© 2006 by The McGraw-Hill Companies, Inc. All rights reserved. 1 Chapter 12 Testing for Relationships Tests of linear relationships –Correlation 2 continuous level variables –Regression 2 or more continuous level variables Identifies statistically significant linear patterns in the association of variables

© 2006 by The McGraw-Hill Companies, Inc. All rights reserved. 2 Basic Assumptions Data collected from sample to draw conclusion about population Data from normally distributed population Appropriate variables are selected to be tested using theoretical models Participants randomly selected

© 2006 by The McGraw-Hill Companies, Inc. All rights reserved. 3 Alternative and Null Hypotheses Inferential statistics test the likelihood that the alternative hypothesis is true and the null hypothesis is not Significance level of.05 is generally the criterion for this decision –If p .05, then alternative hypothesis accepted –If p >.05, then null hypothesis is retained

© 2006 by The McGraw-Hill Companies, Inc. All rights reserved. 4 Four Analytical Steps 1. Statistical test determines if a relationship exists 2. Examine results to determine if the relationship found is the one predicted 3. Is the relationship significant? 4. Evaluate the process and procedures of collecting data

© 2006 by The McGraw-Hill Companies, Inc. All rights reserved. 5 Correlation Also known as Pearson product-moment correlation coefficient Represented by r Correlation reveals one of the following: –Scores on both variables increase or decrease –Scores on one variable increase while scores on the other variable decrease –There is no pattern or relationship

© 2006 by The McGraw-Hill Companies, Inc. All rights reserved. 6 Correlation Correlation coefficient or r reveals the degree to which two continuous level variables are related –Participants provide measures of two variables If r is .05, then the relationship is significant – hypothesis or research question accepted Correlation cannot necessarily determine causation –X causes Y –Y causes X –Third variable causes both

© 2006 by The McGraw-Hill Companies, Inc. All rights reserved. 7 Interpreting the Coefficient Direction of relationship Positive- both variables increase or both variables decrease Negative – one variable increases while the other decreases Relationship strength <.20 – slight, almost negligible – low, definite but small – moderate, substantial – high; marked >.90 – very high or dependable

© 2006 by The McGraw-Hill Companies, Inc. All rights reserved. 8 Scale of Correlation

© 2006 by The McGraw-Hill Companies, Inc. All rights reserved. 9 Amount of Shared Variance r 2 – represents the percentage of variance two variables have in common Known as coefficient of determination Found by squaring r.2 or -.2 =.04 r 2.3 or -.3 =.09 r 2.4 or -.4 =.16 r 2.5 or -.5 =.25 r 2.6 or -.6 =.36 r 2.7 or -.7 =.49 r 2.8 or -.8 =.64 r 2.9 or -.9 =.81 r 2

© 2006 by The McGraw-Hill Companies, Inc. All rights reserved. 10 Example of Correlation Matrix

© 2006 by The McGraw-Hill Companies, Inc. All rights reserved. 11 Other Forms of Correlation Point biserial correlation –One continuous level variable, other variable is a dichotomous measure Spearman correlation coefficient or rho –Both variables are ordinal scale data Both interpreted for their direction and strength

© 2006 by The McGraw-Hill Companies, Inc. All rights reserved. 12 Limitations of Correlation Can only examine relationship between 2 variables Any relationship is presumed to be linear Limited in the degree to which inferences can be made –Correlation does not necessarily equal causation –Causation depends on the logic of relationship

© 2006 by The McGraw-Hill Companies, Inc. All rights reserved. 13 Regression Predicts some variables by knowing others Assesses influence of several continuous level predictor, or IVs, on a single continuous criterion, or DV Used to examine causation without experimentation “Variance accounted for” – describes the % of variance in the criterion variable accounted for by the predictor variable

© 2006 by The McGraw-Hill Companies, Inc. All rights reserved. 14 Linear Regression Regression line – line drawn through the data points that best summarizes the relationship between the IV and DV –The better the fit of the line, the higher R Adjusted R 2 - the proportion of variance explained or accounted for on the DV by the IV

© 2006 by The McGraw-Hill Companies, Inc. All rights reserved. 15 Beta Weights Also known as beta coefficients Represented by β Allows comparison among variables of different measuring units Range from to –1.00

© 2006 by The McGraw-Hill Companies, Inc. All rights reserved. 16 Multiple Regression Tests for significant relationship between the DV and multiple IVs –Independently –As a group Common in communication research Use beta weights to interpret the relative contribution of each IV

© 2006 by The McGraw-Hill Companies, Inc. All rights reserved. 17 Other Forms of Regression Hierarchical regression –Researcher enters IVs in the order in which they are theoretically presumed to influence the DV Stepwise regression –Order of variables is determined by statistical program based on the degree of influence each IV has on the DV

© 2006 by The McGraw-Hill Companies, Inc. All rights reserved. 18 Cautions in Using Statistics Use and interpretation of statistical tests is subjective –Many variations of each test –Researcher must interpret statistical result Are the results worth interpreting statistically? Was appropriate statistical test selected and used? Are the results statistically significant? Are the results socially significant?