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Factors influencing product moment correlation coefficient
- 1. Linearity
- 2. Range of scores in sample
- 3. Extreme scores (esp. in small sample)
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Range of scores in a sample should-
match the population
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Truncated or restricted range of scores in sample:
Correlation likely smaller than is in defined population
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Range of scores in a sample larger than defined population:
Correlation coefficient likely larger than in the defined population
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Coefficient of Determination =
r2
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Statistically Significant Correlation:
- low risk of falsely concluding there is some sort of correlation in the population.
- p<.05
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Factors that determine statistical significance
- Size of sample
- Size of correlation coefficient
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Advantages of Relational (correlational) Studies
- 1. Ecological validity
- 2. Larger range of scores
- 3. Best method available
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Ecological Validity
Extent to which results can be generalized to other situations
(intended target situation-natural environment)
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Disadvantages of Relational (Correlational) Studies
- Single relational study usually not best method for determining cause and effect
- Open to many alternative explanations
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Alternative explanations to Relational (correlational) Studies-
- Third variable problem
- Directionality problem
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Third Variable Problem explanation
An unmeasured variable changes along with the identified variable so that cannot determine which is a true cause
- Identified and measured vs. actual variable
- Maalox & memory loss
- Smoking & lung cancer
- Alcohol & risk taking
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Directionality Problem
- x-->Y
- X<--Y
- X<-->Y
- Sugar
- Corporal punishment
- bad parents
- violent tv
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Variations of Relational Studies- All involve naturally occuring variables (predictor variables)
- 1. Classic correlational study
- 2. Form groups or conditions
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Classic Correlational Study
- Simply measure available values of predictor variable and correlate with value of outcome variable
- Extroversion and car sales
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Form Groups orConditions
- Select, classify, or categorize subjects based on the value of the predictor variable and correlate, orcompare groups/conditions using a test of means (t-test, ANOVA...)
- Subject variables: pysio./psych. Characteristics: gender, age, anxiety, conscientiousness, experiences
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After the fact-
ex post facto
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Confounding Variable
A variable not identified by E that systematically varies with identified variable so that the effect of the confounding variable and the effect of the identified variable can not be separated.
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Example of confounding variable
- To see if blondes have more fun
- Dr. XY compared fun surfeys in blondes from a modeling agency with those of brunettes from a temp agency.
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Factors to consider in evaluating Relational studies
- 1. Cost of ignoring information
- 2. Likelyhood that X causes Y?
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Cost of ignoring info.
- If cost is high, take seriously even if evidence is notoverwhelming
- If benefits high, and the cost low, reasonable to take advantage of infor
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Likelyhood that X causes Y?
- are changes in x a cause of y?
- Touching toads and then cancer
- Radiation then cancer
its a logical fallacy if this is the only info. considered (post hoc ergo)
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Covariation Rule
X and Y are related
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Internal Validity Rule
Other explanations for the relationship b/w x and y
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Most research methods:
Attempt to demonstrate covariation(2), and eliminate 3rd or confounding variables(3) and directionality problems(1)
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Krauter's 4 characteristics of a true experiment:
- 1. manipulation of X
- 2. comparison of the effects of several levels of X on Y
- 3. Subjects begin study equivalent on all important characteristics for each level of X (internal)
- 4. Control over all other important variables
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1. Manipulation of X:Unique advantage-
Evidence for temporal precedence rule, but gives comparison too. 0,1,2,4,8 mg
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All true experiments show:
whether there is a relationship (covariation, correlation) between the IV and DV
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One group post test only design or one-shot case study cant:
- Cant pinpoint cause
- Cant show that X and Y covary
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Between Subjects
- Each subject contributes score or mean for only one level of the IV or PV and there are at least two levels.
- Usually but not always, comparisons are made between groups of subjects
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Within Subjects
Each subject contributes score or mean for all levels of the IV or PV snd there are at least two levels.
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Kinds of comparisos
- 1. List each level of IV or PV
- 2. Ask did each subject contribute data (a mean or score) for all levels (within) of variable or just one(between)
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Control over all other important variables-
All subjects are treated exactly the same except for X(the IV) (external)
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Basic methods of controlling confounding/third variables
- 1. Eliminate variable completely
- 2. Hold constant or control variables across conditions (potentionally variables)
- 3. Random assignment
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Problem with eliminating and holding constant variables
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Some variables are hard to hold constant or eliminate due to lack of knowledge
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Random Assignment
S has equal and independent chance of being assigned to any group-a statistical control
- Randomized groups design
- Post-test only control group design
*this is only possible if X can be manipulated
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Equal chance =
Equal frequency in the long run
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External Validity
Degree to which the findings can be generalized to other subjects, and to other situations (settings, levels of variables, ways of measurement)
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Threats to external validity
- reactivity (measurement)
- People in the sample that dont belong/People notin the sample that who do belong/wrong proportion of people
- Unusual place(situation)
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Threats to internal validity:
Changes or differences in the composition of the groups
- Selection bias
- mortality ordifferential attrition
- Interaction of selection bias with the treatment
-
Research participants learn about treatments given to other groups
Diffusion, compensatory equalization, compensatory rivalry, resentful demoralization
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Other designs (age) with special threats
~Cross-Sectional Designs
Advantages:
-
Other designs (age) withspecial threats:
~Cross sectional Designs
Disadvantages
- Differences among cohorts
- Cohort = companion = accomplice
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Other designs (age) with special threats
~Longitudinal Design
Advantages
Eliminates cohort differences
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Other designs (age) with special threats
~Longitudinal Design
Disadvantages
- Very time consuming
- Expensive
- Lose subjects
- Age effect may be specific to cohort you are studying
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Ways of dealing wit hthreats to internal validity
- True experiments (b/w subjects designs)
- Eliminate, hold constant/control, Random Assignment
- Pretests (check equivalent Ss, no selection bias)
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Ways of dealing with threats to internal validity:
Pretest post control group design with random assignment
- 1. Groups equivalent
- 2. Subjects really change
- 3. Scale attenuation effects:
- ceiling effects and basement (floor) effects
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Ways of dealing with threats to internal validity:
Matching:
- "hold constant" subjects
- Reassign based on pretest or records
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Ways of matching
- 1. Matching by ranking
- --pretest or records
- --Rank subjects best to worst
- --divide ranked subjects into clusters according to number of groups
- --randomly assign subjects from each cluster into the groups
- 2. Matching by using a descriptive statistic
- --No random assignment
- --does not control for unknown sources of variance
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When matching;
hold constant the subjects
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Matching by using a descriptive statistic
- no random assignment
- Does not control for unknown sources of variance
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Advantages of Within subjects designs
- 1. exactly equivalent subjects (3rd characteristic of true experiment)
- a.) perfect matching
- b.)each subj. own control-compared against self, not people from another group(differences across conditions matter-not that some people better than others
- c.)conditions not confounded with subjects (vs. BS designs; treatments ARE confounded with subjects)
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Advantages in within subjects designs
2.
3.
- 2. Fewer subjects (more info from each)
- -terms: levels, conditions, groups
- 3. Statistics hve more power
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How to show that X is a cause of Y:
- 1.Show that Y didnt happen until after X (temporal precedence rrule)
- 2. Show that X and Y are related (covariation rule) The cause and effect must be correlated with each other
- 3. Show that other explanations for the relationship between X and Y can be ruled out (internal validity rule)
- 4. Plausible causal link between X and Y
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Disadvantages of within subjects deesigns
- Not always possible to give all treatments to 1 subject
- Strong possibilities of many threats to internal validity
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Sequencing effects in within subjects designs
- 1. Order effects (maturation)
- -order and treatment condition vary together
- 2. Differential carry over effects(testing sort of)
- -Performance on a condition partially dependent on specific prior treatment
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Carry over is differential-
different prior treatments, different mental set for each list
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Counterbalancing
influence on order effects (maturation) ex: fatigue
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Influence on differential carry over effects:
alcohol
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Kinds of counterbalancing
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Complete counterbalancing
- use all possible orders
- 2 conditions: 2 X 1 = 2
- 4 conditions: 4 X 3 X 2 X 1 = 24
- 6 conditions: 6 X 5 X 4 X 3 X 2 X 1 =72
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Incomplete counterbalancing
- 1. random order-each subject different random order
- 2. balanced latin square
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Latin Squares design
create rows that determine order each S gets each condition
- number of rows=number of treatments (conditions)
- number of columns=number of treatments (conditions)
ex: left side body/alphabet, right side/ silent....
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