This document discusses measuring linear association between variables through scatterplots and correlation. It defines correlation as a measure of the strength and direction of linear association between two quantitative variables. Correlation values range from -1 to 1, with -1 indicating a perfect negative linear relationship and 1 indicating a perfect positive linear relationship. The document cautions that correlation only measures linear association and provides an example where data sets with identical correlations show different relationships.

2.  Explanatory and response variables
 Displaying relationships: scatterplots
 Interpreting scatterplots
 Adding categorical variables to
scatterplots
 Measuring linear association: correlation
 Facts about correlation

3.  A study of 21 children finds that children who start to
speak when very young are more likely to have high
Gesell test scores than children who start to speak at an
average age, while children who start to speak the
oldest have the lowest Gesell test scores.
 What has been measured?
 Is this an ironclad rule?
 What other variables are lurking in the background?

4.  Example
 AIS data

6.  Form
 Linear Non-linear
 Direction
 Negative Positive
 Strength
 Weak Strong
 Then identify outliers

7.  Example: AIS data.
 The sport of each
athlete is also known.

8.  are X and Y associated with one another?
 does large X go with large Y?
 r = correlation coefficient
= Pearson’s product - moment correlation
=

9.  r is always a number between -1 and +1
 r = -1 perfect negative linear
relationship
 r=0 no linear relationship
 r = +1 perfect positive linear
relationship


10.  *** SPSS Gesell

11.  strength of correlation is not related to its sign
(+ or -)
 correlation of 0.7 is as strong as correlation of -
0.7

13.  Correlation coefficient only tells you about the
strength of a linear association

14.  Example: Anscombe data
 Anscombe (1974) invented four data sets to
illustrate the importance of investigating data
using scatter plots and not relying totally on
the correlation coefficient.
 *** data
 r = 0.816 and = 3.0 + 0.5 x

18.  To study relationships between variables, we must
measure the variables on the same group of
individuals.
 A scatterplot displays the relationship between two
quantitative variables measured on the same
individuals.
 Look for an overall pattern showing the direction, form
and strength of the relationship, and then for outliers
or other deviations from this pattern.
 The correlation measures the strength and direction of
the linear association between two quantitative
variables.