Correlations: Linear Relationships Data What kind of measures are used? interval, ratio nominal Correlation Analysis: Pearson’s r (ordinal scales use Spearman’s rho) Chi-Square Analysis:  2 Do you have more than two predictor variables? NoYesNoYes Regression Analysis: R Log-Linear Analysis Logistic Regression

Interpretation of r If the relationship between X and Y are positive: If the relationship between X and Y are negative: -1< r <1 0 < r < 1 -1 < r < 0 If p-value associated with the r is <.05 The variable X and Y are significantly correlated with each other. Positively: 0 < r < 1, Negatively -1 < r < 0 If p-value associated with the r is >. 05 There is NO significant correlation between X and Y, even if the value of r is positive or negative.

Scatterplots as visual representations of correlations Scatterplot Regression Line High School GPA College GPA A graph in which the x axis indicates the scores on the predictor variable and the y axis represents the scores on the outcome variable. A point is plotted for each individual at the intersection of their scores. A line in which the squared distances of the points from the line are minimized.

Linear Relationships and Nonlinear Relationships YY YYY X X X X X Positive LinearNegative Linear Curvilinear Independent

Limitation 1. Cases in which the correlation between X and Y that have curvilinear relationships r = 0 2. Cases in which the range of variables is restricted. Restriction of RangeExample. SAT scores and college GPA 3. Cases in which the data have outliers r > |.99|

Limitations Curvilinear Restricted Range Outlier