shapiro.test() function performs normality test of a data set with hypothesis that it's normally distributed.

shapiro.test(x)

x: numeric data set
...

Let's generate 100 random number near the range of 0, and to see whether they are normally distributed:

> x <- rnorm(100, mean=0)
> shapiro.test(x)

Shapiro-Wilk normality test
data: x
W = 0.9879, p-value = 0.5011

Since the p-value is > 0.05, it is accepted the dataset is normally distributed.

Let's check the CO2 dataset, Carbon Dioxide Uptake in Grass Plants, to see whether the CO2 uptake is normally distributed.

> CO2

Plant Type Treatment conc uptake
1 Qn1 Quebec nonchilled 95 16.0
2 Qn1 Quebec nonchilled 175 30.4
3 Qn1 Quebec nonchilled 250 34.8
4 Qn1 Quebec nonchilled 350 37.2
5 Qn1 Quebec nonchilled 500 35.3
6 Qn1 Quebec nonchilled 675 39.2
7 Qn1 Quebec nonchilled 1000 39.7
8 Qn2 Quebec nonchilled 95 13.6
9 Qn2 Quebec nonchilled 175 27.3
10 Qn2 Quebec nonchilled 250 37.1
11 Qn2 Quebec nonchilled 350 41.8
12 Qn2 Quebec nonchilled 500 40.6
13 Qn2 Quebec nonchilled 675 41.4
14 Qn2 Quebec nonchilled 1000 44.3
15 Qn3 Quebec nonchilled 95 16.2
16 Qn3 Quebec nonchilled 175 32.4
17 Qn3 Quebec nonchilled 250 40.3
18 Qn3 Quebec nonchilled 350 42.1
19 Qn3 Quebec nonchilled 500 42.9
20 Qn3 Quebec nonchilled 675 43.9
21 Qn3 Quebec nonchilled 1000 45.5
22 Qc1 Quebec chilled 95 14.2
23 Qc1 Quebec chilled 175 24.1
24 Qc1 Quebec chilled 250 30.3
25 Qc1 Quebec chilled 350 34.6
26 Qc1 Quebec chilled 500 32.5
27 Qc1 Quebec chilled 675 35.4
28 Qc1 Quebec chilled 1000 38.7
29 Qc2 Quebec chilled 95 9.3
30 Qc2 Quebec chilled 175 27.3
31 Qc2 Quebec chilled 250 35.0
32 Qc2 Quebec chilled 350 38.8
33 Qc2 Quebec chilled 500 38.6
34 Qc2 Quebec chilled 675 37.5
35 Qc2 Quebec chilled 1000 42.4
36 Qc3 Quebec chilled 95 15.1
37 Qc3 Quebec chilled 175 21.0
38 Qc3 Quebec chilled 250 38.1
39 Qc3 Quebec chilled 350 34.0
40 Qc3 Quebec chilled 500 38.9
41 Qc3 Quebec chilled 675 39.6
42 Qc3 Quebec chilled 1000 41.4
43 Mn1 Mississippi nonchilled 95 10.6
44 Mn1 Mississippi nonchilled 175 19.2
45 Mn1 Mississippi nonchilled 250 26.2
46 Mn1 Mississippi nonchilled 350 30.0
47 Mn1 Mississippi nonchilled 500 30.9
48 Mn1 Mississippi nonchilled 675 32.4
49 Mn1 Mississippi nonchilled 1000 35.5
50 Mn2 Mississippi nonchilled 95 12.0
51 Mn2 Mississippi nonchilled 175 22.0
52 Mn2 Mississippi nonchilled 250 30.6
53 Mn2 Mississippi nonchilled 350 31.8
54 Mn2 Mississippi nonchilled 500 32.4
55 Mn2 Mississippi nonchilled 675 31.1
56 Mn2 Mississippi nonchilled 1000 31.5
57 Mn3 Mississippi nonchilled 95 11.3
58 Mn3 Mississippi nonchilled 175 19.4
59 Mn3 Mississippi nonchilled 250 25.8
60 Mn3 Mississippi nonchilled 350 27.9
61 Mn3 Mississippi nonchilled 500 28.5
62 Mn3 Mississippi nonchilled 675 28.1
63 Mn3 Mississippi nonchilled 1000 27.8
64 Mc1 Mississippi chilled 95 10.5
65 Mc1 Mississippi chilled 175 14.9
66 Mc1 Mississippi chilled 250 18.1
67 Mc1 Mississippi chilled 350 18.9
68 Mc1 Mississippi chilled 500 19.5
69 Mc1 Mississippi chilled 675 22.2
70 Mc1 Mississippi chilled 1000 21.9
71 Mc2 Mississippi chilled 95 7.7
72 Mc2 Mississippi chilled 175 11.4
73 Mc2 Mississippi chilled 250 12.3
74 Mc2 Mississippi chilled 350 13.0
75 Mc2 Mississippi chilled 500 12.5
76 Mc2 Mississippi chilled 675 13.7
77 Mc2 Mississippi chilled 1000 14.4
78 Mc3 Mississippi chilled 95 10.6
79 Mc3 Mississippi chilled 175 18.0
80 Mc3 Mississippi chilled 250 17.9
81 Mc3 Mississippi chilled 350 17.9
82 Mc3 Mississippi chilled 500 17.9
83 Mc3 Mississippi chilled 675 18.9
84 Mc3 Mississippi chilled 1000 19.9

> y <- CO2[,5]
> shapiro.test(y)

Shapiro-Wilk normality test
data: y
W = 0.941, p-value = 0.0007908

Since the p-value is smaller than 0.05, it's rejected that the CO2 uptake is normally distributed.