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Social Statistics Exam #1
Key terms and concepts
44
Sociology
Undergraduate 3
09/23/2012
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Term
Empirical Research
 Definition
  • Research that derives its data from direct observation or experiment
  • To answer sociological research questions we cannot rely on reasoning, speculation, moral judgment, or subjective preference.
  • EX: "What is the prevalence of binge drinking on college campuses?
Term
Non-empirical question
 Definition
  • Requires judgment
  • ex: "is binge drinking the most serious problem facing college campuses today?"
Term
What is theory?
 Definition
  •  theory- an explanation of the relationship between two or more observable attributes of individuals or groups
Term
Role of theory
 Definition
  •  used by social scientists to establish a link between what we observe(the data) and our understanding of why certain phenomena are related to each other in a particular way.
Term
Hypotheses
 Definition
  •  tentative answers to research questions (subject to empirical verification) that are derived from theories
  • a statement of relationship betwen characteristics that vary (variables)
Term
Population
 Definition
  •  Population- the total set of individuals, objects, groups, or events in which the researcher is interested.
Term
Sample
 Definition
  •  Sample- a relatively small subset selected from a population
  • We use samples to draw inferences about populations
Term
Variables (definition)
 Definition
  •  Variables- a property of people or objects that takes on two or more values that indicates a concept in the real world.
Term
Dependent Variable
 Definition
  •  Dependent variable- The variable to be explained (the "effect")
  • The dependent variable is what you are trying to explain
Term
Independent Variable
 Definition
  •  Independent variable- the variable expected to account for (the "cause" of) the dependent variable.
  • Usually occurs earlier in time than the dependent variable.
  • The independent variable influences, directly or indirectly, the dependent variable.
  • The value of the dependent variable depends on the value of the independent variable
Term
Nominal level of measurement
 Definition
  •  numbers or other symbols are assigned toa  set of categories for the purpose of naming, labeling, or classifiying the observations
  •  Examples:
    • Political party (democrat, republican)
    • Religion (Catholic, Jewish, Muslim, Protestant)
    • Race (African Americann, Latino, Native American)
Term
Ordinal level of measurement
 Definition
  •  Nominal variables that can be ranked from low to high (IN AN ORDER)
  • Example: College Class
    • Freshman
    • Sophomore
    • Junior
    • Senior
Term
Interval-ratio level of measurement
 Definition
  •  Variables where measurements for all cases are expressed in the same units. Will also be a "pretty exact/specific" number. (Variables with a natural zero point, such as height and weight, are called ratio variables)
  • Examples:
    • Age
    • Income
    • SAT scores
Term
Ratio Variables
 Definition
  • Ratio variables- Variables with a natural zero point, such as height and weight
Term
Discrete variables
 Definition
  •  variables that have a minimum-sized unit of measurement, which cannot be sub-divided
  • EX: the number of children per family
Term
Continuous variables
 Definition
  •  variables that, in theory, can take on all possible numerical values in a given interval
  • EX: length
Term
Descriptive statistics
 Definition
  •  Procedures that help us organize and describe data collected from either a sample or a population.
  • What is there
  • EX: average age, proportion of males and females in population
Term
Inferential statistics
 Definition
  • the logic and procedures concerned with making predictions or inferences about a population from observations and analyses of a sample.
  • saying something about the sample then saying how it reflects an entire population
  • EX: average exam grade from 10 randomly drawn students in the class
Term

Frequency distribution

(definition and how to create them)

 Definition
  •  frequency distribution- A table reporting the number of observations falling into each category of the variable
  • how to create:
    • 1- tally results
    • 2- count frequencies
Term
Proportion (p)
 Definition
  • a relative frequency obtained by dividing the frequency in each category by the total number of cases
  • P=f/N    (expressed in 0.___ form)
  • Proportions and percentages are relative frequencies.
Term
Percentage (%)
 Definition
  •  a relative frequency obtained by dividing the frequency in each category by the total number of cases (proportion) and multiplying by 100.
  • (%) = p x 100
  • Proportions and percentages are relative frequencies.
Term
Percentage Distributions
 Definition
  •  A table showing the percentage of observations falling into each category of the variable.
Term
Cumulative Frequency Distribution
 Definition
  •  A distribution showing the frequency at or below each category (class interval or score) of the variable
Term
Cumulative Percentage Distribution
 Definition
  •  A distribution showing the percentage at or below each category (class interval or score) of the variable.
Term
Rates
 Definition
  • A number obtained by dividing the number of actual occurrences in a given time period by the number of possible occurrences.
  • EX: Number of people in U.S. prisons and jails
    • incarceration rate= #incarcerated
    •                            Population size
  • *Be sure to look at day 3 notes at the last 2 slides*
Term
Pie Chart
 Definition
  • A graph showing the differences in frequencies or percentages among categories of a nominal or an ordinal variable. The categories are displayed as segments of a circle whose pieces add up to 100 percent of the total frequencies.
  • *When there are too many categories, the smaller categories can be reduced into a sort of "miscellaneous" category
Term
Bar Graph
 Definition
  • A graph showing the differences in frequencies or percentages among categories of a nominal or an ordinal variable. The categories are displayed as rectangles of equal width with their height proportional to the frequency or percentage of the category.
  • Ex: could be one bar column for "married people" or can display more by having a "married males" and "married females" columns right next to each  other
Term

Statistical Map (def) 

&

Geographical Variations in Variables(def)

 Definition
  •  Statistical map- displays dramatic geographical changes in a society
  • Geographical Variations in Variables- like population distribution, voting patterns, crimes rates, or labor force participation.
Term
Histogram
 Definition
  • a graph showing the differences in frequencies or percentages among categories of an interval-ratio variable. The categories are displayed as contiguous bars, with width proportional to the width of the category and height proportional to the frequency or percentage of that category. 
Term
Frequency Polygon
 Definition
  •  A graph showing the differences in frequencies or percentages among categories of an interval-ratio variable. Points representing the frequencies of each category are placed above the midpoint of the category and are jointed by a straight line.
Term
Time Series Chart
 Definition
  • A graph displaying changes in a variable at different points in time. It shows time (measured in units such as years or months) on the horizontal axis and the frequencies (percentages or rates) of another variable on the vertical axis.
Term
Measure of Central Tendency
 Definition
  • Numbers that describe what is average or typical of the distribution
  • You can think of this value as where the middle of a distribution lies.
Term
Mode
 Definition
  •  The category or score with the largest frequency (or percentage) in the distrubtion
  • The mode can be calculated for variables with levels of measurement that are: nominal, ordinal, or interval-ratio
Term
Median
 Definition
  • The score that divides the distribution into two equal parts, so that half the cases are above it and half below it.
  • The median is the middle score, or average of middle scores in a distribution
  • Can be calculated for ordinal or interval level variables
  • Middle case= (N+1)/2
Term
Mean
 Definition
  • The arithmetic average obtained by adding up all the scores and dividing by the total number of scores.
  • Formula: Y bar= (sigma Y)/N
  • Formula to calculate mean w/grouped scores:
  • Y bar= (sigma (f)(Y))/N     Where (f)(y)= a score multiplied by its frequency
Term

The measures that can be used with

nominal, ordinal, and interval-ratio variables

 Definition
  •  Nominal variable- the mode is the only measure that can be used.
  • Ordinal variables- the mode and the median may be used. The median provides more information (taking into account the ranking of categories)
  • Interval-ratio variables- the mode, median, and mean may all be calculated. The mean provides the most information about the distribution, but the median is preferred if the distribution is skewed.
Term
Shapes of distributions
 Definition
  • Symmetrical- mean is about equal to median
  • Skewed-a few extreme values on one side of the distribution shift the distribution
    • Negatively- mean ex:children per household
    • Positively- mean>median ex: income
  • Bimodal- two distinct modes
  • Multi-modal- more than 2 distinct modes

*Refer to last slide on day 5 notes to view visual graphs
Term
Measures of Variability
 Definition
  • Numbers that describe diversity or variability in the distribution
  • Measures of variation reveal how far from the typical or central score that the distribution tends to vary
Term

Index of Qualitative Variation

(IQV)

 Definition
  • A measure of variability for nominal variables. It is based on the ratio of the total number of differences in the distribution to the maximum number of possible differences within the same distribution.
  • IQV ranges 0-1. 0=no diversity.1=maximum diversity (evenlydistributed)
  • IQV=K(1002 -Σf2)/1002(K-1)
  • K=# of categories
  • N =total # of cases in the distribution
  • Σf2=the sum of all the squared frequencies or percentages
Term
Range
 Definition
  • A measure of variation in interval-ratio variables. It's the difference between the highest (max) and the lowest (min) scores in the distrib.
Term
Inter-Quartile Range (IQR)
 Definition
  • A measure of variation for interval-ratio data. It indicates the width of the middle 50 percent of the distribution and is defined as the difference between the lower and upper quartiles. Order scores high to low.(Q1 and Q3)
  • IQR= Q3-Q1
  • Q3=75th percentile
  • Q1=25th percentile
Term
Box Plot
 Definition
  • Graphic device that visually presents the following elements: the range, the IQR, the median, the quartiles, the minimum (lowest value) and the maximum (highest value)
Term
Variance (def) and Standard Deviation (def)
 Definition
  • Variance- measure of variation for interval-ratio variables; the average of the squared deviations from the mean.(S2Y equation)
  • Standard Deviation- the square root of the variance.
Term

Measures of variables that can

use IQV or IQR

 Definition
  • Nominal variables- can only use IQV
  • Ordinal variables- can calculate the IQV or the IQR
  • Interval-ratio variables- can use IQV, IQR, or variance/standard deviation. Standard deviation provides most info, since it uses all the values in the distrib in its calc.
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