Correlations Linear Relationships Data What kind of measures

Correlations: Linear Relationships Data What kind of measures are used? nominal interval, ratio Do you have more than two predictor variables? No Yes Correlation Analysis: Pearson’s r Do you have more than two predictor variables? No Yes Chi-Square Analysis: 2 (ordinal scales use Spearman’s rho) Regression Analysis: R Log-Linear Analysis Logistic Regression

Interpretation of r -1< r <1 If the relationship between X and Y are positive: If the relationship between X and Y are negative: 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 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. Regression Line A line in which the squared distances of the points from the line are minimized. 4. 0 3. 0 2. 0 1. 0 2. 0 3. 0 4. 0 High School GPA

Linear Relationships and Nonlinear Relationships Y Y Positive Linear X Y Negative Linear Y Curvilinear X X Y Curvilinear X Independent X

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. Example. SAT scores and college GPA Restriction of Range 3. Cases in which the data have outliers r > |. 99|

Limitations Curvilinear Restricted Range Outlier