Normality Check

Sameer Mathur

mtcars dataset

# reading the data
attach(mtcars)
head(mtcars)  # first few rows of the data frame

                   mpg cyl disp  hp drat    wt  qsec vs am gear carb
Mazda RX4         21.0   6  160 110 3.90 2.620 16.46  0  1    4    4
Mazda RX4 Wag     21.0   6  160 110 3.90 2.875 17.02  0  1    4    4
Datsun 710        22.8   4  108  93 3.85 2.320 18.61  1  1    4    1
Hornet 4 Drive    21.4   6  258 110 3.08 3.215 19.44  1  0    3    1
Hornet Sportabout 18.7   8  360 175 3.15 3.440 17.02  0  0    3    2
Valiant           18.1   6  225 105 2.76 3.460 20.22  1  0    3    1

For data description column please visit Data Description.

Normality Check -- QQ Plot

qqnorm(mpg)
qqline(mpg)

plot of chunk unnamed-chunk-2

The deviations from the straight line are minimal. We can accept that the data is normally distributed.

Normality Check -- Histogram and Density Curve

hist(mpg,freq=FALSE)
lines(density(mpg), lwd=2)

The histogram confirms the non-normality. The distribution is not bell-shaped but negatively skewed (i.e., most data points are in the lower half). Histograms of normal distributions show the highest frequency in the center of the distribution.

Normality Check -- Histogram and Density Curve

plot of chunk unnamed-chunk-4

Normality Check -- Shapiro-Wilk's Test

shapiro.test(mpg)


    Shapiro-Wilk normality test

data:  mpg
W = 0.94756, p-value = 0.1229

Shapiro-Wilk test indicates that data are normally distributed. The mild skewness indicated by the plots.