1. Review Terms from Day 1 Descriptive Statistics
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 Ordinal Interval/ratio
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. Classification: Exclusive/Exhaustive
3 Levels of Measurement
Classification: Exclusive/Exhaustive
Rank Order
Equal Interval
NOMINAL X
ORDINAL
INTERVAL-RATIO

5. 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

6. 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)

7. 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

8. 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

9. 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

10. 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

11. Descriptive Statistics
Example: Prisoners Under Sentence of Death, by Region, 2006
Region f p %
Northeast
236
.074
7.4
Midwest
276
.087
14.4
South
1,750
.549
55.2
West
924
.290
23.2
Total
3,186
1.000
100.0
BASE OF BASE OF 100

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

13. Comparisons between distributions are simpler with percentages OFFENSE
Example: Distribution of violent crimes in 2 different cities
OFFENSE
CITY A
CITY B f %
MURDER 73
2.3 66
2.1
RAPE
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

14. 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!

15. 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

16. 1,750 / 276 = 6.34 = roughly 6:1 or “six to one”
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”

17. 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):
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?

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

19. 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

20. Frequency distributions – Examples:
NOMINAL-LEVEL
ORDINAL-LEVEL
These are right from the GSS data set.
Valid Percent – percent if you exclude missing values
Cumulative Percent – how many cases fall below a
given value?

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

22. Descriptive Statistics
Too little?

23. Descriptive Statistics
Just right:
Considering how few fines there are, probably be good to lump them with probation, but this is better than the other 2 for most purposes.

24. Homework #1 (Group Assignment)
Groups of 2 to 3
Due next Tuesday (9/20)
Assignment has an SPSS component
Also involves searching for table of data on the Web

25. 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.

26. SPSS (for Part C of HW)
Obtain copy of the 2006 GSS data set in SPSS format…
Go to:
Soc 3155 Homepage
Edit  Options  click on “Display Names” & “Alphabetical”
SPSS procedures we’re covering today:
Running a frequency (getting a frequency distribution)
Recoding a variable
SEE ACCOMPANYING NOTES
Data view / variable view
Run a frequency: TVHOURS (interval ratio variable)
Bar
appropriate for nominal or ordinal data
Pie
for nominal or ordinal data w/NO MORE THAN 5 CATEGORIES
Bar chart of HAPPY
Pie chart (maximum of 5 categories) – Race (RACECEN1)
SPSS is handy, but it’s ignorant – it will do whatever you tell it to do: like create a pie chart of age categories.

27. Recoding Exercise From class survey data
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 “siblings” variable create the variable “large fam”
Variable label = whether or not a person has large family (3 or more siblings)
Values
1 Yes