Lesson 4.7 Interpreting the Correlation CoefficientandDistinguishing between Correlation & Causation EQs: How do you calculate the correlationcoefficient?What is the difference betweencorrelation and causation? (S. ID. 8 & 9) Vocabulary: correlation, correlation coefficient,strong/weak positive, strong/weak negative 4.3.2: Calculating and Interpreting the Correlation Coefficient Think-Pair-Share With your partner, come up with anexample of two things that affect eachother (ex. Studying for a test and yourtest grade) and two things that do notaffect each other (ex. Rolling a dieand drawing a card from a deck). 4.3.2: Calculating and Interpreting the Correlation Coefficient Vocabulary A correlation is a relationship between two events,such as x and y, where a change in one event impliesa change in another event. The correlation coefficient, r, is a quantity thatallows us to determine how strong this relationship isbetween two events. It is a value that ranges from 1to 1. 4.3.2: Calculating and Interpreting the Correlation Coefficient Correlation Coefficient (r-value)
The correlation coefficient only assesses the strength of alinear relationship between two variables. The correlation coefficient does not assess causationthatone event causes the other. .51 to 1 0 to .50 -.51 to -1 0 to -.50 4.3.2: Calculating and Interpreting the Correlation Coefficient Correlation vs. Causation
Correlation does not imply causation, or that achange in one event causes the change in the secondevent. If a change in one event is responsible for a change inanother event, the two events have a casualrelationship, or causation. Outside factors may influence and explain a strongcorrelation between two events. 4.3.2: Calculating and Interpreting the Correlation Coefficient Lets Practice!For each scatter plot identify thecorrelation type and coefficient.
4.3.2: Calculating and Interpreting the Correlation Coefficient Guided Practice Example 1
An education research team is interested in determining ifthere is a relationship between a students vocabulary andhow frequently the student reads books. The team gives20 students a 100-question vocabulary test, and asksstudents to record how many books they read in the pastyear. The results are in the table on the next slide. Is therea linear relationship between the number of books readand test scores? Use the correlation coefficient, r, toexplain your answer. 4.3.2: Calculating and Interpreting the Correlation Coefficient Guided Practice: Example 1, continued
Books read Test score 12 23 5 8 3 15 30 19 14 36 9 56 1 13 63 25 4 6 16 78 2 42 7 4.3.2: Calculating and Interpreting the Correlation Coefficient Guided Practice: Example 1, continued
Create a scatter plot of the data. Let the x-axis represent books read and the y-axisrepresent test score. Test score Books read 4.3.2: Calculating and Interpreting the Correlation Coefficient Guided Practice: Example 1, continued
Describe the relationship between thedata using the graphical representation. It appears that the higher scores were from students who read more books, but the data does not appear to lie on a line. There is not a strong linear relationship between the two events. Test score Books read 4.3.2: Calculating and Interpreting the Correlation Coefficient Guided Practice: Example 1, continued
Calculate the correlation coefficient on yourscientific calculator. Refer to the steps in the KeyConcepts section. The correlation coefficient, r, is approximately 0.48. Use the correlation coefficient to describe thestrength of the relationship between the data. A correlation coefficient of 1 indicates a strong positivecorrelation, and a correlation of 0 indicates no correlation. Acorrelation coefficient of 0.48 is about halfway between 1 and 0,and indicates that there is a weak positive linear relationshipbetween the number of books a student read in the past year and his or her score on the vocabulary test. 4.3.2: Calculating and Interpreting the Correlation Coefficient Guided Practice: Example 1, continued
5. Consider the casual relationship betweenthe two events. Determine if it is likely thatthe number of books read is responsible forthe vocabulary test score. Since reading broadens your vocabulary, and althoughthere are other factors related to test performance, it islikely that there is a casual relationship between thenumber of books read and the vocabulary test score. 4.3.2: Calculating and Interpreting the Correlation Coefficient Guided Practice Example 2
Alex coaches basketball, and wants to know if there is arelationship between height and free throw shootingpercentage. Free throw shooting percentage is thenumber of free throw shots completed divided by thenumber of free throws shots attempted: Alex takes some notes on the players in his team, andrecords his results in the tables on the next two slides. 4.3.2: Calculating and Interpreting the Correlation Coefficient Guided Practice: Example 2, continued
Height in inches Free throw % 75 28 76 25 22 70 42 67 30 72 47 80 6 79 24 71 43 69 23 40 27 10 4.3.2: Calculating and Interpreting the Correlation Coefficient Guided Practice: Example 2, continued
Height in inches Free throw % 76 33 75 13 25 71 30 67 54 68 29 79 5 14 55 78 4.3.2: Calculating and Interpreting the Correlation Coefficient Guided Practice: Example 2, continued
Create a scatter plot of the data. Let the x-axis represent height in inches and the y- axis represent free throw shooting percentage. Free throw percentage Height in inches 4.3.2: Calculating and Interpreting the Correlation Coefficient Guided Practice: Example 2, continued
Describe the relationship between thedata using the graphical representation. Free throw percentage Height in inches As height increases, free throw shooting Percentage decreases. It appears that there is a weak negative linear correlation between the two events. 4.3.2: Calculating and Interpreting the Correlation Coefficient Guided Practice: Example 2, continued
Calculate the correlation coefficient on yourscientific calculator. Refer to the steps in theprevious slides. The correlation coefficient, r, is approximately Use the correlation coefficient to describe thestrength of the relationship between the data. A correlation coefficient of 1 indicates a strong negativecorrelation, and a correlation of 0 indicates no correlation. Acorrelation coefficient of 0.727 is close to 1, and indicatesthat there is a strong negative linear relationship betweenheight and free throw percentage. 4.3.2: Calculating and Interpreting the Correlation Coefficient Guided Practice: Example 2, continued
5. Consider the casual relationship,causation, between the two events.Determine if it is likely that height isresponsible for the decrease in free throwshooting percentage. Even if there is a correlation between height and freethrow percentage, it is not likely that height causes abasketball player to have more difficulty making freethrow shots. 4.3.2: Calculating and Interpreting the Correlation Coefficient You Try! Caitlyn thinks that there may be a relationship betweenclass size and student performance on standardized tests.She tracks the average test performance of students from20 different classes, and notes the number of students ineach class in the table on the next slide. Is there a linearrelationship between class size and average test score?Use the correlation coefficient, r, to explain your answer. 4.3.2: Calculating and Interpreting the Correlation Coefficient You Try! Class size Avg. test score 26 28 32 33 36 25 27 30 29 21 19
38 23 41 34 17 43 37 14 42 39 31 4.3.2: Calculating and Interpreting the Correlation Coefficient You Try! Average test score Number of students
4.3.2: Calculating and Interpreting the Correlation Coefficient You Try! Describe the relationship between thedata using the graphical representation. As the class size increases, the average test scoredecreases. It appears that there is a linearrelationship with a negative slope between the two variables. 4.3.2: Calculating and Interpreting the Correlation Coefficient You Try! Calculate the correlation coefficient onyour graphing calculator. Refer to thesteps in the Key Concepts section. The correlation coefficient, r, is approximately 0.84. 4.3.2: Calculating and Interpreting the Correlation Coefficient You Try! Use the correlation coefficient todescribe the strength of the relationshipbetween the data. A correlation coefficient of 1 indicates a strongnegative correlation, and a correlation of 0 indicatesno correlation. A correlation coefficient of 0.84 isclose to 1, and indicates that there is a strongnegative linear relationship between class size and average test score. 4.3.2: Calculating and Interpreting the Correlation Coefficient You Try! 5. Determine if it is likely that class size isresponsible for performance onstandardized tests. Smaller class sizes allow teachers to give each studentmore attention, however, other factors are related totest performance. But we cannot say that smaller classsizes are directly related to higher performance onstandardized tests. Students perform differently on testsregardless of class size. 4.3.2: Calculating and Interpreting the Correlation Coefficient List 3 things you learned this lesson.
3-2-1 List 3 things you learned thislesson. List 2 examples ofcorrelation/causation. List 1 question you still have. 4.3.2: Calculating and Interpreting the Correlation Coefficient