Agriculture Reference
In-Depth Information
The calculated
W
and
W'
statistics indicate the data depart significantly
from normality with
Prob>z
of 0.00000 and 0.00001, respectively.
These tests also give an indication of the departure from normality with
the
V
and
V'
values. The median value is 1 for these indices with a nor-
mally distributed population. The drawback to these tests is the number
of observations must be between 4 ≤ n ≤ 2,000 for the Shapiro-Wilk
test and 5 ≤ n ≤ 5,000 for the Shapiro-Francia test. This is really not
a drawback in most cases, certainly not in most planned experiments.
Finally, two additional tests to consider are the
sktest
and
ladder
.
The former evaluates the skewness and kurtosis for normality combining
the two for an overall test of normality. Enter the following command:
sktest
plantcount seedstems doubles
This results in the following output:
Skewness/Kurtosis tests for Normality
------- joint ------
Variable | Obs Pr(Skewness) Pr(Kurtosis) adj chi2 (2) Prob>chi2
-----------+---------------------------------------------------------
plantcount | 120 0.0000 0.0000 60.57 0.0000
seedstems | 120 0.0000 0.0004 38.18 0.0000
doubles | 120 0.0000 0.0000 . 0.0000
All three variables are significantly different from a normal distribu-
tion. The adjusted chi-square is a measure of deviation from normality.
Using the
ladder
command not only calculates the chi-square
and probability of the data deviating from normality, but also cal-
culates these values for several transformations. Enter the following
command:
ladder
plantcount
This results in the following output:
Transformation formula chi2 (2) P(chi2)
----------------------------------------------------------------
cubic plantc~t^3 . 0.000
square plantc~t^2 . 0.000
identity plantc~t 60.57 0.000
square root sqrt (plantc~t) 26.00 0.000
log log(plantc~t) 1.73 0.420
1/(square root) 1/sqrt (plantc~t) 61.80 0.000
inverse 1/plantc~t . 0.000
1/square 1/(plantc~t^2) . 0.000
1/cubic 1/(plantc~t^3) . 0.000
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