EDUC 5716: Basic
Statistical Methods
This
course covers the basic principles of statistical analysis.
Statistical tools can be used for two general purposes: (1)
summary
and description of data, and (2) testing of inferences to address
relational questions. The course should provide the skills
necessary
to use statistical tools for one’s own descriptive and
inferential
purposes.
As social science researchers, we not only
address our own research questions; we also must read and evaluate the
research of others. Thus, a second course theme is the
critical
scrutiny and evaluation of the research of others. To this
end, we
devote a significant portion of our time to consideration and critique
of examples of journal articles and other research products.
Course content is structured in a progressive manner. Data
analysis –
which is where many statistics courses begin – is meaningless
if your
data is junk (i.e. your study is not
“valid”). Thoughtful design of
research studies and measurement of variables is essential to
“valid”
research. Therefore, before we do anything truly
quantitative, we
discuss how to best design research studies and how to ensure good
measurement. With these basics down we progress to how to
summarize
data. We discuss a variety of tools to make sense of large
groups of
data – both via visual/graphical means and via summary
statistics.
This leads to the final topic – using statistical methods to
answer
inferential questions. Topics under this last
umbrella include
testing of group differences and relationships between variables,
techniques for analyzing data in categorical form, and summarizing and
presenting statistical results. Examples typical of
contemporary
social science research ground the introduction and application of new
ideas and methods.
This course aims to provide the experience and confidence to begin to
carry out the various steps of social science research – from
research
design to data collection, data analysis, and ultimately to
communicating your findings. As such, an
independent research project
(as well as an integrated data collection activity) requires students
to follow a single research question through these various steps.
The
research project is typically due the last day of class.
EDUC
8240: Quantitative Methods II (Intermediate Quantitative
Methods)
Quote describing findings from a national study of 2003 charter school performance:
In mathematics, fourth-grade charter school students as a whole did not perform as well as their public school counterparts [in 2003]. In reading, there was no measurable difference in performance between charter school students in the fourth grade and their public school counterparts as a whole. -NCES
Quote describing findings from a national study of 2003 charter school performance:
Charter schools are succeeding in their mission to provide an educational alternative more likely to lead to student proficiency, according to a study released today by Harvard economist Caroline Hoxby. Across the nation, charter school students are more likely to be proficient in math and reading than students in the nearest comparable regular public school. –Heritage Foundation
Do charter schools "work"? Whom should we believe?
Quantitative
methods are often employed to address problems in education,
psychology, and the social sciences. As demonstrated above,
however,
results from quantitative studies often confuse and obfuscate rather
than provide clarity. The field of statistics provides a
variety of
powerful analytic tools – as with any power tools, however,
expertise
and caution are necessary for responsible use.
A
general class of statistical methods – known collectively as
the
“General Linear Model” (“GLM”)
– provides the basis for analyzing data
from randomized experiments, quasi-experiments, surveys, and
correlational/observational studies. Two special cases of the
GLM –
multiple regression and ANalysis Of VAriance (or
“ANOVA”) – are common
to social science research and receive the bulk of our
attention. We
especially focus on how to incorporate regression and ANOVA into the
unified GLM framework. In doing so, this course covers the
GLM in
detail – from positing alternative hypotheses to specifying
and
comparing models based on these hypotheses, to assessing the fit of
various models, and finally to interpretation within the substantive
context of interest.
The object of this course is to provide the context and experience
necessary to build quantitative reasoning skills. Students
leaving
this course should be able to carry out quantitative methods
responsibly and read others’ quantitative research with
informed
skepticism.
Multivariate Statistics Sequence: EDUC 7396 (Multivariate Statistics) & EDUC 7456 (Advanced Multivariate Statistics)
Complex statistical techniques -- such as "factor analysis"; "latent variable" , "LISREL" or "structural equation" models; and "multilevel" or "hierarchical linear models" -- have gained much prominence as tools for analyzing complex social science systems. The two-course sequence EDUC 7396 and EDUC 7456 cover these and other multivariate statistical techniques currently de rigueur in quantitative social science research.
EDUC
7396: Multivariate Statistics
This
course covers the basic principles and applications of several
multivariate statistical techniques. Multivariate
methods generally
fall into one of two families: dependence
models (e.g.,
multiple and multivariate regression, multivariate analysis of
variance, analysis of covariance, path analysis, canonical analysis,
discriminant analysis, and logistic regression) and interdependence
models (e.g.,
principal
components, factor analysis, cluster analysis, multidimensional
scaling, and loglinear models).
The course starts with dependence models: we review the
general linear
model and show how most inferential techniques (simple and multivariate
regression, analysis of variance, etc.) actually represent special
cases of this more general model. From there we move onto
interdependence
models and discuss how these techniques help identify
interrelatedness among a large number of variables. We cover
the idea
of “latent” factors in the context of factor
analysis.
After establishing the basics of both dependence and interdependence
models, we move to an even more general class of models: structural
equation models. Characterized
by both dependence and interdependence elements, structural equation
models are increasingly central to research in many fields.
Finally, we introduce another statistical tool that is increasingly
employed in social science research – the mixed-effects
model.
Examples of mixed-effects
models include “multilevel” or
“hierarchical linear” models
(“HLM”) and individual growth curve models
Matrix
algebra is
the mathematical language of multivariate techniques. We
introduce the
fundamentals of matrix algebra toward the beginning of the course in
the context of understanding the general linear model
formulation.
From then on each new model is introduced using matrix algebra as well
as visual geometrical descriptions.
EDUC 7456: Advanced Multivariate Methods
EDUC 7456 picks up from the introduction provided in EDUC 7396 to examine more deeply both mixed-effects and structural equation models. In EDUC 7456 these models are discussed within the general context of longitudinal (growth) models, although extensions to other contexts are also made.
Social science researchers frequently face questions about individual growth and change over time. The unique aspects of longitudinal data require appropriate statistical models for analysis. The last 20 years has seen an explosion of methods developed specifically for analysis of longitudinal data; traditionally providing insight into only inter-individual differences (i.e., variability across individuals), longitudinal models now facilitate modeling change at the intra-individual level (i.e., change within each individual) as well. Such methodological advances provide promise for researchers whose longitudinal questions were previously limited by available quantitative methods.
The goal of EDUC 7456 is to provide students the foundations for modeling individual growth. Researchers use individual growth models to address questions of change over time. Two broad classes of contemporary statistical methods will be introduced as tools for longitudinal analysis: structural equation models (a.k.a. latent variable or LISREL models) and mixed-effects models (a.k.a. multilevel or hierarchical linear models).