Advanced Math Topics 11.4 The Reliability of “r”

This lesson is very similar to and can reinforce sections 11. 2/11 This lesson is very similar to and can reinforce sections 11.2/11.3 as it Is the same principles with one added technique. Yesterday we learned how to compute “r”, the correlation coefficient between two variables. We also learned that as the value of r approaches 1 or -1, the correlation between the two variables is strong and approaches a straight line. But how do we know if the value of “r” is close enough to 1 or -1? We can use Table V in the appendix on page A10 to see if the correlation is significant or not?

464 449 23,396 22,137 22,729 r = 0.9867 10 Remember this example? 1) Find the coefficient of correlation of the following: Math Scores: 52 48 49 26 27 28 24 63 59 44 40 70 72 32 31 49 50 51 49 Business Scores: 464 449 23,396 22,137 22,729 r = 0.9867 Round to the nearest ten-thousandth. Is this value significant or may the correlation be purely by chance? 10

Steps to Determine if r is Significant 1) Compute r using the formula 2) Look in the chart for the appropriate r-value corresponding to a given n (the # of pairs of scores) 3) The value of r is not significant if it is between -r0.025 and r0.025

From the previous example, n = 10. If r is between -0.632 and 0.632, then the correlation between math scores and business scores is not significant. Since r = 0.9867, the correlation is significant.

From the HW: P. 548 9) The table shows the number of years of schooling beyond high school and salary. Find r to determine if there is a correlation between the two variables and determine if it is significant. # Years of Schooling Salary($1000) 2 25 3 27 5 30 1 24 22 7 38 6 33 4 29 r = 0.9739 vs. -0.707 and 0.707 The correlation is significant.

HW: P. 548 #9-12 Find r and see if it is significant for each. Mr HW: P. 548 #9-12 Find r and see if it is significant for each. Mr. Willis can show you an alternative #12 (y = 3x + 5) if you want.