DESCRIPTIVE STATISTICS
January 12, 2006
SOCI 2003B
FREQUENCY DISTRIBUTIONS & GRAPHICAL PRESENTATIONS
Reading: Thorne & Giesen: Chapters 3 & 4 (pp. 22-62)
1. Weekly questions #1
Class midterm evaluation – the collection and presentation of quantitative data
Quick review of Sirkin reading…
2. Statistical symbolism
3. Organizing and presenting data
- Organizing raw data
- Presenting raw data in tables (frequency distributions & graphs)
TABLES
1. Types of frequency distributions (tables):
- Univariate and bivariate
2. Forms of frequency distribution
LEVELS OF MEASUREMENT
- Simple frequency distribution for each level of measurement
SIMPLE FREQUENCY DISTRIBUTION
- Absolute f
- Relative f
- Cumulative f
- Relative cumulative f
GRAPHS
1. Graphing univariate frequency distribution
- Common graphs: Pie chart, bar chart, line chart, ogive
2. Graphing bivariate frequency distribution
- Scattergraph
4. Weekly Questions
REVIEW
STATISTICS
The study of how we describe and make inferences from data (Sirkin 27)
DESCRIPTIVE STATISTICS
Summarizing information in such a manner as to make it more usable (Blalock 1972)
INFERENTIAL STATISTICS
Making generalizations about a population based on a subset (Blalock 1972)
EMPIRICAL VS. NORMATIVE
- Empirical – based in observation, fact, based on questions about what is
- Normative – based in values, value judgement, based on questions of what ought to be
Empirical facts tell us how close we are to the normative ideal or how far we still must
go to achieve this ideal (Sirkin 3)
EMPIRICAL ANALYSIS:
How we establish facts, how we determine what is, what actually does exist (Sirkin 3).
READING/ASSIGNMENTS (SIRKIN)
- A lot about hypotheses --- (WHERE YOU ARE AT WITH YOUR PROJECTS…)
HYPOTHESIS:
The hypothesis names the two variables that appear to be related and indicates the nature
of that relationship (Sirkin 9)
An expectation about the nature of things derived from a theory. It is a statement of
something that ought to be observed in the real world if the theory is correct. Derived
from propositions, it is a specified, testable expectation about empirical reality (Babbie
and Benaquisto 493)
* Remember --- “…by the rules of formal logic, we never in sampling actually prove
anything. Instead, we demonstrate that all other possible alternatives are unlikely to be
true. Thus leaving us with only one remaining possibility --- the thing that we are
proving” (Sirkin 11).
EXAMPLE FROM: Dell, C.A (2001). Correctional Service of Canada Ideology and
“Violent” Aboriginal Female Offenders. Dissertation: Carleton University.
The research hypotheses are based on the application of the unified systems variant of
socialist feminist theory to the reviewed literature on:
- theoretical and empirical explanations of the “violent” female offender;
- the oppression of Aboriginal peoples, specifically women, in Canada and the criminal
justice system;
- and the ideology characterizing the history of the Canadian correctional system, with
specific attention allotted to CSC and the “violent” Aboriginal female offender.
Applying a socialist feminist understanding to the literature generated the research focus
on CSC ideological control (CSC policy and views) and CSC material control (CSC
practice). The hypotheses mirror the research questions/concerns posed in Chapter One
(Introduction). Once again, the methodological focus of this research is not confined to
the outlined hypotheses. Rather, the process of developing the hypotheses served to
initiate the research direction.
The aim of this research is to focus on the Canadian penitentiary system and CSC’s
construction and treatment of the “violent” Aboriginal female offender.
POLICY
#1 CSC ideology supports the identification of “violent” female offenders as
“unnatural/evil”.
#2 CSC ideology supports the greater identification of “violent” Aboriginal female
offenders, in comparison to “violent” non-Aboriginal female offenders, as
“unnatural/evil”.
#3 CSC ideology is a manifestation of control of “violent” female offenders.
#4 CSC ideology is a manifestation of greater control of “violent” Aboriginal female
offenders, in comparison to “violent” non-Aboriginal female offenders.
PRACTICE
#5 CSC practice reveals harsh treatment of “violent” female offenders.
#6 CSC practice reveals harsher treatment of “violent” Aboriginal female
offenders, in comparison to “violent” non-Aboriginal female offenders.
#7 CSC practice is a manifestation of control of “violent” female offenders.
#8 CSC practice is a manifestation of greater control of “violent” Aboriginal female
offenders, in comparison to “violent” non-Aboriginal female offenders.
2. STATISTICAL SYMBOLISM
Use upper case letters at the end of the alphabet to name sets or groups of scores
N = total population
n = subset of the total population (sample)
F = frequency
“Headcounts or tallies indicating the number of cases in a particular category or the total
number of cases measured” (Sirkin 44)
3.
ORGANIZING AND PRESENTING DATA
A. Organizing raw data
To make sense of number must organize them into a format that is consistent and
understandable to yourself and others.
B. Presenting raw data in tables
TABLES
1. Types of frequency distribution:
Univariate Frequency Distribution
One variable – each subject contributes one observation
Bivariate Frequency Distribution
Two variables – each subject contributes two observations
2. Forms of frequency distribution:
A. LEVELS OF MEASUREMENT
The form of frequency distribution depends on the level of measurement (nominal,
ordinal, interval, ratio); number of values; purpose for presenting the data
When collecting your data, you are to do it AT THE HIGHEST LEVEL OF
MEASUREMENT POSSIBLE!
B. SIMPLE FREQUENCY DISTRIBUTION
- Absolute f: Number of times a score occurs within a distribution
- Relative f: Number of times a score occurs within a distribution, divided by the total
number of scores
- Cumulative f: when interested in determining relative standing at a glance
- Relative cumulative f: Useful for locating a particular score in a distribution
GRAPHS
Graphs are the most popular way to present statistical data
Aim is to “easily” and “succinctly” provide information to our audience
1. Graphing univariate frequency distribution
General rules:
1. Graphs are called figures
2. The figure number and label are below the graph
3. Frequency is on the ordinate axis (Y) and the values of the variable are on the abscissa
(X axis)
4. General ¾ rule – the ordinate should be ¾ as long as the abscissa
2. Graphing bivariate frequency distribution
Scattergraph:
- for bivariate frequency distributions
- see if the variables are related or correlated at a glance
WEEKLY QUESTIONS
THORNE AND GIESEN
1.
Page 31, checking your progress
2.
Page 34, question 6
3.
Page 34, question 11
4.
Page 58, question 2