###LESSON 5 CORRELATION COEFFICIENT (27/4/2021)

library(ISwR)
data(thuesen) 
attach(thuesen)
thuesen
###
#   blood.glucose short.velocity
#1           15.3           1.76
#2           10.8           1.34
#3            8.1           1.27
#4           19.5           1.47
#5            7.2           1.27
#6            5.3           1.49
#7            9.3           1.31
#8           11.1           1.09
#9            7.5           1.18
#10          12.2           1.22
#11           6.7           1.25
#12           5.2           1.19
#13          19.0           1.95
#14          15.1           1.28
#15           6.7           1.52
#16           8.6             NA
#17           4.2           1.12
#18          10.3           1.37
#19          12.5           1.19
#20          16.1           1.05
#21          13.3           1.32
#22           4.9           1.03
#23           8.8           1.12
#24           9.5           1.70

###PEARSON CORR.

shapiro.test(blood.glucose)
shapiro.test(short.velocity)
plot(blood.glucose,short.velocity)
cor(blood.glucose,short.velocity)

cor(blood.glucose,short.velocity,use="complete.obs")
#[1] 0.4167546

cor.test(blood.glucose,short.velocity)

##Pearson's correlation
#data:  blood.glucose and short.velocity
#t = 2.101, df = 21, p-value = 0.0479
#alternative hypothesis: true correlation is not equal to 0
#95 percent confidence interval:
#0.005496682 0.707429479
#sample estimates:
#      cor 
#0.4167546 

###SPEARMAN CORR.
cor(blood.glucose,short.velocity,method="spearman")
cor(blood.glucose,short.velocity,method="spearman",use="complete.obs")
cor.test(blood.glucose,short.velocity,method="spearman")

##Spearman's rank correlation rho

#data:  blood.glucose and short.velocity
#S = 1380.4, p-value = 0.1392
#alternative hypothesis: true rho is not equal to 0
#sample estimates:
#     rho 
#0.318002 

#Warning message:
#In cor.test.default(blood.glucose, short.velocity, method = "spearman") :
#  Cannot compute exact p-value with ties