Correlational ResearchDesigns Correlational 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 studies 1. Observational Research e.g. class attendance and grades 2.Survey Research e.g. living together and divorce rate 3. Archival Research e.g.violence and economics
Advantages of thecorrelational method 1. 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 correlationsmeasure? 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 Correlations Scattergram- a pictorial representation of correlations between two variables Use of a scattergram An x and y axes are produced perpendicular to each other Results of correlates are plotted The relationship of these plots are interpreted
Interpreting Correlationscontinued 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 CorrelationsContinued 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 inCorrelational 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
Correlation and Causality If there is no association between two variables, then there is no causal connection Correlation does not always prove causation a third variable may have the causal relation example: Women surveyed during pregnancy that smoked correlated with arrest of their sons 34 years later. Is a third variable the cause. Other variables- socioeconomic status, age, father’s or mother’s criminal history, Parent’s psychiatric problems
Use of causal-comparativeapproach However, 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 RelationshipStudies Researcher 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 ofcorrelational Design Add more variables to the model Replicate design Convert 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 providedin a prediction study The extent to which a criterion pattern can be predicted Data for developing a theory for determining criterion patterns Evidence about predicting the validity of a test
Basic Design of PredictionStudies 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 PredictionStudies 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 Facts Too large of a sample may cause faulty data to occur 15 to 54 people should be sampled per variable used.
Statistical Factors inPrediction Research Prediction research in useful for practical purposes Definitions- 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 inPrediction 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 analyzeBivariates Product-Moment Correlation- Used when both variables are expressed as continuous scores Correlation Ratio- Used to detect nonlinear relationships
Part and Partial CorrelationThis 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 correlationalStatistics These 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 CoefficientDeterminates 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 Isa 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 Isan 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 Analysis This is subgroup analysis in relationship studies This 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 aprediction Study There 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