Introduction to Quantitative
Methods
10/23/13 Pearson
Bivariate
Correlation
Follow up from Last lectures
Compare
notation in Chapter 6 to
Notation in Chapter 13
Notation from Chapter 6
Individual
score = Grand Mean + Effect +
Residual
Yij = + i + ij
Tot
Basic Statistics, Sampling Error,
and Confidence Intervals
Chapter 2
Review of Notation
Review of Basic Statistics:
Central Tendency
For categorical scores, we can use the mode
(most frequently occurring score) to indicate
what response is most typical.
F
Introduction to Quantitative
Methods
Preliminary Data Analysis
David Cicero, PhD
Problems in Real Data
Errors
Inconsistencies
in responses or
measurements
Outliers
Missing Values
Thorough
screening of the data is
necessary to deal with problems
Ident
Introduction to Quantitative
Methods
One-Way Between-Subjects
Analysis of Variance
Situations to Use a One-Way
Anova
When
the researcher wants to compare
means on a quantitative variable across
two or more groups
Group
membership is determined by
scores
Chapter 9: Bivariate
Regression
Bivariate Regression
Regression Notation
Regression Notation
Predictor
or independent variable: X
X may be quantitative or dichotomous
Outcome
or dependent variable: Y
Y must be quantitative
Two versions of the predicti
Introduction to Quantitative
Methods
David Cicero, PhD
Factorial ANOVA
Research Situations and
Research Questions
Factorial ANOVA is
used in research
situations where two or more group
membership variables are used to predict
scores on one quantitative o
General Review
Chapter 6
Mean:
Std Dev.:
Variance:
Yij = score for person j in group i
MY = Grand Mean
Mi = Yi = mean for group i
M
s/SD
s2
2
z = (X-M)/s or (X-)/
z = (M-)/M
DevGroup = ij (error) = (Yij - Yi) or (Yij - Mi)
Effect = i = (Yi - MY) or (Mi -
Chapter 7
Chapter 8
Pearsons r: X and Y should be quantitative and normally
distributed. Only identifies linear relationship. Should have
homoschedasticity.( for dichotomous variables)
r = (ZX * ZY) / (N)
Zx = (X-Mx) / sx
Zy = (X-MY) / sY
zy = r x zx or z
Moderation: Tests for Interaction
in Multiple Regression
Introduction to
Quantitative Methods
1
Path model for a regression in which X2
moderates the influence of X1 on Y
(X1 and X2 interact as predictors of Y)
2
Figure 15.1 Alternate model to
represent i
Mediation
Introduction to
Quantitative Methods
1
Path diagrams or causal models:
Researchers can represent their hypotheses
about relations among variables using path
diagrams.
If X causes Y (and assuming the X, Y relation is
linear), then X should be cor
Adding a Third
Variable: Preliminary
Exploratory Analysis
Why consider a third variable?
Why consider a third
variable?
Does
the nature or strength of the
predictive association between X1 and Y
change when we take another variable,
X2, into account?
Wh
Introduction to Quantitative
Methods
Dummy Predictor
Variables in Multiple
Regression
As discussed in Chapter 8:
Dummy Coding
A dummy
or dichotomous variable
may be used as a predictor in a
regression equation
For
example, Gender (D) can be a
predictor
Multiple Regression with More
Than Two Predictors
Chapter 14
Multiple quantitative predictor
variables and one quantitative
outcome variable
Raw score equation:
Y = b0 + b1X1 + b2X2 + + bkXk
Standard
score/z score equation:
zY = b1zX1 + b2zX2 + + bkzXk
U