Reviewing a paper that uses a shapiro-wilk test to see if their response variable is normally distributed before using linear regression. This is not necessary! Linear regression does not assume a normally distributed response, it's the residuals that are normally distributed.
ALT
set.seed(3)
n <- 500
# create covariate
covariate <- runif(n, -10, 10)
# generate response variable
y <- rnorm(n, 1 + 2 * covariate, 5)
# oh no, not normally distributed (p < 0.05)!
shapiro.test(y)
# Shapiro-Wilk normality test
#
# data: y
# W = 0.98609, p-value = 0.0001039
# fit linear regession anyways
m1 <- lm(y ~ covariate)
# get model residuals, this is what we assume to be
# normally distributed.
m_resid <- resid(m1)
# oh wow, normally distributed (p > 0.05)!
shapiro.test(m_resid)
# Shapiro-Wilk normality test
#
# data: m_resid
# W = 0.99728, p-value = 0.5847