Chapter 4: Describing the relation between two variables Univariate data: Only one variable is measured per a subject. Example: height. Bivariate data: Two variables are measured per a subject. Example: height and weight. This chapter deals with bivariate data.

Section 4.1: Scatter diagrams and correlation Scatter diagrams(plots) show the data. Correlation is a statistic measuring linear relationship between x and y variables.

Quantitative bivariate data are usually displayed in a scatter plot (also called scatter diagram).

The “X” variable is called many names: Explanatory variable Predictor variable Independent variable Weeks of gestation is our x-variable here.

The “Y” variable is also called many names: Response variable Dependent variable Outcome variable Birth weight is our y-variable here.

When trying to determine which variable you should put on the x or y axes, think “cause and effect”. The “cause” variable should be on the x-axis. The “effect” variable should be on the y-axis.

Sample correlation coefficent (Also called “linear” or “Pearson product moment” correlation coefficient) -1 <= r <= 1

If the slope is negative, r 1 r=-1 or 1 means all points lie on straight line. Bottom row shows pattern, but it’s not linear.

Practice: xy n=? Mean(x)=? Mean(y)=? SD(x)=? SD(y)=? x’s z-scoresy’s z-scores

Practice: xy n=? Mean(x)=? Mean(y)=? SD(x)=? SD(y)=? x’s z-scoresy’s z-scores n=3 Mean(x)= 6, Mean(y)=3 SD(x) = 2, SD(y)=3 r=0.5

Correlation=? (A) 0 (B) 0.41 (C) 0.97 (D) 1

A) -1.2 B) -1 C) D) 100

A) -1 B)-0.99 C) -0.5 D) -0.25

A) -1 B) +0.5 C) +1 D) 100

A) -0.9 B) C) +0.9 D) +1

A) B) C) D) +1

A) -1 B) C) +1 D) +1.5

A) B) -0.2 C) D) 1

A) -1 B) C) D) +1