Question

Your task as a social worker is to decide which of two programs to use to help troubled teens. The scores below reflect how well (or poorly) each of the programs performed in the past for 16 individuals (8 who participated in Program A, and 8 who participated in Program B) (i.e., their outcomes). (0 = very poor outcomes, 5 = average outcomes, 10 = very good outcomes).

•          Program A (Outcomes for 8 individuals): 0, 0, 0, 3, 5, 7, 8, 9

•          Program B (Outcomes for 8 individuals): 2, 3, 3, 4, 4, 4, 5, 5

[Note: the values do NOT represent a sequence over time, just the final result for each of the 16 individuals who participated]

Based on these results, which program would you support? Why? Support your position with 1 statistic that you have learned. (Please select a statistic from chapters 1-4---do NOT use z scores for this exercise)

Answer 1

Program A:

Mean of program A = = =(0+0+....+9)/8 =32/8 =4

Standard deviation of A =S_A = =3.7796

Coefficient of variation for program A =CV(A) =S_A/ =3.7796/4 =0.9449 =94.49%

Program B:

Mean of program B = = =(2+3+....+5)/8 =30/8 =3.75

Standard deviation of B =S_B = =1.0351

Coefficient of variation for program B =CV(B) =S_B/ =1.0351/3.75 =0.2760 =27.60%

Conclusion:

I would support program B because CV(B) < CV(A).

That is, 27.60% is less than 94.49% which tells us that program B is more consistent than A as the coefficient of variation for program B is less than that of A.