Factors influencing product moment correlation coefficient
1. Linearity
2. Range of scores in sample
3. Extreme scores (esp. in small sample)
Range of scores in a sample should-
match the population
Truncated or restricted range of scores in sample:
Correlation likely smaller than is in defined population
Range of scores in a sample larger than defined population:
Correlation coefficient likely larger than in the defined population
Coefficient of Determination =
r^{2}
Statistically Significant Correlation:
low risk of falsely concluding there is some sort of correlation in the population.
p<.05
Factors that determine statistical significance
Size of sample
Size of correlation coefficient
Advantages of Relational (correlational) Studies
1. Ecological validity
2. Larger range of scores
3. Best method available
Ecological Validity
Extent to which results can be generalized to other situations
(intended target situation-natural environment)
Disadvantages of Relational (Correlational) Studies
Single relational study usually not best method for determining cause and effect
Open to many alternative explanations
Alternative explanations to Relational (correlational) Studies-
Third variable problem
Directionality problem
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
Directionality Problem
x-->Y
X<--Y
X<-->Y
Sugar
Corporal punishment
bad parents
violent tv
Variations of Relational Studies- All involve naturally occuring variables (predictor variables)
1. Classic correlational study
2. Form groups or conditions
Classic Correlational Study
Simply measure available values of predictor variable and correlate with value of outcome variable
Extroversion and car sales
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...)
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.
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.
Factors to consider in evaluating Relational studies
1. Cost of ignoring information
2. Likelyhood that X causes Y?
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
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)
Covariation Rule
X and Y are related
Internal Validity Rule
Other explanations for the relationship b/w x and y
Most research methods:
Attempt to demonstrate covariation(2), and eliminate 3^{rd} or confounding variables(3) and directionality problems(1)
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
1. Manipulation of X:Unique advantage-
Evidence for temporal precedence rule, but gives comparison too. 0,1,2,4,8 mg
All true experiments show:
whether there is a relationship (covariation, correlation) between the IV and DV
One group post test only design or one-shot case study cant:
Cant pinpoint cause
Cant show that X and Y covary
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
Within Subjects
Each subject contributes score or mean for all levels of the IV or PV snd there are at least two levels.
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)
Control over all other important variables-
All subjects are treated exactly the same except for X(the IV) (external)
Basic methods of controlling confounding/third variables
1. Eliminate variable completely
2. Hold constant or control variables across conditions (potentionally variables)
3. Random assignment
Problem with eliminating and holding constant variables
Some variables are hard to hold constant or eliminate due to lack of knowledge
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
Equal chance =
Equal frequency in the long run
External Validity
Degree to which the findings can be generalized to other subjects, and to other situations (settings, levels of variables, ways of measurement)
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)
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
Other designs (age) with special threats
~Cross-Sectional Designs
Advantages:
Cheap
Fast
Other designs (age) withspecial threats:
~Cross sectional Designs
Disadvantages
Differences among cohorts
Cohort = companion = accomplice
Other designs (age) with special threats
~Longitudinal Design
Advantages
Eliminates cohort differences
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
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)
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
Ways of dealing with threats to internal validity:
Matching:
"hold constant" subjects
Reassign based on pretest or records
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
When matching;
hold constant the subjects
Matching by using a descriptive statistic
no random assignment
Does not control for unknown sources of variance
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)
Advantages in within subjects designs
2.
3.
2. Fewer subjects (more info from each)
-terms: levels, conditions, groups
3. Statistics hve more power
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
Disadvantages of within subjects deesigns
Not always possible to give all treatments to 1 subject
Strong possibilities of many threats to internal validity
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
Carry over is differential-
different prior treatments, different mental set for each list
Counterbalancing
influence on order effects (maturation) ex: fatigue
Influence on differential carry over effects:
alcohol
Kinds of counterbalancing
1. complete
2. incomplete
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
Incomplete counterbalancing
1. random order-each subject different random order
2. balanced latin square
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....