2. Characteristics of Scatterplots
Form
Direction
Strength

3. FORM
Linear
Curvilinear
Clustering
Outliers
Other patterns

4. DIRECTION POSITIVE NEGATIVE
Large values of X are associated with large values of Y, and small values of X are associated with small values of Y.
For example, IQ and SAT.
NEGATIVE
Large values of one variable are associated with small values of the other variable
For example, SPEED and ACCURACY.

5. STRENGTH
If the points do not fall along a straight line, then there is NO linear association.
If the points fall nearly along a straight line, then there is a STRONG linear association.
If the points fall exactly along a straight line, then there is a PERFECT linear association.

17. Dinosaur-bone example

19. How to calculate Pearson’s r

20. How to calculate Pearson’s r

21. How to calculate Pearson’s r

22. How to calculate Pearson’s r

23. The Pearson product-moment correlation coefficient

24. The Pearson product-moment correlation coefficient
Convert the X variable to z scores
Convert the Y variable to z scores
Multiply each pair of z scores
Add up the products and divide by n-1

25. The range of the correlation coefficient-1 +1
perfect
negative
linear
relationship no
positive

37. Outliers and influential cases
An outlier is a case which does not follow the overall pattern of the others
An influential case is one which draws the regression line toward its point in the scatterplot.

43. ESTABLISHING CAUSATION
Association
does not imply
causation

44. When there is association between X and Y
Perhaps X causes Y
Perhaps Y causes X
Perhaps some third variable causes both X and Y

45. COMMON RESPONSE
Two variables might be associated because they share a common cause.
For example, SAT scores and College Grades are highly associated, but probably not because scoring well on the SAT causes a student to get high grades in college.
Being a good student, etc., would be the common cause of the SATs and the grades.

47. CONFOUNDING
For example, there is a strong positive association between Number of Years of Education and Annual Income.
In part, getting more education allows people to get better, higher-paying jobs.
But these variables are confounded with others, such as socio-economic status (SES).

48. ESTABLISHING CAUSATION
The best way to establish that X causes Y is to have a controlled experiment, in which X is varied by the experimenter and the effects on Y can be seen.
But experimentation is not always possible.

49. ESTABLISHING CAUSATION
The association is strong
The association is consistent
Stronger treatments are associated with stronger responses
The alleged cause precedes the effect in time
The alleged cause is plausible