Research Designs Correlational

By Mike Rippy

Correlational Research DesignsCorrelational studies may be used to A. Show relationships between two

variables there by showing a cause and effect relationship

B. show predictions of a future event or outcome from a variable

Types of Correlation studies1. Observational Research e.g. class

attendance and grades2.Survey Research e.g. living together

and divorce rate3. Archival Research e.g.violence and

economics

Advantages of the correlational method1. It allows the researcher to analyze

the relationship among a large number of variables

2. Correlation coefficients can provide for the degree and direction of relationships

Planning a Relationship Study Purpose to identify the cause and effects of

important phenomena Method 1. Define the problem 2. Review existing literature 3. Select participants who can have measurable

variables-reasonably homogeneous 4. Collect data-test, questionnaires, interviews,

&etc. 5. Analysis of data

What do correlations measure? Correlations measure the association, or co-

variation of two or more dependent variables. Example: Why are some students

aggressive? Hypothesis: Aggression is learned from

modeling Test: Look for associations between

aggressive behavior and…

Interpreting CorrelationsScattergram- a pictorial representation

of correlations between two variablesUse of a scattergram An x and y axes are produced

perpendicular to each otherResults of correlates are plottedThe relationship of these plots are

interpreted

Interpreting Correlations continued The amount of correlation is expressed as r= The r scores can range from –1 to 1 If r= 1 there is said to be perfect correlation

with the other variable An r score of 0 shows no relationship If r= -1 there is a lack of relationship between

the two variables Anything between 1 and –1 shows a varying

degrees of relationships

Interpreting Correlations Continued The expression r squared = the percent of

variation accounted for between the relations between two variables like x and y this is called the explained variance

Example: correlation between G.P.A. scores and A.C.T. if r=.6 then r squared =.36 so the per cent of accuracy is 36% in predicting A.C.T. scores from the person G.P.A.

A complete interpretation would include attempts to explain nonsignificant results

Other measures of interest in Correlational StudiesR is multiple correlation (0 to 1) (b) is regression weight which is a

multiplier added to a predictor variable to maximize predictive value

B is beta weight which is used in a multiple regression equation to establish the equation in a standard score form

Use of causal-comparative approachHowever, when comparing two

variables sometimes inference may be made that one causes the other.

Only an experiment can provide a definitive conclusion of a cause and effect relationship.

Limitations of Relationship StudiesResearcher tend to break down

complex patterns into two simple components.

Researcher identify complex components that interest them but could probably be achieved in many different ways.

Ways to fix problems of correlational DesignAdd more variables to the modelReplicate designConvert question to the experimental

design

Prediction StudiesA variable whose value is being used to

predict is known as the predictor variable

A variable whose value is being predicted is the criterion variable.

The aim of prediction studies is to forecast academic and vocational success.

Types of Information provided in a prediction studyThe extent to which a criterion pattern

can be predictedData for developing a theory for

determining criterion patternsEvidence about predicting the validity of

a test

Basic Design of Prediction Studies The problem-reflect the type of information

you are trying to predict Selection of research participants- draw from

population most pertinent to your study Data collection-predictor variables must be

measured before criterion patterns occur Data Analysis- correlate each predictor

variable with the criterion

Definitions useful in Prediction Studies Bivariate correlational statistics- express the

magnitude of relationships between two variables

Multiple regression- uses scores on two or more predictor variables to predict performance of criterion variables. The purpose is to determine which variables can be combined to form the best prediction of each criterion variable.

Multiple Regression FactsToo large of a sample may cause faulty

data to occur15 to 54 people should be sampled per

variable used.

Statistical Factors in Prediction ResearchPrediction research in useful for

practical purposesDefinitions- selection ratio- proportion of

the available candidates that must be selected

Base rate- percentage of candidates who would be selected without a selection process

Statistical Factors in Prediction Research cont. Taylor-Russell Tables- a combination of three

factors; predictive validity, selection ratio, and base rate (If these three factors are present the researcher should be able to predict the proportion of candidates that will be successful)

Shrinkage- The tendency for predictive validity to decrease when research is repeated

Techniques used to analyze BivariatesProduct-Moment Correlation- Used

when both variables are expressed as continuous scores

Correlation Ratio- Used to detect nonlinear relationships

Part and Partial Correlation

This is an application employed to rule out the influence of one or more variables upon the criterion in order to clarify the role of the other variables.

Multivariate correlational StatisticsThese are used when examining the

interrelationship of three or more variables.

Correlation Coefficient It measures the magnitude of the relationship

between a criterion variable and some combination of predictor variables

Correlation coefficient of determination equals R squared. This expresses the amount of variance that can be explained by a predictor variable of a combination of predictor variables

Correlation Coefficient Determinates cont.R can range from 0.00 to 1.00. The

larger R is the better the prediction of the criterion variable.

There is more statistical significance if the R squared value is significantly different from zero.

Canonical Correlations Is when there is a combination of

several predictor variables used to predict a combination of several criterion variables

Path Analysis Is a method of measuring the validity of

theories about causal relationships between two for more variables that have been studied in a correlational research design

Steps of Path Anaylsis Formulate a hypothesis that causally link the

variables of interest Select or develop measures of the variables

that are specified by the hypothesis Compute statistics that show the strength of

relationship between each pair of variables that are causally linked in the hypothesis

Interpret to determine if they support the theory

Correlation Matrix Is an arrangement of row ad columns

that make it easy to see how measured variables in a set correlate with other variables in the set

Structural Equation Modeling Is a method of multivariate analysis that

test causal relationships between variables and supplies more reliable and valid measures than path analysis

It is also called LISREL which stands for Analysis of Linear Structural Relationships

Differential AnalysisThis is subgroup analysis in relationship

studiesThis application is used when the

researcher believes that correlated variables might be influenced by a particular factor. Then subjects from the sample are selected who have this characteristic

Moderator Variables in a prediction StudyThere are times when a certain test is

more valid in predicting a subgroups behavior. The variable that is used in this instance is called a moderator variable