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Education 795 Class Notes
Quasi-Experimental DesignPath Analysis
Note set 9
Today’s Agenda
Announcements (ours and yours
Q/A
Quasi-experimental design
Path analysis as an approach to variance partitioning and causal modeling
Quasi-Experimental Design
Historical HappeningsStatistical analyses evolved to meet needs of experimental designsQuasi-experimental designs evolved in the social sciencesResearchers continue to used experimental analyses for quasi and non experimental designsStatistical analyses emerged to meet the challenges of quasi and non experimental designsResearchers adopt new and improved techniquesNew statistical analyses continue to emerge to meet the many challenges that quasi and non experimental designs face…
non-random assignmentno manipulation of treatment
Nomenclature
Quasi-experimental designs refer to studies where no random assignment is in place
We cannot separate the irrelevant causal forces hidden within the ceteris paribus of random assignment (Cook & Campbell, 1979).
Refer to quasi-experimental when there is a treatment in place but no random assignment and we are interested in ‘causal effects’.Refer to non-experimental when we want to explain differences among groups
The Term “Treatment”
Treatments can be: interventions
direct manipulation of a variable
naturally occurringabrupt and precisely dated
training programs
exposure to a condition
The Omitted Variables Conundrum
Y
X
Y e
X
Y e
AA B
When the error is correlated with the treatment (X) we cannot separate out the “treatment” effect from spurious effects
How Do We Deal With This Problem to Get at Causation?
Return to a regression-based approach, and introduce a special kind of regression called Path Analysis
Introduce Structural Equation Modeling
Review Regression Formula
Raw score depiction:
where each b:is the unique and independent contribution of that predictor to the modelfor quantitative IVs, the expected direction and amount of change in the DV for each unit change in the IV, holding all other IVs constantFor dichotomous IVs, the direction and amount of group mean difference on DV, holding all other IVs constant
Review Venn Diagram
CorrelationRegression Coefficients
Venn Diagrams
CorrelationPartial
Correlation
Relationships among 3 variables
B
S
A
B
S
A
B
S
A
B
S
A
A.
B.
C.
D.
Path Analysis
A structured approach to regression analysis allowing intervening variables
NomenclaturePath AnalysisLISREL ModelsCausal ModelsANCOVA ModelsLatent Variable ModelsStructural Equation Models
Causation
Most controversial topic in philosophy of science and has been characterized as ‘a notorious philosophical tar pit’ (Davis, 1985, p. 8)
The history of the topic extends over centuries
Random Selection of Quotes
‘Cause is the most valuable concept in the methodology of the applied sciences’ (Scriven, 1968, p. 79)
‘Let’s drop the word cause and bring educational research out of the middle ages’ (Travers, 1981, p. 32)
‘It would be very healthy if more researchers abandon thinking of and using terms such as cause and effect’ (Muthien, 1987, p. 180)
No causation without manipulation (Holland & Rubin, 1986)
Return to the Role of Theory
Causal analyses are based on theory.The temptation to apply sophisticated state-of-the-art methodologies seem irresistable
It is important to recognize when a given methodology is inapplicable
‘In sum, the formulation of a causal model is an arduous and long process entailing a great deal of critical thinking, creativity, insight and erudition’ (Pedhazur & Pedhzur, 1991, p. 699)
Definitions
Exogenous Variable– variable with arrows ONLY going out of it in the model (Strictly predictor)
Endogenous Variable—variable with arrows going IN—it can also have arrows going out (Outcome and possibly a mediated predictor)
Definitions
Direct Effect—the effect of a variable that has a direct path to the outcome.
Indirect Effect—the effect of a variable on an outcome that travels through (is mediated by) other variables in the model
Total Effect—Sum of the direct and indirect effects for one variable on the outcome
Definitions
X, Z predictors, Y, outcome
SpuriousnessThe relationship between X and Y is said to be spurious if Z causes X and Y
Unexplained covariationBoth X and Y are exogenous and so variation between them is not explained by the model
Example: Understanding the Effects of Frog Ponds
Theoretical discussion started by odd findings related to student achievement
Reference-group theory: Environmental press or relative deprivation?
Is it better to be a small frog in a big pond, or a big frog in a small pond?
Path Analysis Example
Bassis model
With respect to academic self-evaluation, is it better to be a small frog in a big pond, or a big frog in a small pond?
Bassis Model
Descriptive statistics
Bassis Results
Decomposition of r
Correlation between two endogenous variables:
r = Direct Effect + Indirect Effects + Spuriousness
Correlation between an endogenous variable and an exogenous variable:
r = Direct Effect + Indirect Effects + Unspecified Covariance
Calculating Path Coefficients
Compute the appropriate regression analyses, and organize the resulting coefficientsFirst, calculate the indirect components by multiplying the involved coefficientsSecond, sum the indirect components and add to the direct coefficient (if any) to calculate the total effect
Computing Exercise
Calculate the direct and indirect effects of:
a) Selectivity on 4-year academic self-ratingb) HS grades on college grades
Comparing Models
One interesting use of path analysis is to directly compare models
Higher education as a contextualized experience:
Are frog pond effects similar in majority / specialized institutions for students served by such specialized institutions?
African American Students inPWIs and HBCUs
PWIs
HBCUs
Women Students in Coed and Single-sex Institutions
Coed
Womens’colleges
For Next Week
Read Pedhazur Ch 7 p 152-157
Read Aldrich & Nelson, ALL