1. Unit 5E Correlation and Causality

2. CORRELATION Heights and weights Study Time and Test Score Available Gasoline and Price of Gasoline A correlation exists between two variables when higher values of one variable consistently go with higher values of another or when higher values of one variable consistently go with lower values of another. EXAMPLES:

3. SCATTER DIAGRAM A scatter diagram is a graph in which each point represents the values of two variables.

4. EXAMPLE OF A SCATTER DIAGRAM Registered Florida Pleasure Craft (in tens of thousands) and Watercraft- Related Manatee Deaths Year1991199219931994199519961997199819992000 x: Boats68 6770717376818384 y: Manatee Deaths 53383549426054678278

5. TYPES OF CORRELATION No correlation – There is no apparent relationship between the two variables. Positive correlation – Both variables tend to increase (or decrease) together. Negative correlation – The two variables tend to change in opposite directions, with one increasing while the other decreases. Strength of a correlation – The more closely two variables follow the general trend, the stronger the correlation. In a perfect correlation, all data points lie on a straight line. Relationships between two variables.

6. NO CORRELATION (a) No correlation between x and y.

7. POSITIVE CORRELATION (b) Positive correlation between x and y (c) Strong positive correlation between x and y (d) Perfect positive correlation between x and y

8. NEGATIVE CORRELATION (e) Negative correlation between x and y (g) Perfect negative correlation between x and y (f) Strong negative correlation between x and y

9. MAKING SCATTER DIAGRAM ON THE TI-83/84 1.Select STAT, 1:Edit…. 2.Enter the x-values for the data in L1 and the y- values in L2. 3.Select 2nd, Y= (for STATPLOT). 4.Select Plot1. 5.Turn Plot1 on. 6.Select the first graph Type which resembles a scatter diagram. 7.Set Xlist to L1 and Ylist to L2. 8.Press ZOOM. 9.Select 9:ZoomStat.

10. CLEARING THE ENTRIES FROM A LIST ON THE TI-83/84 1.Select STAT, 1:Edit…. 2.Use the up arrow to highlight the list that you want to clear. For example, if you want to clear L1, then highlight L1. 3.Press the CLEAR key. 4.Press the ENTER key. The list should now be cleared.

11. POSSIBLE EXPLANATIONS FOR A CORRELATION 1.The correlation may be a coincidence. 2.Both variables might be directly influenced by some common underlying cause. 3.One of the correlated variables may actually be a cause of the other. However, we may have identified only one of several causes!

12. GUIDELINES FOR ESTABLISHING CAUSALITY 1.Look for situations in which the effect is correlated with the suspected cause even while other factors vary. 2.Among groups that differ only in the presence or absence of the suspected cause, check that the effect is similarly present or absent. 3.Look for evidence that larger amounts of the suspected cause produce larger amounts of the effect. To investigate whether a suspected cause actually causes an effect:

13. GUIDELINES (CONCLUDED) 4.If the effect might be produced by other potential causes, make sure that the effect still remains after accounting for these other potential causes. 5.If possible, test the suspected cause with an experiment. If the experiment cannot be performed on humans for ethical reasons, consider doing the experiment with animals, cell cultures, or computer models. 6.Try to determine the physical mechanism by which the suspected cause produces the effect.