
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 situationnatural 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 (ttest, ANOVA...)
 Subject variables: pysio./psych. Characteristics: gender, age, anxiety, conscientiousness, experiences

After the fact
ex post facto

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.

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 oneshot 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 groupa statistical control
 Randomized groups design
 Posttest 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
Diffusion, compensatory equalization, compensatory rivalry, resentful demoralization

Other designs (age) with special threats
~CrossSectional Designs
Advantages:

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 controlcompared against self, not people from another group(differences across conditions matternot 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

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 ordereach 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....

