Soc 3155 Review Terms from Day 1

Descriptive Statistics

Review IVariable = any trait that can change values

from case to case. Must be: Exhaustive: variables should consist of all

possible values/attributesMutually 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 IILevels 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 Equal Interval

NOMINAL X

ORDINAL X X

INTERVAL-RATIO

X X X

Review IIISort 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/percentagesRatios and RatesPercentage changeFrequency distributions Cumulative frequency/percentage Charts/Graphs

Data ReductionUnavoidably: 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 StatisticsPercentages & proportions:

Most common ways to standardize raw data Provide a frame of reference for reporting results Easier to read than frequencies

FormulasProportion(p) = (f/N)Percentage (%) = (f/N) x 100

Descriptive StatisticsExample: Prisoners Under Sentence of

Death, by Region, 2006

Region f

Northeast 236

Midwest 276

South 1,750

West 924

Total 3,186

Descriptive StatisticsExample: 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 1 BASE OF 100

Comparisons between distributions are simpler with percentagesExample: 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

Comparisons between distributions are simpler with percentagesExample: Distribution of violent crimes in 2 different

cities

OFFENSECITY A CITY B

f % 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 3,071 100.0

Descriptive StatisticsMisconceptions 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 StatisticsRatio – 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

1,750 / 276 = 6.34

Region f

Northeast 236

Midwest 276

South 1,750

West 924

Total 3,186

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 StatisticsRate – 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

Descriptive StatisticsFrequency 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:RESPONDENTS SEX

622 44.8 44.8 44.8

765 55.2 55.2 100.0

1387 100.0 100.0

MALE

FEMALE

Total

ValidFrequency Percent Valid Percent

CumulativePercent

SATISFACTION WITH FINANCIAL SITUATION

421 30.4 30.4 30.4

617 44.5 44.6 75.0

346 24.9 25.0 100.0

1384 99.8 100.0

1 .1

2 .1

3 .2

1387 100.0

SATISFIED

MORE OR LESS

NOT AT ALL SAT

Total

Valid

DK

NA

Total

Missing

Total

Frequency Percent Valid PercentCumulative

Percent

NOMINAL-LEVEL

ORDINAL-LEVEL

• Valid Percent – percent if you exclude missing values• Cumulative Percent – how many cases fall below a given value?

Descriptive StatisticsExample: Homogeneity of attributes – how much detail

is too much?

TOO MUCH? (too many categories?)

SPECIFIC SENTENCE CATEGORY

36 1.0 1.0 1.0

469 12.8 12.8 13.8

379 10.3 10.3 24.1

445 12.1 12.1 36.2

1007 27.4 27.4 63.6

1123 30.6 30.6 94.2

213 5.8 5.8 100.0

3672 100.0 100.0

Fine Only

Probation Only

Probation Plus

Jail Only

Jail - Probation

Prison Only

Prison - Probation

Total

ValidFrequency Percent Valid Percent

CumulativePercent

Descriptive StatisticsToo little?

INCARCERATION SENTENCE

2788 75.9 75.9 75.9

884 24.1 24.1 100.0

3672 100.0 100.0

Incarcerated

Not Incarcerated

Total

ValidFrequency Percent Valid Percent

CumulativePercent

Descriptive StatisticsJust right:

Most Severe Sentence Category

1336 36.4 36.4 36.4

452 39.5 39.5 75.9

884 24.1 24.1 100.0

3672 100.0 100.0

Prison

Jail

Non-custodial

Total

ValidFrequency Percent Valid Percent

CumulativePercent

Homework #1 (Group Assignment)Groups of 2 to 3Due next Tuesday (2/03)Assignment has an SPSS componentAlso 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 asks1. 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.