Quantitative apps (ch.2)

variable

A property or characteristic of the sample or population that takes on more than one value.

constant

A property or characteristic of the sample or population that takes on one and only one value.

proportion

A relative frequency - it's the frequency of some value relative to the total number of events. P = fi /N where fi = number of cases at value, N = total number of cases Proportions are bound by 0.0 and 1.0 Proportion can also be understood as a probability.

percent

A standardized proportion - it's what the frequency would be if N = 100. Percentages are bound by 0.0 and 100.0

If I was interested in knowing if older boys were more likely to be delinquent than younger boys, what would be my independent variable and what would be my dependent variable?

Age is the independent variable and delinquency is the dependent variable.

Calculate the rate of hate crimes for the following cities: # of Hate Crimes Population Rate per 100,000 Boston, MA 234 6,453,442 Columbus, OH 112 1,132,475 Montgomery, AL 100 425,185 Los Angeles, CA 198 8,453,809 Chicago, IL 202 9,535,000 New York, NY 255 10,435,333 In which city are you most likely to become the victim of a hate crime? In which city are you least likely to become the victim of a hate crime?

Boston 3.63 Columbus 9.89 Montgomery 23.52 L.A. 2.34 Chicago 2.12 NY 2.44 Montgomery, AL is the most likely and Chicago is the least likely for becoming the victim of a hate crime.

Implications of Levels of Measurement

Certain analytic (statistical) techniques have level of measurement requirements. Higher levels of measurement can be converted to lower ones, however; you cannot convert a lower level of measurement to a higher one. Therefore, seek the highest level of measurement possible

independent variables, dependent variables

DV - what we are measuring IV - treatment/stimulus/impact

If I was interested in knowing whether or not boys who had low IQ scores were more delinquent than boys with higher IQ scores, what would be my independent variable and what would be my dependent variable?

IQ is the independent variable and delinquency is the dependent variable.

percent change

Measures the percent change in some event from one time to another.

Levels of measurment

Nominal - offer names or labels for characteristics (race, gender, state of residence), categories that provide distinctions of kind Ordinal - attributes can be logically rank-ordered (education, opinions, occupational status) Interval - meaningful distance between attributes (temperature, IQ) Ratio - has a true zero point (age, # of priors, sentence length, income) We will use interval/ratio as the same level for the purpose of statistical tests.

The Role of Variables

Point Estimation: -We want to know or to estimate the value of a particular variable. Examining Relationships: - We want to know if one variable is related to/correlated or associated with another. Concern whether two variables are related to each other - X & Y. Two variables are said to be related or associated or correlated when variation in X is related to variation in Y. They change together: - THIS IS CALLED COVARIATION. Covariation tells us about association.

Here is a frequency distribution of the number of executions in several U.S. states in the past five years. State # of executions p % Alabama 6 Virginia 13 Texas 52 Maryland 1 Louisiana 8 Oklahoma 24 Total Calculate the total number of executions in these states, and fill in the column of proportions and percentages. a) What percent of the total number of executions were done in Texas? b) What proportion of the total number of executions were done in Virginia? c) How many executions were done in Oklahoma?

State # of exec. p % Alabama 6 .06 6% Virginia 13 .13 13% Texas 52 .50 50% Maryland 1 .01 1% Louisiana 8 .08 8% Oklahoma 24 .23 23% Total 104 a) 50% b) .13 c) 24

Units of Analysis

The unit or object we have gathered our data about & to which we apply our statistical methods. Whatever constitutes an observation in our data set: Individuals - (police, victims, defendants, inmates, gang members, burglars) Groups - multiple persons with same characteristics - (gangs, police beats, patrol districts, households, city blocks, cities, counties) Organizations - formal groups w/established leaders and rules - (prisons, police departments, courtrooms, drug treatment facilities, businesses, agencies) Social artifacts - products of social beings and their behavior (stories in newspapers, posts on the Internet, photographs of crime scenes, incident reports, police/citizen interactions) Important because we can only make generalizations about the units of analysis for which our data represent.

What is the level of measurement for the following variables: a. Age measured as the number of years old someone is. b. Age measured as: under 10 years old 10-29 years old 30-59 years old 60 years old or older c. Whether someone went to a public, private or parochial elementary school. d. Number of prior convictions measured as the actual number of convictions. e. Number of prior convictions measured as: None 1-2 convictions 3-4 convictions 5-6 convictions 7 or more convictions f. Number of months sentenced to prison in actual months. g. Type of weapon used in committing a murder: - gun, knife, club or other blunt instrument, hands, some other means.

a. ratio/interval b. ordinal c. nominal d. ratio/interval e. ordinal f. ratio/interval g. nominal

If I measured the age, IQ, and number of prior delinquent acts committed within a sample of 200 boys sent to juvenile court: a. Would age be a variable or a constant? b. Would IQ be a variable or a constant? c. Would sex (gender) be a variable or a constant?

a. variable b. variable c. constant

rate

frequency or count per some standard unit of measurement When do you want to calculate a rate? When the things you are counting can vary in their opportunity to take place. Rate can also be measured at the individual level- frequency or count per some standard unit of measurement Rate = {f/population} x standard unit