Correlational Methods and Statistics

Correlation  Nonexperimental method that describes a relationship between two variables.  Allow us to make predictions  If smoking is correlated with lung cancer, then we can predict, with some accuracy, that a person who smokes can develop lung cancer.  Used when:  Unethical to conduct experimental study (i.e., smoking condition)  Researchers want to assess the relationship among many variables at once.  Ex: variables that correlate with personality traits

Characteristics of Correlations  Magnitude  strength of the relationship  measured by a correlation coefficient weak moderate strong no relationship

How strong is an association?

Scatterplots  Graphical representation of the relationship between 2 variables. r = -.60

Curvilinear relationship No Correlation Negative Correlation Positive Correlation

Interpretation Difficulties  Only experiments allow us to infer causality and directionality  factor A caused factor B to change.  Correlational studies  no inferences of causality or directionality  “Correlation does not imply causation”  be a critical consumer of information

Third- Variable Problem  Despite strong correlation, the results could be due to something else…  Third-variable problem: the correlation between 2 variables is dependent on another variable.  Ex: teenage delinquency increases with sales of ice-cream

Restrictive Range  Occurs when a variable has limited variability due to restrictions in range exposure to noise (months) exposure to noise (years) Hearing ability

Pearson’s r Duration of Cold symptoms Hours of sleepzColdzHours zCold*zHour s Mean = 4.73Mean = 5.53N = 15SUM = SD = 1.79SD = 1.46r = Population r = ∑ (zA)(zB) __________ N Sample r = ∑ (zA)(zB) __________ N - 1

Alternative correlation coefficients  range of coefficients: -1, 0, + 1  Spearman’s rank order correlation coefficient  both variables are ordinal (ranked)  Point-Biserial  one variable is interval or ratio  other variable is nominal (and has only 2 levels; ex: gender)  Phi  both variables are nominal and have only 2 levels in each.

Regression Analysis  Procedure that allows us to predict an individual’s performance on variable A from knowing variable B.  Determines the best-fitting line for a data set.  Y’ = bX + a  Y’ is the predicted value  b is the slope of a line  X is the subject’s score  a is the Y-intercept

Multiple Regression  Combines several predictor variables into one regression equation.  Allows for access of the effects of multiple predictor variables on a dependent measure.  Represented by “R”  Ex: smoking influences the likelihood of developing cancer, but other factors like genetic predisposition, life style and nutrition can help us predict cancer development.