Agriculture Reference
In-Depth Information
If you examine statistical textbooks, they usually present such
transformations in degrees with the original data often presented as
percentages (i.e., 1-100%). The asin() function in Stata requires that
the input data be in the range of -1 to 1 and the results are presented
as radians. This can easily be accommodated by dividing percent data
by 100. Load the dataset Lettuce Seed Arcsine Transformation.dta
(Little and Hills, 1978, p. 158). This is a dataset of the number of
germinating lettuce seeds in samples of 50 seeds. The experimental
design was a CRD (completely randomized design).
Examine the dataset by using the ladder and oneway commands
with germ as the dependent variable. The ladder command indi-
cates that the dataset is not normally distributed and the oneway com-
mand calculates an ANOVA with Bartlett's test for equal variance. The
assumption that the treatments have equal variance is suspect.
Because this transformation is used with percent data, we will mul-
tiple each data point by 2 so the values are on a scale of 0-100. Then
divide each by 100, so it is in the range that the asin() function
requires. Enter the following command:
generate trangerm = asin(sqrt( germ*2/100 ))
This generates a new variable with the transformed germination data.
Because this is a CRD, we can compare the analysis of the original
data and the transformed data with the oneway command and see
how Bartlett's test differs between them. Enter the commands and
see the results.
oneway germ trt
Original data:
Analysis of Variance
Source SS df MS F Prob > F
----------------------------------------------------------------
Between groups 25265.9861 23 1098.52114 148.12 0.0000
Within groups 356 48 7.41666667
----------------------------------------------------------------
Total 25621.9861 71 360.873044
Bartlett's test for equal variances: chi2(23) = 35.6874
Prob>chi2 = 0.044
Search WWH ::




Custom Search