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 valuesattributes ID: 429334
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Slide1
Soc 3155
Review Terms from Day 1
Descriptive StatisticsSlide2
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)
Slide3
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)Slide4
3 Levels of Measurement
Classification:
Exclusive/Exhaustive
Rank Order
Equal Interval
NOMINAL
X
ORDINAL
X
X
INTERVAL-RATIO
X
X
XSlide5
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) Slide6
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 Slide7
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 hypothesesSlide8
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 100Slide9
Descriptive Statistics
Example: Prisoners Under Sentence of Death, by Region,
2006
Region
f
Northeast
236
Midwest
276
South
1,750
West
924
Total
3,186Slide10
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
.29023.2Total3,1861.000100.0
BASE OF 1 BASE OF 100Slide11
Comparisons between distributions are simpler with percentages
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
3,071Slide12
Comparisons between distributions are simpler with percentages
Example: Distribution of violent crimes in 2 different cities
OFFENSE
CITY A
CITY B
f
%
f
%
MURDER
73
2.3
66
2.1
RAPE
206
6.5
243
7.9
ROBBERY
1,117
35.01,30742.6ASSAULT1,792
56.2
1,455
47.4
TOTAL
3,188
100.0
3,071
100.0Slide13
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!Slide14
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
Slide15
Example: ratio of prisoners on death row, South compared to Midwest
1,750
/
276
=
6.34
Region
f
Northeast
236
Midwest
276
South
1,750
West
924
Total
3,186Slide16
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.Slide17
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 Slide18
Descriptive Statistics
Frequency distributions:
Tables that summarize the distribution of a variable by reporting the number of cases contained in each category of that variableSlide19
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?Slide20
Descriptive Statistics
Example: Homogeneity of attributes – how much detail is too much?
TOO MUCH? (too many categories?)Slide21
Descriptive Statistics
Too little?Slide22
Descriptive Statistics
Just right:Slide23
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
Slide24
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.