# creating 100 random numbers that are normally distributed
# mean is 0, standard deviation is 0
a = rnorm(100,0,1)

# the same for 1000 random numbers with normal distribution
a = rnorm(1000,0,1)

# plot histogram
hist(a)

# plot density
plot(density(a))

# creating both images on top of each other
# second image does not contain axes and labels 
# label size of first image are larger than standard for better readability
hist(a,cex.axis=1.3)
par(new=T)
plot(density(a),xaxt="n",yaxt="n",col=2,lwd=2,main="",xlab="",ylab="")
 
# save image as pdf
dev.print("image.pdf",device=pdf)

# looking up t-value, p=0.95, df = 59
qt(0.95,59)

# calv example
calv.male = c(46,37,39,37,33,48,35)
calv.female = c(27,37,35,41,35,34,43,38,40)
plot(density(calv.male))
plot(density(calv.female))

# boxplot
boxplot(calv.male,calv.female,col=2)

# F-test
var.test(calv.male,calv.female)

# t-test with equal variances
t.test(calv.male,calv.female,var.equal=T)

# t-test with non-equal variances
t.test(calv.male,calv.female) # non-equality is the default