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Correlational ResearchCorrelational Research

Chapter FifteenChapter Fifteen

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Correlational ResearchCorrelational ResearchChapter FifteenChapter Fifteen

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The Nature of Correlational The Nature of Correlational ResearchResearch

Correlational Research is also known Correlational Research is also known as Associational Research.as Associational Research.

Relationships among two or more Relationships among two or more variables are studied without any variables are studied without any attempt to influence them.attempt to influence them.

Investigates the possibility of Investigates the possibility of relationships between two variables.relationships between two variables.

There is no manipulation of variables There is no manipulation of variables in Correlational Research.in Correlational Research.

Correlational studies describe the variable relationship via a correlation coefficient

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Three Sets of Data Showing Different Three Sets of Data Showing Different Directions and Degrees of CorrelationDirections and Degrees of Correlation

(Table 15.1)(Table 15.1)

X Y X Y X Y

5 5 5 1 2 1

4 4 4 2 5 4

3 3 3 3 3 3

2 2 2 4 1 5

1 1 1 5 4 2

(A) (B) (C) r = +1.00 r = -1.00 r = 0

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Purpose of Correlational ResearchPurpose of Correlational Research

Correlational studies are carried out to explain Correlational studies are carried out to explain important human behavior or to predict likely important human behavior or to predict likely outcomes (identify relationships among outcomes (identify relationships among variables).variables).

If a relationship of sufficient magnitude exists If a relationship of sufficient magnitude exists between two variables, it becomes possible to between two variables, it becomes possible to predict a score on either variable if a score on predict a score on either variable if a score on the other variable is known (Prediction Studies).the other variable is known (Prediction Studies).

The variable that is used to make the prediction The variable that is used to make the prediction is called the is called the predictor variable.predictor variable.

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Purpose of Correlational ResearchPurpose of Correlational Research(cont.)(cont.)

The variable about which the prediction is made The variable about which the prediction is made is called the is called the criterion variablecriterion variable..

Both Both scatterplotsscatterplots and and regression linesregression lines are used are used in correlational studies to predict a score on a in correlational studies to predict a score on a criterion variablecriterion variable

A predicted score is never exact. Through a A predicted score is never exact. Through a prediction equation (see p. 585), researchers use prediction equation (see p. 585), researchers use a predicted score and an index of prediction a predicted score and an index of prediction error (standard error of estimate) to conclude if error (standard error of estimate) to conclude if the score is likely to be incorrect.the score is likely to be incorrect.

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Scatterplot Illustrating a Correlation Scatterplot Illustrating a Correlation of +1.00of +1.00 (Figure 15.1)(Figure 15.1)

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Prediction Using a Scatterplot Prediction Using a Scatterplot (Figure 15.2)(Figure 15.2)

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More Complex Correlational More Complex Correlational TechniquesTechniques

Multiple RegressionMultiple Regression Technique that enables Technique that enables

researchers to determine a researchers to determine a correlation between a criterion correlation between a criterion variable and the best variable and the best combination of two or more combination of two or more predictor variablespredictor variables

Coefficient of multiple Coefficient of multiple correlation (R)correlation (R)

Indicates the strength of the Indicates the strength of the correlation between the correlation between the combination of the predictor combination of the predictor variables and the criterion variables and the criterion variablevariable

Coefficient of DeterminationCoefficient of Determination Indicates the percentage of the Indicates the percentage of the

variability among the criterion variability among the criterion scores that can be attributed to scores that can be attributed to differences in the scores on the differences in the scores on the predictor variablepredictor variable

Discriminant Function AnalysisDiscriminant Function Analysis Rather than using multiple Rather than using multiple

regression, this technique is regression, this technique is used when the criterion value used when the criterion value is categoricalis categorical

Factor AnalysisFactor Analysis Allows the researcher to Allows the researcher to

determine whether many determine whether many variables can be described by variables can be described by a few factorsa few factors

Path AnalysisPath Analysis Used to test the likelihood of Used to test the likelihood of

a causal connection among a causal connection among three or more variablesthree or more variables

Structural ModelingStructural Modeling Sophisticated method for Sophisticated method for

exploring and possibly exploring and possibly confirming causation among confirming causation among several variablesseveral variables

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Scatterplot Illustrating a Correlation Scatterplot Illustrating a Correlation of +1.00 of +1.00 (Figure 15.3)(Figure 15.3)

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Prediction Using a ScatterplotPrediction Using a Scatterplot (Figure 15.4)(Figure 15.4)

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Path Analysis Diagram Path Analysis Diagram (Figure 15.5)(Figure 15.5)

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Partial Correlation Partial Correlation (Figure 15.6)(Figure 15.6)

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Scatterplots Illustrating How a Factor Scatterplots Illustrating How a Factor (C) May Not be a Threat to (C) May Not be a Threat to Internal Validity Internal Validity (Figure 15.7)(Figure 15.7)

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Circle Diagrams Illustrating Circle Diagrams Illustrating Relationships Among VariablesRelationships Among Variables

(Figure 15.8)(Figure 15.8)

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Basic Steps in Correlational Basic Steps in Correlational ResearchResearch

Problem selectionProblem selection

Choosing a sampleChoosing a sample

Selecting or Selecting or choosing proper choosing proper instrumentsinstruments

Determining design Determining design and proceduresand procedures

Collecting and Collecting and analyzing dataanalyzing data

Interpreting resultsInterpreting results

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What Do Correlational Coefficients What Do Correlational Coefficients Tell Us?Tell Us?

The meaning of a given correlation coefficient The meaning of a given correlation coefficient depends on how it is applied.depends on how it is applied.

Correlation coefficients below .35 show only a Correlation coefficients below .35 show only a slight relationship between variables.slight relationship between variables.

Correlations between .40 and .60 may have Correlations between .40 and .60 may have theoretical and/or practical value depending on theoretical and/or practical value depending on the context.the context.

Only when a correlation of .65 or higher is Only when a correlation of .65 or higher is obtained, can one reasonably assume an obtained, can one reasonably assume an accurate prediction.accurate prediction.

Correlations over .85 indicate a very strong Correlations over .85 indicate a very strong relationship between the variables correlated.relationship between the variables correlated.

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Threats to Internal ValidityThreats to Internal Validityin Correlational Researchin Correlational Research

Subject Subject characteristicscharacteristics

MortalityMortality LocationLocation Instrument decayInstrument decay

TestingTesting HistoryHistory Data collector Data collector

characteristicscharacteristics Data collector biasData collector bias

The following must be controlled to reduce threats to internal validity