Chapter 7: Advanced Correlational Strategies

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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.

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Regression Line
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• 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.

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• The regression equation is expressed by
• y ?0 ?1x
• 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

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• 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 ?1x
• Attendance 114.35 - .61 (82)
• Attendance 114.35 50.02
• Attendance 64.33

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• 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.

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• 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)

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• 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.

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Motivation .40
Grad School y
GRE .50
GPA .68
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• 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.

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• 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 childs
  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.

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• 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.

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• 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.

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• 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?

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• 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.

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• 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 Time 2
• TV violence r .05
  TV violence
• r .31 r .01
• r .21 r -.05
• Aggression r .38 Aggression

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• 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 Time 2
• Energy r .65
  Energy
• r .45 r .37
• r .51 r .49
• Exercise r .23 Exercise

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• 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.

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• 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

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• Present the data in a factor matrix with factor
  loadings which represent the correlations of the
  variables with the factors.
• Variable Factor 1 Factor 2
• A .90 .02
• B .87 -.01
• C .03 .92
• D .07 .93
• Then you can identify labels for the factors.
  This is usually related to the researchers
  underlying hypotheses and theory, but can be
  subjective.

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• 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.

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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.

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• 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)

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• 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.

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• 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

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• Subject variable reflects existing
  characteristics of the participant (age, gender)
• Dependent variable response being measured in
  the study

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• 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

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• 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).

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• Order effects the order in which the levels of
  the independent variable are received may affect
  the participants 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.

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• 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

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• 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

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• Error variance reflects unsystematic differences
  among the participants
• Random variations in the setting (temp, lighting)
  and procedure (experiments 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.

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• 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. Experimenters 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.

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• 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

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Random Assignment
A A B B C B B C
A B B C B C A B C B C A A B B C B A B B
A A B B C B B C
Biased Assignment
A A A B B B B B
A B B C B C A B C B C A A B B C B A B B
A B B B C C C C
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• 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.

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• 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.

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• 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

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• 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

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• 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.