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Chapter 8 Correlational Research (Correlation Coefficients identifies…
Chapter 8
Correlational Research
Definition: Whether and to what degree variables are related
Purpose: Determine relationships
Limitation: Cannot indicate cause and effect
The Process
Problem selection
Variables to be correlated are selected on the basis of some rationale
e.g. Math attitudes and math achievement
e.g. Teachers’ sense of efficacy and their effectiveness
Increases the ability to meaningfully interpret results
Participant
and
instrument
Minimum of 30 subjects
Instruments must be valid and reliable
Design and procedures
Collect data on two or more variables for each subject
Data analysis
Compute the appropriate correlation coefficient
Correlation Coefficients
identifies the size and direction of a relationship
size of correlations
Less than .35 is a low correlation
Between .36 and .65 is a moderate correlation
Above .66 is a high correlation
predictions
Between .60 and .70 are adequate for group predictions
Above .80 is adequate for individual predictions
common variance
The extent to which variables vary
in a systematic manner
Interpreted as the percentage of variance
in the criterion variable explained
by the predictor variable
squared correlation coefficient
statistical significance vs statistical significance
Small correlation coefficients can be statistically significant even though they have little practical significance
Types of correlation coefficients
Pearson r - continuous predictor and criterion variables
e.g. Math attitude and math achievement
Spearman rho – ranked or ordinal predictor and criterion variables
e.g. Rank in class and rank on a final exam
Phi coefficient – dichotomous predictor and criterion variables
e.g. Gender and pass/fail status on a high stakes test
Factors that influence correlations
Sample size
The larger the sample the higher the likelihood of a high correlation
Variation
The greater the variation in scores the higher the likelihood of a strong correlation
The lower the variation in scores the higher the likelihood of a weak correlation
Attenuation
Correlation coefficients are lower when the instruments being used have low reliability
Relationship studies
General purpose
Gain insight into variables that are related to other variables relevant to educators
Two specific purposes
Suggest subsequent interest in establishing cause and effect between variables found to be related
Control for variables related to the dependent variable in experimental studies
Conducting RS:
Identify a set of variables
Identify a population and select a sample
Identify appropriate instruments for measuring each variable
Collect data for each instrument from each subject
Compute the appropriate correlation coefficient
Prediction Studies
Attempts to describe the predictive relationships between or among variables
Purposes
Facilitates decisions about individuals to help a selection decision
Tests variables believed to be good predictors of a criterion
Determines the predictive validity of an instrument
Types of regression
linear: one predictor; one criterion
multiple regression: multiple predictors; one criterion
Issues of concern
Shrinkage – the tendency of a prediction equation to become less accurate when used with a group other than the one on which the equation was originally developed
Cross validation – validation of a prediction equation with another group of subjects to identify problematic variables
Errors of measurement (e.g., low validity or reliability) diminish the accuracy of the prediction
Intervening variables can influence the predictive process if there is too much time between collecting the predictor and criterion variables
Criterion variables defined in general terms (e.g., teacher effectiveness, success in school) tend to have lower prediction accuracy than those defined very narrowly (e.g., overall GPA, test scores)
Differences between studies
Correlational research is a general category that is usually discussed in terms of two variables
Relationship studies develop insight into the relationships between several variables
Predictive studies involve the predictive relationships between or among variables
Other correlation analyses
Path analysis
Investigates the patterns of relationships among a number of variables
Discriminant function analysis
Similar to multiple regression except that the criterion variable is categorical
Cannonical correlation
An extension of multiple regression in which more than one predictor variable and more than one criterion variable are used
Factor analysis
A correlational analysis used to take a large number of variables and group them into a smaller number of clusters of similar variables called factors