1. Advanced Math Topics
11.4 The Reliability of “r”

2. 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?

3. 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 =
Round to the nearest ten-thousandth.
Is this value significant or may the correlation
be purely by chance? 10

4. 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

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

6. 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 = vs and 0.707
The correlation is significant.

7. 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.