Question

WEIGHT (WT)	WHITE
64.4	8.7
61.8	5.9
78.5	7.3
86.3	6.2
73.1	5.9
58.5	6.4
134.3	3.9
79.8	6.4
64.8	9.8
58.1	4.0
76.1	3.8
118.4	5.6
56.2	6.6
73.4	4.9
126.9	9.6
84.4	8.6
97.8	5.2
66.5	9.2
90.5	6.6
83.7	3.2
88.7	6.9
80.4	7.1
64.0	6.9
65.7	7.0
58.9	8.4
82.4	5.9
85.1	5.1
87.7	10.0
111.9	4.4
70.9	7.1
101.8	7.9
99.0	8.1
100.5	5.6
78.9	4.1
79.2	9.5
86.1	4.9
100.8	8.9
76.4	11.0
77.4	8.6
89.7	6.9

(a) Determine the correlation coefficient between the ‘weight’ data (WT) and the white blood cell count (WHITE).

(b) Is the value you calculated statistically significant?

(c) Why or why not?

Answer 1

a)

X Values - Weight
∑ = 3319
Mean = 82.975
∑(X - M_x)² = SS_x = 13388.355

Y Values - White Blood Cell
∑ = 272.1
Mean = 6.802
∑(Y - M_y)² = SS_y = 148.23

X and Y Combined
N = 40
∑(X - M_x)(Y - M_y) = -163.647

R Calculation
r = ∑((X - M_y)(Y - M_x)) / √((SS_x)(SS_y))

r = -163.647 / √((13388.355)(148.23)) = -0.1162

r = -0.1162

b) No, Not significant

c) X Ranks
Mean: 20.5
Standard Dev: 11.69

Y Ranks
Mean: 20.5
Standard Dev: 11.68

Combined
Covariance = -489 / 39 = -12.54
R = -12.54 / (11.69 * 11.68) = -0.092

r_s = -0.0918, p (2-tailed) = 0.57316 ( looking at the table)

By normal standards, the association between the two variables would not be considered statistically significant.

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