Question

Researchers are looking to compare two groups of patients sampled from two different drug interventions. The columns for group 1 and 2 represent the patient’s addiction scores for the two different interventions while column 3 represents the average susceptibility measures for patients in group 2 (assume normality).

Group 1			Group 2	Susceptibility
5			4	3.56
3			3	2.23
1			4	-4.93
2			5	-4.97
3			4	-1.92
7			1	2.85
6			6	-1.98
5			3	4.35
2			7	-0.44
4			6	-2.48

Calculate the correlation between group 2 addiction score and patient susceptibility. Comment on the strength and the direction of the correlation.

Answer 1

X Values
∑ = 43
Mean = 4.3
∑(X - M_x)² = SS_x = 28.1

Y Values
∑ = -3.73
Mean = -0.373
∑(Y - M_y)² = SS_y = 106.257

X and Y Combined
N = 10
∑(X - M_x)(Y - M_y) = -29.221

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

r = -29.221 / √((28.1)(106.257)) = -0.5348

As we see that correlation is having negative sign which means there is negative correlation between x and y

And as value is -0.5348, there is moderate correlation between x and y