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Chapter 12 Chapter 12

Correlational DesignsCorrelational Designs

EDUC 640 Dr. William M. EDUC 640 Dr. William M. BauerBauer

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Key IdeasKey Ideas

Brief history of correlational researchBrief history of correlational researchExplanatory and predictor designsExplanatory and predictor designsCharacteristics of correlational researchCharacteristics of correlational researchScatterplots and calculating associationsScatterplots and calculating associationsSteps in conducting a correlational studySteps in conducting a correlational studyCriteria for evaluating correlational Criteria for evaluating correlational

researchresearch

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A Brief History of A Brief History of Correlational DesignsCorrelational Designs

1895 Pearson develops correlation 1895 Pearson develops correlation formulaformula

1897 Yule develops solutions for 1897 Yule develops solutions for correlating two, three and four correlating two, three and four variablesvariables

1935 Fisher prisoners significance 1935 Fisher prisoners significance testing and analysis of variancetesting and analysis of variance

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A Brief History of A Brief History of Correlational DesignsCorrelational Designs

1963 Campbell and Stanley write on 1963 Campbell and Stanley write on experimental and quasi-experimental experimental and quasi-experimental designsdesigns

1970’s and 1980’s computers give 1970’s and 1980’s computers give the ability to statistically control the ability to statistically control variables and do multiple regressionvariables and do multiple regression

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Explanatory DesignExplanatory Design

Investigators correlate two or more Investigators correlate two or more variablesvariables

Researchers collect data at one point Researchers collect data at one point in timein time

Investigator analyzes all participants Investigator analyzes all participants as a single groupas a single group

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Explanatory DesignExplanatory Design

Researcher obtains at least to scores Researcher obtains at least to scores for each individual in the group - one for each individual in the group - one for each variablefor each variable

Researcher reports the use of the Researcher reports the use of the correlation statistical test (or an correlation statistical test (or an extension of it) in the data analysisextension of it) in the data analysis

Researcher makes interpretations or Researcher makes interpretations or draws conclusions from statistical draws conclusions from statistical test resultstest results

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Prediction Design: VariablesPrediction Design: Variables

Predictor Variable: a variable that is Predictor Variable: a variable that is used to make a forecast about an used to make a forecast about an outcome in the correlational study.outcome in the correlational study.

Criterion Variable: the outcome Criterion Variable: the outcome being predictedbeing predicted

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Prediction Design: Prediction Design: CharacteristicsCharacteristics

The authors typically include the The authors typically include the word “prediction” in the titleword “prediction” in the title

The researchers typically measure The researchers typically measure the predictor variables at one point the predictor variables at one point in time and the criterion variable at a in time and the criterion variable at a later point in time.later point in time.

The authors are interested in The authors are interested in forecasting future performanceforecasting future performance

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Key Correlational Key Correlational CharacteristicsCharacteristics

Graphing pairs of scores to identify Graphing pairs of scores to identify the form of association (relationship)the form of association (relationship)direction of the associaitondirection of the associaitondegree of associationdegree of association

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Example of a ScatterplotExample of a ScatterplotHours ofInternet useper week

Depression scoresfrom 15-45

Laura 17 30Chad 13 41Patricia 5 18Bill 9 20Mary 5 25Todd 15 44Angela 7 20David 6 30Maxine 2 17John 18 48Mean Score 10 29.3

50

40

30

20

10 M

M

+

+

-

-

Depression scoresY=D.V.

Hours of Internet UseX=I.V.

5 10 15 20

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Patterns of Association Patterns of Association Between Two VariablesBetween Two Variables

A. Positive Linear (r=+.75) B. Negative Linear (r=-.68)

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Patterns of Association Patterns of Association Between Two VariablesBetween Two Variables

D. CurvilinearC. No Correlation (r=.00)

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Patterns of Association Patterns of Association Between Two VariablesBetween Two VariablesE. Curvilinear F. Curvilinear

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Calculating Association Calculating Association Between VariablesBetween Variables

Pearson Product Moment (bivariate) rPearson Product Moment (bivariate) rxyxy degree to which X and Y vary togetherdegree to which X and Y vary together

degree to which X and Y vary separatelydegree to which X and Y vary separatelyUses of Pearson Product MomentUses of Pearson Product Moment

““+” or “-” linear association (-1.00 to +1.00)+” or “-” linear association (-1.00 to +1.00)test-retest reliabilitytest-retest reliabilityinternal consistencyinternal consistencyconstruct validityconstruct validityconfirm disconfirm hypothesesconfirm disconfirm hypotheses

r=

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Calculating Association Calculating Association Between VariablesBetween Variables

Display correlation coefficients in a Display correlation coefficients in a matrixmatrix

Calculate the coefficient of Calculate the coefficient of determinationdeterminationassesses the proportion of variability in one assesses the proportion of variability in one

variable that can be determined or variable that can be determined or explained by a second variableexplained by a second variable

Use Use rr2 2 e.g. if r=.70 (or -.70) squaring the e.g. if r=.70 (or -.70) squaring the value leads to rvalue leads to r22=.49. 49% of variance in Y =.49. 49% of variance in Y can be determined or explained by Xcan be determined or explained by X

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Using Correlations For Using Correlations For PredictionPrediction

Use the correlation to predict future Use the correlation to predict future scoresscores

Plotting the scores provides information Plotting the scores provides information about the direction of the relationshipabout the direction of the relationship

Plotting correlation scores does not Plotting correlation scores does not provide specific information about provide specific information about predicting scores from one value to predicting scores from one value to anotheranother

Use a regression line (‘best fit for all”) for Use a regression line (‘best fit for all”) for predictionprediction

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Simple Regression LineSimple Regression Line

Slope

Depression Scores Regression Line

Hours of Internet Use Per Week14 15 20105

50

4140

30

20

10Intercept

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Other Measures of Other Measures of AssociationAssociation

Spearman rho (rSpearman rho (rss) - correlation ) - correlation coefficient for nonlinear ordinal datacoefficient for nonlinear ordinal data

Point-biserial - used to correlate Point-biserial - used to correlate continuous interval data with a continuous interval data with a dichotomous variabledichotomous variable

Phi-coefficient - used to determine Phi-coefficient - used to determine the degree of association when both the degree of association when both variable measures are dichotomousvariable measures are dichotomous

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Advanced Statistical Advanced Statistical ProceduresProcedures

Partial Correlations - use to Partial Correlations - use to determine extent to which determine extent to which mediating variable influences both mediating variable influences both independent and dependent independent and dependent variablevariable

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Common Variance Shared for Common Variance Shared for Bivariate CorrelationBivariate Correlation

Independent Variable Independent Variable

Time on Task Achievementr=.50

Time on Task Achievement

r squared = (.50)2

Shared Variance

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Advanced Statistical Advanced Statistical ProceduresProcedures

Multiple Correlation or Regression - Multiple Correlation or Regression - multiple independent variables multiple independent variables may combine to correlate with a may combine to correlate with a dependent variabledependent variable

Path analysis and latent variable Path analysis and latent variable causal modeling (structural causal modeling (structural equation modeling)equation modeling)

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Regression and Path AnalysisRegression and Path Analysis

Regression

Time - on - Task

Motivation

Prior Achievement

Peer Friend Influence

Peer Achievement Motivation Student Learning

Peer Friend Influence

Student Learning

Path Analysis

-.05

.18.13

Time - on - Task

.24 .11

++

+-

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Steps in Conducting a Steps in Conducting a Correlational StudyCorrelational Study

Determine if a correlational study best Determine if a correlational study best addresses the research problemaddresses the research problem

Identify the individuals in the studyIdentify the individuals in the study Identify two or more measures for each Identify two or more measures for each

individual in the studyindividual in the studyCollect data and monitor potential Collect data and monitor potential

threatsthreatsAnalyze the data and represent the Analyze the data and represent the

resultsresults Interpret the resultsInterpret the results

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Criteria For Evaluating Criteria For Evaluating Correlational ResearchCorrelational Research

Is the size of the sample adequate for Is the size of the sample adequate for hypothesis testing? (sufficient power?)hypothesis testing? (sufficient power?)

Does the researcher adequately display Does the researcher adequately display the results in matrixes or graphs?the results in matrixes or graphs?

Is there an interpretation about the Is there an interpretation about the direction and magnitude of the direction and magnitude of the association between the two variables?association between the two variables?

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Criteria For Evaluating Criteria For Evaluating Correlational ResearchCorrelational Research

Is there an assessment of the Is there an assessment of the magnitude of the relationship based magnitude of the relationship based on the coefficient of determination, on the coefficient of determination, pp-values, effect size, or the size of -values, effect size, or the size of the coefficient?the coefficient?

Is the researcher concerned about Is the researcher concerned about the form of the relationship so that the form of the relationship so that an appropriate statistic is chosen for an appropriate statistic is chosen for analysis?analysis?

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Criteria For Evaluating Criteria For Evaluating Correlational ResearchCorrelational Research

Has the researcher identified the Has the researcher identified the predictor and criterion variables?predictor and criterion variables?

If a visual model of the relationships is If a visual model of the relationships is advanced, does the researcher advanced, does the researcher indicate the expected relationships indicate the expected relationships among the variables, or, the predicted among the variables, or, the predicted direction based on observed data?direction based on observed data?

Are the statistical procedures clearly Are the statistical procedures clearly defined?defined?

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Applying What you Have Applying What you Have Learned: A Correlational Learned: A Correlational

StudyStudyReview the article and look for the Review the article and look for the

following:following: The research problem and use of quantitative The research problem and use of quantitative

researchresearch Use of the literatureUse of the literature The purpose statement and research hypothesisThe purpose statement and research hypothesis Types and procedures of data collectionTypes and procedures of data collection Types and procedures of data analysis and Types and procedures of data analysis and

interpretationinterpretation The overall report structureThe overall report structure