Transcript Chapter 5: Descriptive Research

Chapter 7: Advanced Correlational
Strategies
Regression: Predict scores on one variable from
scores on another variable
• Use GRE scores to predict success in grad school
• Regression equation: predict one score on the
basis of another score.
• Goal is to find an equation for a regression line
that best fit the data.
Regression Line
• A regression line is a straight line that
summarizes the linear relationship between two
variables.
• The regression line minimizes the sum of the
squared deviations around the line.
• It describes how an outcome variable y changes
as a predictor variable x changes.
• A regression line is often used as a model to
predict the value of the response y for a given
value of the explanatory variable x.
• The regression equation is expressed by:
y = 0 +  1 x
• y is the variable you are predicting (dependent
variable, criterion variable, or outcome variable)
• x is the predictor variable that we are using to
predict y
0 is the regression constant (beta-zero), which is
the y intercept of the line that best fits the data
in the scatter plot
1 is the regression coefficient which is the slope
of the line that best represents the relationship
between x and y
Example: Correlation between outside temp and
how many students attend class.
The regression equation values are:
0 is 114.35 and 1 is -.61
• If it is supposed to be 82 degrees on Friday how
many students would you expect to attend class
that day?
y = 0 +  1 x
Attendance = 114.35 - .61 (82)
Attendance = 114.35 – 50.02
Attendance = 64.33
Multiple Regression is used when there is more
than one predictor variable.
• If you are predicting success in grad school you
may use three predictor variables: GRE scores,
University GPA, and IQ scores.
• Then you can predict success in grad school
based on all three predictors, which usually is
more accurate than one predictor.
• Allows the researcher to simultaneously consider
the influence of all the predictor variables on the
outcome variable.
Types of Multiple Regression
1. Standard multiple regression (simultaneous
multiple regression): enter all the predictor
variables at the same time.
• You can predict grad school success by entering
GPA, GRE, and IQ score simultaneously.
• You will get one regression constant (0) and a
separate regression coefficient (1) for each
predictor variable, which is based on the
correlation between each predictor variable and
the outcome variable.
• Grad school success: = -2.14 + .29(GPA) +
.98(GRE) + 1.21 (IQ)
2. Stepwise Multiple Regression: enter the predictor
variables one at a time.
• First enter the predictor variable that correlates
the highest with the outcome variable.
• Next, you enter the variable that relates the
strongest to the outcome variable after the first
variable is entered.
• It will account for the highest amount of variance in
the outcome variable after the the first predictor
variable is entered
• This may or may not be the second highest
correlation. If the second highest correlation was
highly correlated with the first variable than it may
not predict a unique amount of the variance in the
outcome variable.
Motivation
.40
Grad School
y
GPA .68
GRE .50
3. Hierarchical Multiple Regression: enter the
predictor variables in a predetermined order,
based on hypotheses the researcher wants to
test.
• Can partial out the effects of predictor variables
entered in early steps to see if other predictor
variables still have a contribution uniquely to the
variance in the outcome variable.
• Confounding variables: variables that tend to
occur together, making it hard to determine their
unique effects.
E.g. We want to determine the relation between
drinking while pregnant and child's IQ score.
• But, we know that mothers who drink while
pregnant also tend to smoke and do other drugs
while pregnant, which could also decrease child’s
IQ.
• We can enter smoking and other drug use into the
regression equation first and then enter drinking:
• to see if after smoking and other drug use are
accounted for (partialled out), if drinking uniquely
predicts IQ scores above and beyond smoking and
other drug use.
Mediation Effects: occur when the effect of x on y is
actually occurring because of a third variable, z.
• First enter the possible mediator variables.
• Then you can see if x uniquely predicts variance
in y after z is accounted for and partialled out
(statistically removed)
• Correlation between drowning and eating ice
cream, but this relation may be related to a
mediator variable called summer (heat).
• We could fist enter heat in to the regression to
determine how strongly heat is uniquely related to
drowning, then after heat is removed we can
determine whether eating ice cream is actually
uniquely related to drowning.
Multiple correlation coefficient (R)
• The ability of all the predictor variables together
to predict the outcome variable.
• Represents the degree of the relationship
between the outcome variable and the set of
predictor variables.
• Ranges from .00 to 1.00, the larger the R the
better the predictor variable accounts for the
variance the outcome variable.
• R can be squared to show the percent of the
variance in the outcome variable (y) that is
accounted for by the set or predictor variables.
• R = .50, accounting for 25% of the variance in y.
• Studying the correlations between happiness and
various predictor variables
Predictor Variables
Happiness
Self-Esteem
.15
Social Network
.33
Money
.02
Life Satisfaction
.20
• In a stepwise regressions, which variable would be
entered first? Which will enter the equation second?
• Which variable is least likely to be included as a
predictor in the final equation?
• If a standard regression was done, what is the smallest
that the multiple correlation b/w the 4 predictor
variables and the criterion variable could possibly be?
Cross-Lagged Panel Design
• The correlation between two variables is
calculated at two different points in time.
• Then calculate the correlation between the two
variables across time.
• If we want to determine whether watching violent
TV leads to aggressive behavior, OR if
aggressive children prefer to watch more violent
TV we can use a cross-lagged panel design
• Look at correlation between TV violence (x) at
time 1 and aggression (y) at time 2.
• Look at correlation between aggression (y) at
time 1 and TV violence (x) at time 2.
• If TV violence leads to aggression then the
correlation between x at time 1 and y at time 2
should be stronger than the correlation between y
at time 1 and x at time 2.
Time 1
TV violence
r =.05
r =.31
r =.01
r = .21
Aggression
Time 2
TV violence
r = -.05
r =.38
Aggression
• In this cross-lagged panel design foes x appear to
cause y, does y appear to cause x, do both
variables influence each other, or are x and y
unrelated?
Time 1
Energy
r =.65
r =.45
r =.37
r = .51
Exercise
Time 2
Energy
r = .49
r =.23
Exercise
Structural Equations Modeling
• Allows you to test hypotheses about the pattern of
correlations.
• Researcher makes precise predictions about how
three or more variables are causally related.
• x caused y which cases z
• Then you can compare your hypothesized
correlation matrix against the real correlation
matrix.
• This analysis determines the degree to which the
patterns of correlations observed matches or fits
with the researchers predictions or model.
• Can also test two different models against each
other to see which one fits best with the observed
correlation matrix.
Factor Analysis
• Analyze the interrelationships among a number of
variables.
• Look for a pattern in the correlation matrix; look for
correlations among the correlations.
• Can determine if some variables are all highly
correlated with each other but not with other
variables that may only correlate with each other.
A
B
C
D
A 1.00 .69
.04
-.03
B -1.00 .09
.10
C --1.00
.75
D ---1.00
• Present the data in a factor matrix with factor
loadings which represent the correlations of the
variables with the factors.
Variable
A
B
C
D
Factor 1
.90
.87
.03
.07
Factor 2
.02
-.01
.92
.93
• Then you can identify labels for the factors. This
is usually related to the researchers underlying
hypotheses and theory, but can be subjective.
Factor analysis can be used to:
• Study the underlying structure of psychological
constructs (personality traits).
• To reduce a large number of variables to a
smaller, more manageable set of data.
• May include 40 measures of three different types
of working memory, knowing that there are only a
few basic constructs
• In the development of self-report measures of
attitudes and personality.
• Want to ensure certain measures are measuring
the same construct.
Chapter 8: Basic Issues in
Experimental Research
• Experimental designs allow researchers to make
cause and effect conclusions.
Three characteristics:
• Researcher must vary at least one independent
variable and assess its effects one a dependent
variable.
• Researcher must assign participants to
experimental conditions in a way that ensures
initial equivalence.
• Researcher must control extraneous variables
that may influence the participants’ behavior.
Manipulating the independent variable:
• Independent variable is the variable that is
manipulated by the researcher.
• Must have two or more levels (conditions)
• Different does of a drug (100, 200, or 300 mg)
• Quantitative differences (numerical differences
in amount of drug, or amount of time etc)
• Qualitative differences (one condition people
study with back ground noise and in another
with no background noise)
Types of independent variables:
• Environmental manipulations: experimentally
modify the physical or social environment
• Different levels of lighting, group size.
• Instructional manipulations: vary the instructions
that participants receive.
• One condition may tell participants the task will be
very difficult, in another may tell them it will be easy
• Invasive manipulations: invoke changes in the
participant's body through surgery or drugs.
• Different doses of a drug, rats with parts of their
brain damaged.
Experimental groups: participants who receive
some level of the independent variable
Control group: participants who do not receive a
level of the independent variable.
• Helps to identify the baseline level of performance
To ensure their independent variable is strong
enough to produce and effect researchers may:
• Pilot test: test the independent variable on a
small sample of participants to ensure the levels
of the independent variable are different enough
to produce an effect.
• Manipulation check: ask the participants if they
noticed the difference in the independent variable
Subject variable: reflects existing characteristics of
the participant (age, gender)
Dependent variable: response being measured in
the study
Assigning participants to conditions:
• Want to ensure that the participants are the same
before they are assigned to conditions, so effects
are due to the manipulation of the independent
variable and not due to pre-existing participant
characteristics.
Between subject designs:
• Simple random assignment: Each participant has
an equal probability of being placed in each
condition.
• Matched random assignment: test the participants
on a measure related to the dependent variable
and then assign to conditions by matching to
ensure you have the same number of people who
are high and low on the measure in each condition
Within-subjects design
• Repeated measures design: each participant
completes all conditions
• No need for random assignment
• Participants may participate in the experimental
and control group or in all the different levels of the
independent variable
• More powerful than b/w subjects
• Because the participants serve as their own
controls
• Require less participants (can have 30 who
participate in all three conditions, instead of 30
per condition making 90).
• Order effects: the order in which the levels of the
independent variable are received may affect the
participant’s behavior
• If studying memory for words under different
lighting conditions (each condition has more light)
participants may be tired by the last condition
which may reduce performance.
• Participants may show a practice effect in that they
get better at the task in subsequent conditions.
• Counterbalancing: A procedure in which the
order of conditions in a repeated-measures
design is arranged so that each condition
occurs equally often in each order.
• Latin square design: each condition occurs
once at each ordinal position and also follows
equally often after each of the other conditions
• Carryover effects: occurs when the effects at
one level of the independent variable are still
present at another level (condition).
• Must ensure drug of one dosage wears off
before the next conditions started
Experimental Control:
• Eliminate or hold constant the effects of other
extraneous variables that may effect the
dependent variable.
• Systematic variance: (b/w groups variance) is the
part of the total variance that reflects the
differences among the experimental groups or
conditions.
Systematic variance = treatment variance +
confound variance
• Treatment variance: is due to the independent
variable
• Confound variance: is due to extraneous
variables that differ between the groups and not
due to the independent variable
Error variance: reflects unsystematic differences
among the participants
• Random variations in the setting (temp, lighting)
and procedure (experiment’s mood), or due to
differences among participants within the group.
• Can remove error variance from treatment variance
using statistics.
Total variance = treatment variance + confound
variance + error variance
• Want to maximize treatment variance, eliminate
confound variance, and minimize error variance.
Sources of Error Variance
• Individuals differences: participants may differ
cognitively, physiologically, and behaviorally.
– Get participants that are homogenous, more alike.
• Transient states: participants may differ in transient
states (mood, tiredness, health)
• Environmental factors: differences in the study
environment (noise, time of day).
– Researchers should try to hold the environment constant
• Differential treatment: researchers should treat all
participants the same. Experimenter’s mood or
health can influence how they treat some
participants, or the participants behavior (friendly,
mean etc) may affect their treatment
• Measurement error: error in measuring. Try to use
reliable measures.
Eliminating Confounds
• Internal validity: the extent to which changes in
the dependent variable can be attributed to the
influence of the independent variable rather than
to confounding variables.
– Degree to which researchers can draw accurate
conclusions about the effects of the independent
variable.
Internal validity threats:
• Biased assignment of participants to conditions:
participants in each condition differ at the
beginning, so differences in the dependent
variable may reflect pre-existing differences
among the participants rather than differences
due to the independent variable
Random Assignment
ABBC
BCABCB
CAAB B
CBABB
AA B
BCB
BC
AA B
BCB
BC
Biased Assignment
ABBC
BCABCB
CAAB B
CBABB
AAA
BBB
BB
ABB
BCC
CC
• Differential attrition: participates who do not
continue in the study (drop out). Attrition can
occur at a different rate in the different conditions
• Problematic when more participants drop out of
one condition as compared to the other condition
• People who drop out may be different than those
who stay (more scared of experiment, less
motivated).
• Pretest sensitization: taking a pretest may affect
how participants behave in the experiment, so it is
hard to determine whether effect is due to the
pretest or the independent variable.
• History: history effects can effect the dependent
variable
• Testing anxiety in participants, perhaps a participant
in one groups had just gone through a very anxious
situation and may be more anxious already due to
other factors than in the experiment.
• Maturation: Participants may change overtime in a
longitudinal experiment. May be difficult to
distinguish effect of the independent variable from
maturation changes over time.
• More problematic in research with children.
• Miscellaneous design confounds: due to
participants being treated differently in different
conditions, which results in confounding.
• Experimenter expectancy effects: researchers
may observe behavior in a biased way that
reflects what they expect to happen.
• Their expectations can distort the results
• Demand characteristics: participants may behave
differently because of noticeable aspects of the
experiment
• They may be able to guess what the researchers
are researching and act accordingly.
• Double-blind procedure: neither the participant
nor the researcher knows which condition a
participant is in.
• Helps to eliminate experimenter expectancy effects
and demand characteristics
• Placebo Effects: an artifact that occurs when
participant's expectations about what effect an
and experimental manipulation is supposed to
have influence the dependent variable
• If participants think they are in a drug group they
may be more likely to say the drug produced an
effect.
• Placebo control group: receive a pill but with no
drug, so participants do not know if they are truly
receiving the drug
External validity: the extent to which the results of
the study can be generalized beyond the study to
other places, people, times, and procedures.
• Experimenter's dilemma: the more the researcher
controls the study setting the more internal validity
the experiment has, but the lower the external
validity.
• Most researchers prefer strong internal validly over
external validity, because they must ensure their
effects are due to the independent variable.
• Usually researchers are testing a theory about the
relation between variables, so their relations
should hold under different conditions and settings
• Replication is important.