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Correlation & Quasi-Experimental Designs
Correlation.
Ex Post Facto.
Pre-test/Post-test.
Non-Equivalent Control Groups.
Prediction via Regression.
Quasi-Experimental Designs.
Longitudinal vs. Cross -Sectional.
Advanced Topics.
Correlation Basics.
Lab: Racism Scale; IAT; Organize & Analyze TV data.
Why use correlational methods?
Correlation Basics
1. Reveal relationships, enable prediction (regression),
suggest causal relations.
Correlational methods are used to (a) establish relations among variables, (b) predict one variable from one or more other variables, and (c) to suggest possible causal relations among variables.
2. Inability to use experimental methods.
Correlation Is Not Causation.
Correlation Does Not Imply Causation.
3. Explore relations among variables before
experiments are conducted.
Correlations are used to examine many types of
relations including, for example, that between ...
Correlation Basics
- TV Violence & Aggression; TV Sex & Promiscuity.
- Smoking & Disease (Lung Cancer, Heart Disease, etc.).
Correlations Coefficients ( r ) vary from -1.0 to +1.0.
- The sign indicates the direction of the correlation.
- The # indicates the strength of the correlation.
- The stronger the correlation the better it predicts, irrespective of its sign (positive or negative). [r = -.75 is stronger than +.50].
- Personality & Academic (or Career) Success.
Correlations between two variables are known as
"simple" or "zero-order" correlations and are shown
graphically in scatterplots.
Positive Correlation (aka. direct relation )
r =.
X Y
X Y
Or
Negative Correlation (aka. inverse relation)
r = -.
X Y
X Y
Or
r =.
No Correlation
Restriction of Range
r =.
r =.
The Coefficient of Determination is simply the
correlation squared ( r^2 = r * r ).
The Coefficient of Determination ( r^2 ) The Coefficient of Determination is an estimate of the amount of variability in scores of a variable that is accoun ted for (explained by) the variability in scores of another variable.
The additive inverse of r^2 [i.e., 1 - r^2 ] is called the
Coefficient of Nondetermination and provides an
estimate of how much variability in one variable is
not explained by variability in the other variable.
r r^2 1 - r^2
Correlation Does Not Imply Causation
Why Correlation Does Not Imply Causation
Directionality of Relation.
- Correlations are insensitive to what causes what. Thus, although it might be the case that X causes Y [X Y] the correlation would be exactly the same if Y caused X [X Y].
Bi-Directionality.
- Many relations are bi-directional, meaning that although X causes Y, Y also causes X [X Y].
Third Variables.
- Many observed relations are caused by variables that are not even being considered in the correlation that is computed. Thus, although we may observe a correlation between X & Y, their relation might be caused by a third variable (Z) of which we are unaware.
Prediction via Regression
Correlation allows us to determine if relations exist between variables. Regression allows us to estimate (predict) the values of a variable based on the values of other variables.
Bivariate Linear Regression: Estimating the values of
one variable (Y) from the values of another (X) based on
the least squares regression line (aka. line of best fit ).
The regression line is the best-fitting line through all of
the data points; the line that minimizes the (sum of
squared) distances between each point and the line,
measured on the y axis.
The equation for the regression line is Y' = bX + a where
Y' is the predicted score (aka criterion variable ), b is the
slope of the regression line, X is the value of the X
variable, and a is the y-intercept where X=0.
Prediction via Regression Predicting how many MySpace Friends someone has from how Extroverted they are.
15 33 40
14 82 97
13 64 54
12 90 88
11 11 28
10 74 88
9 66 62
8 13 17
7 43 21
6 56 84
5 79 74
4 34 70
3 25 66
2 14 21
1 23 55
Subject Extroversion (X) MySpace Friends (Y)
Partial Correlation
If Z is causing the causing the correlation between X & Y then the partial correlation between X & Y will decrease when the effect of Z is removed ("controlled", "partialed out", or "held constant").
Allows you to examine the correlation between two variables [X&Y ] after removing the influence of a third variable [Z].
If Z is not causing the correlation between X & Y then the partial correlation between X & Y will show little or no change (from the simple correlation) when Z is partialed out.
Example: You correlate Reading Speed & Reading Comprehension and find r = .55. However, you suspect that IQ is driving this relation.
To investigate, you correlate IQ & Reading Speed ( r = .70) and IQ & Reading Comp. ( r = .72). The results suggest that IQ may be a third var.
You then conduct a partial correlation which takes all three correlations into account; the resulting partial correlation ( r = .10) tells you how Read Speed & Reading Comprehension are related when IQ is partialed out.
What do you conclude?
Multiple Regression
Multiple Regression: Estimating the values of one variable (Y) from the value of two or more other variables (X1, X2, etc.).
Bivariate (two-variable) Linear (straight- line) Regression allows us to predict the value of one variable from the value of one other value when those two share a linear relation. What if the variable we're trying to predict is related to more than one other variable? Can we use these other variables in our prediction?
The equation for multiple regression is:
where Y' is the predicted score (criterion var.), b 1 , b 2 , etc. are the regression weights, X 1 , X 2 , etc. are the values of the predictors, and a is the y-intercept where all X's = 0.
Y' = b 1 X 1 + b 2 X 2 + b 3 X 3 + bn Xn + a
For the above equation, the "b" values (regression weights) woul d be "raw" (in the original units of measurement). In most multip le regressions, these raw values are standardized, thereby producin g "Beta weights" ( ß 1 , ß 2 , etc.).
Multiple Regression yields R (like r ) and R^2 (like r^2 ).
Advanced Topics in Correlational Methods
Simple correlations (a) are based on only two variables, (b) ass ume linearity, and (c) cannot establish causation. What if multiple variables are correlated with each other? or relations are non-linear? And can we ever use correlation to at least suggest causal relations?
Multiple Regression : Estimating the values of one variable (Y) from the value of two or more other variables (X1, X2, etc.).
Nonlinear Regression: Estimating the values of one variable (Y) on the basis of one or more other variables that have non-linear relations with the criterion variable (Y).
Partial Correlation: Removing the influence of a third variable [Z] so that the relation between two variables [X & Y] can be examined.
Causal Modeling: Correlational techniques that allow one to make inferences about possible causal relations between variables. These techniques include (a) Cross- Lagged Panel designs, (b) Path Analysis, and (c) Structural Equation Modeling.
Factor Analysis : Extracting "factors" (constructs) from a number measures by examining all possible bivariate correlations.
Factor Analysis
Often done when one has many measures and wants to perform a "data reduction"-- reducing the # of measures to a few key factors.
Allows you to identify the factors (constructs) underlying a lar ge number of measures (such as traits, behaviors, survey rsps, etc.).
Imagine you conduct a survey in which a person says they like to (a) go to parties, (b) meet new people, and (c) talk on the phone; but do not like to (d) be alone or (e) play solitary sports. Do these separate response reflect separate psychological factors? Or do they reflect the same underlying factor?
Factors are first identified by computing bivariate correlations among all measures; when a group of variables are inter- correlated at a sufficiently high level, they are identified as a factor.
Once factors are identified, factors loadings are computed which consist of correlations between each measure and each factor.
The different factors that emerge in a Factor Analysis do not come labeled; that is the job of the researcher, based on his/her theory.
Factor Analysis
Example: Imagine you are asked to assess the intellectual abilities of a group of school children. To do so, you administer the kids a bunch of different tests that appear to measure different abilities.
Your tests include measures of vocabulary (VOCAB), reading comprehension (COMP), comprehension of analogies (ANA), geometry (GEO), puzzle completion (PUZ), & figure rotation (ROT).
One approach: Construct a correlation matrix--a table of all of the bivariate correlations among your different measures:
ROT -0.08 -0.02 0.09 0.49 0.68 1.
PUZ 0.02 0.01 -0.08 0.78 1.
GEO -0.09 0.04 -0.07 1.
ANA 0.65 0.55 1.
COMP 0.76 1.
VOCAB 1.
VOCAB COMP ANA GEO PUZ ROT
How do you go about analyzing all the data you've collected?
Factor Analysis
Example: Imagine you are asked to assess the intellectual abilities of a group of school children. To do so, you administer the kids a bunch of different tests that appear to measure different abilities.
Your tests include measures of vocabulary (VOCAB), reading comprehension (COMP), comprehension of analogies (ANA), geometry (GEO), puzzle completion (PUZ), & figure rotation (ROT).
How do you go about analyzing all the data you've collected?
One approach: Construct a correlation matrix--a table of all of the bivariate correlations among your different measures:
Factor Analysis finds corr. groupings like this to "extract" factors.
ROT -0.08 -0.02 0.09 0.49 0.68 1.
PUZ 0.02 0.01 -0.08 0.78 1.
GEO -0.09 0.04 -0.07 1.
ANA 0.65 0.55 1.
COMP 0.76 1.
VOCAB 1.
VOCAB COMP ANA GEO PUZ ROT
Partial Correlation
Original (direct) correlation:.
Partial correlations between Preference for TV Violence in Grade 3 (TVV3) and Aggression in Grade 13 (AGG13) in Eron et al. (1972).
Correlation after partialing out: 3rd grade variables
- Child's IQ:.
- Father's aggressiveness:.
- Mother's aggressiveness:. 13th grade variables
- Father's Occupation Status:.
- Subject's Aspirations:.
- Hours of TV watched:.
Causal Modeling: Path Analysis
Path Analysis applies multiple regression techniques to the question of causal relations. It is a highly theory-driven technique primarily used to test competing ideas about how variables are causally related. The heart of Path Analysis is creating causal models: That is, relevant variables and the paths (causal relations) between them. Example: Why does long -term memory (LTM) decline with age?
Age LTM
Age Speed^ LTM
Age WM^ LTM
Causal Modeling: Path Analysis
Example: Why does memory decline with age?
Age
Speed
Memory
WM
Age
Speed
Memory
WM
Causal Modeling: Path Analysis
Structural Equation Model from Park et al. (2002) showing how age deficits on Verbal and Visual- Spatial memory tasks are mediated by Speed of processing and Working Memory (WM).
SEM/Neural -Network model used to examine changes in patterns of connectivity as a function of real vs. placebo nicotine patches.
Correlation & Quasi-Experimental Designs
Correlation.
Prediction via Regression.
Quasi-Experimental Designs.
Advanced Topics.
Correlation Basics.
Ex Post Facto.
Pre-test/Post-test.
Non-Equivalent Control Groups.
Longitudinal vs. Cross -Sectional.
Lab: Racism Scale; IAT; Organize & Analyze TV data.
Why use Quasi-Experimental Designs?
Overview of Quasi-Experimental Designs
Inability to randomly assign participants to
conditions, manipulate antecedent conditions,
or control extraneous factors.
Quasi-Experimental Designs are similar to experiments but lack one of the key experimental techniques that allow a research to confidently determine cause-and- effect.
The most important experimental techniques that allow one to determine cause-and -effect are (1) Random Assignment of Participants to Treatments, Conditions or Groups; (2) Manipulation of Antecedent Conditions; and (3) Control of Extraneous Factors.
Quasi-Experimental Design allow more control over antecedent conditions and extraneous factors than Non -Experimental Designs but less control than that afforded by True Experiments.
Pre-test/Post-test Designs Let's add a Pretest, thus making our study a One-Group/Pretest -Posttest Design:
What can we conclude?
This is better than the previous design but it is still low in internal validity because numerous things could have produced the change in score:
Participants Relaxation Training
Desire to Smoke
DV (Posttest)
6 on a scale of 1 to 10.
Desire to Smoke
DV (Pretest) IV
8 on a scale of 1 to 10.
History: Any (external) event that occurs between the Pre- & Post-tests. Maturation: Any physical or psych change that occurs betw. Pre- & Post-. Testing: A change in performance due to practice or pre-test sensitization. Regression toward the mean: Movement away from an extreme value.
Pre-test/Post-test Designs
Let's remove the Pretest but add a Nonequivalent Control Group: A Nonequivalent Control Group/Post-test-Only Design:
What can we conclude?
Volunteer ("I want to quit") Participants
Relaxation Training
Desire to Smoke
DV (Posttest)
6 on a scale of 1 to 10.
IV
Volunteer ("I want $") Participants
No Relaxation Training
Desire to Smoke
8 on a scale of 1 to 10.
This is a bit better than the previous design but it is still lo w in internal validity because of Selection Differences & Demand Characteristics. Selection Differences – placing subjects into groups in a non-random fashion that fails to distribute subject differences across conditions. Demand Characteristics – any aspects of the research situation that elicits particular behaviors, esp. those that the P thinks the E expects.
Nonequivalent Groups Designs Similar to an Ex Post Facto Design except that the groups are formed by a "treatment" that naturally occurs; one group may be designa ted as a "control group" that is matched to the treatment group but is otherwise "nonequivalent" (and not randomly assigned).
"Expt'al" Participants in Company A
New Benefits Package
Productivity
DV (Posttest)
25 units per work hour
IV
"Control" Participants in Company B
No Change in Benefits
Productivity 18 units per work hour
Any Problems?
Pre-test/Post-test Designs Let's include both a Pre -test & a Control Group, thus making our study a Two-Group/Pretest-Posttest Design:
Conclusions? This is the best pre -/post-test design yet, although the nonequivalent groups still lowers its internal validity. ( Why??? )
Relaxation Training
Desire to Smoke
DV (Posttest)
Desire to Smoke
DV (Pretest) IV Volunteer ("I want to quit") Participants 8 on a scale of 1 to 10.
6 on a scale of 1 to 10.
Volunteer ("I want $") Participants
No Relaxation Training
Desire to Smoke
Desire to Smoke
6 on a scale of 1 to 10.
6 on a scale of 1 to 10.
How could we make this pre-test/post-test design even better???
All methods can be described along 2 dimensions.
Degree of Manipulation of Antecedents (Control)
D egre e of Imposition of Units(Constraints on Responding)
Low Medium High
Low
Medium
High
True Experiments
Non-Experimental Research
Constraining Antecedents & Responses
Correlational Techniques & Quasi-Experimental Designs
Lab Activities for Tuesday, Oct. 2nd
- Do the online Race (Black-White) Implicit Association Test (IAT) and the associated survey. Instructions for finding & completin g this are on "Assignment 8" which will be handed out in class and posted on the course webpage. FOLLOW THE INSTUCTIONS! And make sure to RECORD YOUR IAT RESULT ON THE FORM PROVIDED (Last Question) BEFORE CLOSING YOUR BROWSER.
- Fill out the class-designed Racism Scale. Make sure to write your class code (or last 4 digits of Student #) on the form. And please answer honestly!
Remember that your final report is due Oct. 16 and will be graded based on format, content (org., analysis, & interp.), & effort.
- TV-Sex data organization & analysis. You are the researcher! How are you going to organize & analyze this data??? The decisions you make now will affect how you think about and write up your observational project report.
