# Soc 3155 - d.umn.edu

Soc 3155 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 Order NOMINAL X

ORDINAL X X INTERVALRATIO X X Equal Interval X In Class Assignment Bust into groups: 2-3 per group Put names on top of assignment and write legibly Develop Six Survey items that could be included as part of general survey of UMD students. Must include 2 examples of each type of variable:

Nominal (NOT gender or race/ethnicity) Ordinal Interval - Ratio (NOT age) Make sure to include all attributes of each Remember: Mutually exclusive & exhaustive Review III Types 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, describingquantitative 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 Region f Northeast 236 Midwest

276 South 1,750 West 924 Total 3,186 Descriptive Statistics Example: Prisoners Under Sentence of Death, by Region, 2006 Region f p Northeast 236

.074 7.4 Midwest 276 .087 8.7 1,750 .549 54.9 West 924 .290 29.0

Total 3,186 1.000 100.0 South BASE OF 1 % BASE OF 100 Comparisons between distributions are simpler with percentages Example: Distribution of violent crimes in 2 different cities OFFENSE CITY A

MURDER RAPE ROBBERY ASSAULT TOTAL 73 206 1,117 1,792 3,188 CITY B 66 243 1,307 1,455 3,071 Comparisons between distributions are simpler with percentages Example: Distribution of violent crimes in 2 different cities

CITY A OFFENSE MURDER f CITY B % f % 73 2.3 66 2.1 206 6.5 243

7.9 ROBBERY 1,117 35.0 1,307 42.6 ASSAULT 1,792 56.2 1,455 47.4 TOTAL 3,188

100.0 3,071 100.0 RAPE 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= f1 f2

Ratios are good for showing the relative predominance of 2 categories Example: ratio of prisoners on death row, South compared to Midwest Region f Northeast 236 Midwest 276 South 1,750 West 924

Total 3,186 1,750 / 276 = 6.34 = roughly 6:1 or six to one 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 You could make two comparisons of sales progress (based on above info): 1. 2.

A increased its sales by \$10M & B increased its sales by \$30M, 3 times that of A (a ratio of 3:1!). A increased its sales by 100%. B increased its sales by 75%, three-fourths the increase of A. Which is correct? 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 23,904,380 MN and WI rate per 100,000? MN Population = 5,263,610 WI Population = 5,641,581

x 100,000 = 719 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: NOMINA L-LEVEL RESPONDENTS SEX Valid MALE FEMALE Total Frequency 622

765 1387 Percent 44.8 55.2 100.0 Valid Percent 44.8 55.2 100.0 ORDINAL-LEVEL Cumulative Percent 44.8 100.0 SATISFACTION WITH FINANCIAL SITUATION Valid Missing Total

SATISFIED MORE OR LESS NOT AT ALL SAT Total DK NA Total Frequency 421 617 346 1384 1 2 3 1387 Percent 30.4 44.5 24.9 99.8 .1 .1 .2

100.0 Valid Percent 30.4 44.6 25.0 100.0 Cumulative Percent 30.4 75.0 100.0 Valid Percent percent if you exclude missing values Cumulative Percent how many cases fall Descriptive Statistics Example: Homogeneity of attributes how much detail is too much? TOO MUCH? (too many categories?) SPECIFIC SENTENCE CATEGORY

Valid Fine Only Probation Only Probation Plus Jail Only Jail - Probation Prison Only Prison - Probation Total Frequency 36 469 379 445 1007 1123 213 3672 Percent 1.0 12.8 10.3 12.1

27.4 30.6 5.8 100.0 Valid Percent 1.0 12.8 10.3 12.1 27.4 30.6 5.8 100.0 Cumulative Percent 1.0 13.8 24.1 36.2 63.6 94.2 100.0 Descriptive Statistics Too little?

INCARCERATION SENTENCE Valid Incarcerated Not Incarcerated Total Frequency 2788 884 3672 Percent 75.9 24.1 100.0 Valid Percent 75.9 24.1 100.0 Cumulative Percent 75.9 100.0

Descriptive Statistics Just right: Most Severe Sentence Category Valid Prison Jail Non-custodial Total Frequency 1336 452 884 3672 Percent 36.4 39.5 24.1 100.0 Valid Percent 36.4 39.5

24.1 100.0 Cumulative Percent 36.4 75.9 100.0 Homework #1 (Group Assignment) Groups of 2 to 3 Due next Wednesday (2/1) Assignment has an SPSS component Also involves searching for table of data on the Web This will be the ONLY ASSIGNMENT where you turn in the same paper for a group Interpreting Tables (Part B of HW) Locating tables Sourcebook of Criminal Justice Statistics Minnesota Milestones Page Addressing questions the HW asks

1. 2. 3. Contents of table: Who collected data? What population does it represent? How many cases is the table based on? Who might be interested in this information? What relevance might it have to policy? Description of variables: Name each variable & its level of measurement. SPSS (for Part C of HW) Obtain copy of the 2010 GSS data set in SPSS format Go to: Soc 3155 Homepage Edit Options click on Display Names & Alphabetical

SPSS procedures were covering today: Running a frequency (getting a frequency distribution) Recoding a variable Recoding Exercise From class survey data (off web site) From the nfl variable, create the variable packer Variable label = whether or not a person is a packer fan Values: 1 = Yes 0 = No From the sibs variable create the variable large fam Variable label = whether or not a person has large family (3 or more siblings) Values 1 = Yes 0 = No

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