Spearman

Spearman correlation test

corr.test function

Install R package psych

update.packages() # update all installed R packages

install.packages('psych') # download and install

Spearman correlation test

# import 'psych' package

library(psych)

# generate a test data set (data.frame table)

x1 = sample(100:200,10)

x2 = sample(100:200,10)

x3 = sample(100:200,10)

y1 = sample(1000:2000,10)

y2 = sample(1000:2000,10) + 10*x1 # create correlation between x1 and y2

mydata = data.frame(x1,x2,x3,y1,y2)

rownames(mydata) <- letters[1:10]

mydata

x1 x2 x3 y1 y2

a 116 187 123 1741 2557

b 171 179 180 1128 2970

c 189 136 158 1898 3524

d 194 134 159 1683 3528

e 145 170 161 1498 2676

f 168 125 156 1078 3190

g 177 190 119 1360 2806

h 119 181 184 1032 2402

i 109 130 176 1605 2406

j 138 139 118 1460 2850

# Spearman correlation - pairwise between all columns of a table

spearman <- corr.test(mydata, method="spearman", adjust="none")

spearman$r # Correlation matrix

x1 x2 x3 y1 y2

x1 1.00000000 -0.09090909 -0.13939394 0.1272727 0.8545455

x2 -0.09090909 1.00000000 -0.09090909 -0.1393939 -0.4424242

x3 -0.13939394 -0.09090909 1.00000000 -0.2606061 -0.2848485

y1 0.12727273 -0.13939394 -0.26060606 1.0000000 0.2484848

y2 0.85454545 -0.44242424 -0.28484848 0.2484848 1.0000000

spearman$p # p-values (significant correlation < 0.05)

x1 x2 x3 y1 y2

x1 0.000000000 0.8027717 0.7009319 0.7260570 0.001636803

x2 0.802771731 0.0000000 0.8027717 0.7009319 0.200422687

x3 0.700931885 0.8027717 0.0000000 0.4670891 0.425038155

y1 0.726057015 0.7009319 0.4670891 0.0000000 0.488776305

y2 0.001636803 0.2004227 0.4250382 0.4887763 0.000000000

Correlation between two datasets

# Spearman correlation - only between columns of two different tables

# same, but data spitted into two tables

x = mydata[1:3]

y = mydata[4:5]

spearman <- corr.test(x, y, method="spearman", adjust="none")

spearman$r # Correlation matrix, only of x and y column-pairs

y1 y2

x1 0.1272727 0.8545455

x2 -0.1393939 -0.4424242

x3 -0.2606061 -0.2848485

spearman$p # p-values

y1 y2

x1 0.7260570 0.001636803

x2 0.7009319 0.200422687

x3 0.4670891 0.425038155

A p-value < 0.05 shows a strong evidence for a correlation between x and y.

Bonferroni correction for multiple comparison

# Spearman correlation - Bonferroni correction for multiple comparison

spearman <- corr.test(x, y, method="spearman", adjust="bonferroni")

spearman$r # Correlation matrix (same values)

y1 y2

x1 0.1272727 0.8545455

x2 -0.1393939 -0.4424242

x3 -0.2606061 -0.2848485

spearman$p # p-values (corrected/adjusted N*p)

y1 y2

x1 1 0.00982082

x2 1 1.00000000

x3 1 1.00000000

# alternative correction methods: "fdr", "bonferroni", "hochberg", "holm", "hommel", "BH", "BY", "none"

Correlation plot (circle heatmap): R package corrplot

# install (if not already done)

update.packages() # update all installed R packages

install.packages('corrplot') # download and install

# plot correlations

library(corrplot)

corrplot(spearman$r, method = "circle")

# save as pdf

dev.copy(pdf, 'fig_corrplot.pdf', width = 6, height = 6)

dev.off()