Question

Problem Set 2: Pearson Correlation Coefficient Analysis

Research Scenario: A social worker involved in suicide prevention efforts wants to study the relationship between social isolation and possible suicide risk. She collects scores from a sample of 13 patients on two measures: one is a measure of social isolation on which higher scores indicate higher isolation (possible range of scores = 0- 20), and the other is the Suicide Risk Measure (SRM) (Plutchik et al., 1989), on which higher scores indicate a higher risk of suicide (possible range of scores = 0-15). These scores are listed in the table below.

Using this table, enter the data into a new SPSS data file and run a Pearson correlation coefficient analysis to test whether there is a relationship between social isolation and possible suicide risk. Create a scatterplot to show the relationship between the variables.

Social Isolation X	SRM Y
3 6 8 7 17 2 14 10 7 3 11 9 9	1 3 3 5 11 5 11 10 9 6 5 12 5

Answer 1

	ΣX	ΣY	Σ(x-x̅)²	Σ(y-ȳ)²	Σ(x-x̅)(y-ȳ)
total sum	106.00	86.00	223.69	153.08	118.77
mean	8.15	6.62	SSxx	SSyy	SSxy

correlation coefficient ,    r = SSxy/√(SSx.SSy) =   0.64184
There is moderate positive relationship between given two variables

Ho:   ρ = 0  
Ha:   ρ ╪ 0  
n=   13  
alpha,α =    0.05  
correlation , r=   0.6418  
t-test statistic = r*√(n-2)/√(1-r²) =        2.7760
DF=n-2 =   11  
p-value =    0.0180  
Decision:   p value < α , So, Reject Ho  
correlation coefficient is significant