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© 2011 Pearson Education, Inc. All rights reserved. 2 Correlations Human (logical) thought tends to reflect linearity If “A” Measures of relationship between variables Can permit future predictions of one variable from knowledge of another Can raise questions about cause-and-effect patterns (can only be established with experimental research) then “B”

© 2011 Pearson Education, Inc. All rights reserved. 3 The Nature of Correlational Research Purpose is to discover corelationships between two or more variables; seeks out conditions that covary, or correlate, with each other A corelationship exists when an individual’s status (score) on one variable tends to reflect the status (score) on another Correlations help us: » Understand related events, behaviors, etc. » Predict future events, etc. from what we know about another » Sometimes obtain strong suggestions that one variable may be causing another

© 2011 Pearson Education, Inc. All rights reserved. 4 Cautions about Cause-and-Effect… Post hoc fallacy, Post hoc ergo propter hoc. “after the fact, because of the fact” » The “cause” can actually be the “effect” (or vice versa) » This is a common fallacy of logical thinking

© 2011 Pearson Education, Inc. All rights reserved. 5 Topics for Correlational Research If a relationship is suspected If you wish to predict values on one variable from another If you need to establish instrument validity or reliability

© 2011 Pearson Education, Inc. All rights reserved. 6 Correlational Research Design Typically oriented by research questions or hypotheses A relatively straightforward design: » Identify variables for inclusion » Formulate questions or hypotheses » Select a random sample (preferably with n > 30) » Obtain data for each member of the sample on each variable being investigated » Compute correlations in order to determine degree of relationship

© 2011 Pearson Education, Inc. All rights reserved. 7 Types of Bivariate (2 variables) Correlation Coefficients Pearson product-moment correlation (a.k.a., Pearson r or r )—correlation between two continuous variables Biserial correlation —one continuous variable and one artificial dichotomous variable Point-biserial correlation —one continuous variable and one natural dichotomous variable Phi correlation (  )—two natural dichotomous variables Tetrachoric correlation —two artificial dichotomous variables

© 2011 Pearson Education, Inc. All rights reserved. 8 Types of Bivariate (2 variables) Correlation Coefficients (cont’d.) Spearman rho ( r s )—two ranked variables, with larger samples Kendall’s tau (  )—two ranked variables, with samples < 10

© 2011 Pearson Education, Inc. All rights reserved. 9 Types of Multivariate (> 2 variables) Correlation Coefficients Partial correlation (partial r )—correlation between two variables with the effects of a third variable “partialed out” Multiple regression —used to determine degree of relationship between one continuous dependent variable (“ criterion variable ”) and a combination of independent variables (“ predictor variables ”) Discriminant analysis —analogous to MR, but criterion variable is categorical (e.g., “pass-fail”) Factor analysis —used with a large number of correlated variables; variables are statistically grouped into clusters, known as “ factors”

© 2011 Pearson Education, Inc. All rights reserved. 10 Interpretation of Correlation Coefficients Most coefficients range from to (some range from 0 to +1.00)  1.00 = a perfect correlation/relationship; 0 = no correlation/relationship General rule of thumb for interpretation: | | | | | | | weak relationship moderate relationship strong relationship moderate relationship strong relationship

© 2011 Pearson Education, Inc. All rights reserved. 11 Published Example of Correlational Research “Influence of Reading Attitude on Reading Achievement: A Test of the Temporal-Interaction Model”

© 2011 Pearson Education, Inc. All rights reserved. Dr. Rousey’s discussion of "Correlational Research" ( A second page of examples from Dr. Rousey ( 12 Applying Technology… Web sites related to correlational research

© 2011 Pearson Education, Inc. All rights reserved. 13 Causal-Comparative Research Explores the possibility of cause-and-effect relationships when experimental and quasi- experimental approaches are not feasible Used when manipulation of the independent variable is not ethical or is not possible

© 2011 Pearson Education, Inc. All rights reserved. 14 The Nature of Causal-Comparative Research Conducted to explore possible cause-and-effect relationships Differs from experimental and quasi-experimental research: »Independent variable is not manipulated »Focuses first on the effect, then tries to determine possible causes ( ex post facto ) Questions will remain about the effect following the cause, or vice versa Other conditions must also be considered as “plausible causes”

© 2011 Pearson Education, Inc. All rights reserved. 15 “Blended Learning and Sense of Community: A Comparative Analysis with Traditional and Fully Online Graduate Courses” Published Example of Causal- Comparative Research