1. Spearman’s Rank Correlation
:1, 1, 3

2. Spearman’s Rank Correlation Coefficient
Measures correlation between ranks
Corresponds to Pearson product moment correlation coefficient
Values range from –1 to +1
Formula (shortcut)
di = ui – vi (difference in ranks of ith observation
for samples 1 and 2)
n = number of pairs of observations

3. Spearman’s Rank Correlation Procedure
Assign ranks, Ri , to the observations of each variable separately
Calculate differences, di , between each pair of ranks
Square differences, di2, between ranks
Sum squared differences for each variable
Use shortcut approximation formula

4. Spearman’s Rank Correlation Example
You’re a research assistant for the FBI. You’re investigating the relationship between a person’s attempts at deception and percent changes in their pupil size. You ask subjects a series of questions, some of which they must answer dishonestly. At the .05 level of significance, what is the correlation coefficient?
Subj. Deception Pupil size
112

5. Spearman’s Rank Correlation Table2
Subj.
Decep.
R1i
Pupil
R2i di di 1 87 10 2 63 6 3 95 11 4 50 7 5 43 4 4 1 -1 1 2 3 2 5 5 2 3 1 1
Σdi2=

6. Spearman’s Rank Correlation Solution

7. Correlation using Rstudio
Hours, x 1 2 3 5 6 7 10
Test score, y 96 85 82 74 95 68 76 84 58 65 75 50
x<- c(0, 1, 2, 3, 3, 5, 5, 5, 6, 7, 7, 10)
y<- c(96, 85, 82, 74, 95, 68, 76, 84, 58, 65, 75, 50)
cor(x,y)
[1]
cor.test(x,y)
data: x and y
t = , df = 10, p-value =
alternative hypothesis: true correlation is not equal to 0
95 percent confidence interval:
sample estimates:
cor

8. Plot X and Y using Rstudio
Hours, x 1 2 3 5 6 7 10
Test score, y 96 85 82 74 95 68 76 84 58 65 75 50
x<- c(0, 1, 2, 3, 3, 5, 5, 5, 6, 7, 7, 10)
y<- c(96, 85, 82, 74, 95, 68, 76, 84, 58, 65, 75, 50)
cor(x,y)
[1]
cor.test(x,y)
data: x and y
t = , df = 10, p-value =
alternative hypothesis: true correlation is not equal to 0
95 percent confidence interval:
sample estimates:
cor

9. cor(x, y = NULL, use = "everything",
method = c("pearson", "kendall", "spearman"))
Dec<-c(87,63,95,50,43)
Pup<-c(10,6,11,7,0)
Data<-data.frame(cbind(Dec, Pup))
cor(Dec, Pup, method="spearman")