Soc 3155

1. Soc 3155 Review Terms from Day 1 Descriptive Statistics

2. 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)

3. 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)

4. 3 Levels of Measurement

5. 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)

6. 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

7. 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

8. 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

9. Descriptive Statistics • Example: Prisoners Under Sentence of Death, by Region, 2006

10. Descriptive Statistics • Example: Prisoners Under Sentence of Death, by Region, 2006 BASE OF 1 BASE OF 100

11. Comparisons between distributions are simpler with percentages • Example: Distribution of violent crimes in 2 different cities

12. Comparisons between distributions are simpler with percentages • Example: Distribution of violent crimes in 2 different cities

13. 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!

14. 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

15. Example: ratio of prisoners on death row, South compared to Midwest • 1,750 / 276 = 6.34

16. 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): • 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.

17. 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 = 719 23,904,380 • MN and WI rate per 100,000? • MN Population = 5,263,610 • WI Population = 5,641,581

18. 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

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

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

21. Descriptive Statistics • Too little?

22. Descriptive Statistics • Just right:

23. 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

24. Interpreting Tables (Part B of HW) • Locating tables • Sourcebook of Criminal Justice Statistics • “Minnesota Milestones” Page • Addressing questions the HW asks • 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.