Correlation measures the strength of the relationship between two variables.
Tip: Correlation indicates association, not causation.
Download the data used in this tutorial.
Load CSV data:
df<- read.csv("D:\\R4Researchers\\LAI_factors.csv")
#View(df)
Using the cor() function:
cor(df$LAI_India,df$LST_India, method="pearson")
# -0.5035808 # inversely correlated
Using the cov() function:
cov(df$LAI_India,df$LST_India) #Covariance
# -0.0080975
Pearson correlation coefficient (r)
cor.test(df$LAI_India,df$LST_India, method="pearson")
#Pearson's product-moment correlation
#data: df$LAI_India and df$LST_India
#t = -2.1809, df = 14, p-value = 0.04674
#alternative hypothesis: true correlation is not equal to 0
#95 percent confidence interval:
# -0.79966707 -0.01049536
#sample estimates:
# cor
#-0.5035808
In the above output:
t is the t-test statistic value (t = -2.1809),
df is the degrees of freedom (df = 14),
p-value is the significance level of the t-test (p-value = 0.04674).
conf.int is the confidence interval of the correlation coefficient at 95% (conf.int = [-0.79966707, -0.01049536]);
sample estimates is the correlation coefficient (cor = -0.5035808).
Spearman's rank correlation coefficient (rho)
cor.test(df$LAI_India,df$LST_India, method="spearman")
#data: df$LAI_India and df$LST_India
#S = 1074.7, p-value = 0.01842
#alternative hypothesis: true rho is not equal to 0
#sample estimates:
# rho
#-0.5803983
#Warning message:
#In cor.test.default(df$LAI_India, df$LST_India, method = "spearman") :
# Cannot compute exact p-value with ties
Kendall rank correlation coefficient (tau)
Kendall's tau is the same as Pearson's r and Spearman's rho
cor.test(df$LAI_India,df$LST_India, method="kendall")
#Kendall's rank correlation tau
#data: df$LAI_India and df$LST_India
#z = -2.1475, p-value = 0.03175
#alternative hypothesis: true tau is not equal to 0
#sample estimates:
# tau
#-0.4109547
#Warning message:
#In cor.test.default(df$LAI_India, df$LST_India, method = "kendall") :
# Cannot compute exact p-value with ties
Extract correlation coefficient and p-value from correlation tests:
pe<- cor.test(df$LAI_India,df$LST_India, method="pearson")
# Extract the p.value
pe$p.value
# 0.04673796
# Extract (r) correlation coefficient
pe$estimate
#cor
#-0.5035808
spe<- cor.test(df$LAI_India,df$LST_India, method="spearman")
# Extract the p.value
spe$p.value
# 0.01841523
# Extract (rho) correlation coefficient
spe$estimate
# rho
# -0.5803983
ken<- cor.test(df$LAI_India,df$LST_India, method="kendal")
# Extract the p.value
ken$p.value
# 0.0317547
# Extract (tau) correlation coefficient
ken$estimate
# tau
# -0.4109547
Interpret correlation coefficient
-1 indicates a strong negative correlation.
0 means that there is no association between the two variables.
1 indicates a strong positive correlation.
Based on the previous tests, a significant negative relationship was found between land surface temperature and LAI vegetation index in India.
Create simple data and perform correlations between them:
cor.test(c(1,3,5,7), c(1,3,5,7), method="pearson")
cor.test(c(1,3,5,7), c(1,3,5,7), method='spearman')
cor.test(c(1,3,5,7), c(1,3,5,7), method='kendal')
cor.test(c(1,3,5,7), c(1,3,5,1), method="pearson")
cor.test(c(1,3,5,7), c(1,3,5,1), method='spearman')
cor.test(c(1,3,5,7), c(1,3,5,1), method='kendal')
Matrix of correlations with significance levels
Tip: Usually, statistically significant correlations should be considered.
library(Hmisc)
rcorr(as.matrix(df), type="pearson") # type can be pearson or spearman
rcorr(as.matrix(df), type='spearman') # data should be matrix
IQ score and weekly hours of watching TV
Create data:
iq<- c(86, 97, 99, 100, 101, 103, 106, 110, 112, 113)
tv<- c(2, 20, 28, 27, 50, 29, 7, 17, 6, 12)
Correlation test:
cor.test(iq, tv, method="pearson")
cor.test(iq, tv, method='spearman')
cor.test(iq, tv, method='kendal')
Based on all three tests, no significant correlation was found between IQ score and weekly hours of watching TV.
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