West Total3, BASE OF 1 BASE OF 100

Comparisons between distributions are simpler with percentages Example: Distribution of violent crimes in 2 different cities OFFENSECITY ACITY B MURDER7366 RAPE ROBBERY1,1171,307 ASSAULT1,7921,455 TOTAL3,1883,071

Comparisons between distributions are simpler with percentages Example: Distribution of violent crimes in 2 different cities OFFENSE CITY ACITY B f%f% MURDER RAPE ROBBERY1, , ASSAULT1, , TOTAL3, ,

Descriptive Statistics Misconceptions arise with misuse of summary stats: Example: A town of 90,000 experienced 2 homicides in 2000 and 4 homicides in 2001 This is a 100% increase in homicides in just one year! …But, the difference in raw numbers is only 2!

Descriptive Statistics Ratio – precise measure of the relative frequency of one category per unit of the other category Ratio= f 1 f 2 Ratios are good for showing the relative predominance of 2 categories

Example: ratio of prisoners on death row, South compared to Midwest 1,750 / 276 = 6.34 Regionf Northeast236 Midwest276 South1,750 West924 Total3,186

Making Your Argument w/Stats… Example 2: Suppose that… Company A increased its sales volume from one year to the next from $10M to $20M Company B increased its sales from $40M to $70M 2 comparisons of sales progress (based on above info): 1. A increased its sales by $10M & B increased its sales by $30M, 3 times that of A (a ratio of 3:1!). 2. A increased its sales by 100%. B increased its sales by 75%, three-fourths the increase of A.

Descriptive Statistics Rate – proportion (p) multiplied by a useful “base” number with a multiple of 10 Example: As of the end of 2007: MN had 9,468 prisoners WI had 23,743 TX had 171,790 TX rate per 100,000 = 171,790 x 100,000 = ,904,380 MN and WI rate per 100,000? MN Population = 5,263,610 WI Population = 5,641,581

Descriptive Statistics Frequency distributions: Tables that summarize the distribution of a variable by reporting the number of cases contained in each category of that variable

Frequency distributions – Examples: NOMINAL -LEVEL ORDINAL-LEVEL Valid Percent – percent if you exclude missing values Cumulative Percent – how many cases fall below a given value?

Descriptive Statistics Example: Homogeneity of attributes – how much detail is too much? TOO MUCH? (too many categories?)

Descriptive Statistics Too little?

Descriptive Statistics Just right:

Homework #1 (Group Assignment) Groups of 2 to 3 Due next Tuesday (2/03) Assignment has an SPSS component Also involves searching for table of data on the Web

Interpreting Tables (Part B of HW) Locating tables Sourcebook of Criminal Justice Statistics “Minnesota Milestones” Page Addressing questions the HW asks 1. Contents of table: – Who collected data? What population does it represent? How many cases is the table based on? 2. Who might be interested in this information? What relevance might it have to policy? 3. Description of variables: Name each variable & its level of measurement.