Question

• A researcher measures the relationship between the number of interruptions during a class and time spent "on task" (in minutes). Answer the following questions based on the results provided.

  Number of Interruptions	Time Spent "On Task"
  8	15
  4	38
  7	18
  2	32

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• Part (a)

  Compute the Pearson correlation coefficient. (Round your answer to three decimal places.)

• Part (b)

  Multiply each measurement of interruptions times 3 and recalculate the correlation coefficient. (Round your answer to three decimal places.)

• Part (c)

  Divide each measurement in half for time spent "on task" and recalculate the correlation coefficient. (Round your answer to three decimal places.)

• Part (d)

  True or false: Multiplying or dividing a positive constant by one set of scores (X or Y) does not change the correlation coefficient. Note: Use your answers in (a) to (c) to answer true or false.

  True False    

Answer 1

Solution:
Pearson Correlation coefficient can be calculated as
Correlation coefficient = (n*Summation(XY) - Summation(X)*Summation(Y))/sqrt((n*Summation(X^2)-(Summation(X))^2)*(n*Summation(Y^2)-(Summation(Y))^2) = ((4*462)-(21*103))/sqrt((4*133-21*21)*(4*3017-103*103)) = -315/sqrt(91*1459) = -0.864

X	Y	X^2	Y^2	XY
8	15	64	225	120
4	38	16	1444	152
7	18	49	324	126
2	32	4	1024	64
21	103	133	3017	462

Solution(b)
Multiply each measurement of interruptions times 3 than table would be

X	Y	X^2	Y^2	XY
24	15	576	225	360
12	38	144	1444	456
21	18	441	324	378
6	32	36	1024	192
63	103	1197	3017	1386

Correlation coefficient = (4*1386)-(63*103)/sqrt(((4*1197)-(63*63))*((4*3017)-(103*103)) = -0.864
Solution(c)
After dividing each measurement in half for time spent "On task" table can be written as

X	Y	X^2	Y^2	XY
8	7.5	64	56.25	60
4	19	16	361	76
7	9	49	81	63
2	16	4	256	32
21	51.5	133	754.25	231

Correlation coefficient = ((4*231)-(21*51.5))/sqrt(((4*133)-(21*21))*(4*754.25)-(51.5*51.5))) = -0.864
Solution(d)
As we can see from the above solutions that Multiplying or dividing a positive constant by one set of scores (X or Y) does not change the coefficient coefficient. This statement is true.