Agriculture Reference
In-Depth Information
hypothesis or original mean (μ
o
) that represents 5%. There is a second
type of error, the type II error that is often represented as β. A type II
error is when the original mean (μ
o
) is selected when, in fact, the new
mean (μ
1
) or alternate hypothesis is correct. We are not as concerned
about this error because, as we said, the farmer is doing okay with his
current fertilizer rate.
The power of a test is represented by 1-β, which is 80% in this case.
This region of the new mean (μ
1
) represents the region that might be
selected to find a difference or select the alternate hypothesis. If you
slide the new mean (μ
1
) to the right, the power of the test increases
and the ability to detect this new mean also increases. Conversely, if
you slide this mean to the left, the power of the test is reduced.
Going back to our pipe example above and inputting a power value
greater than 0.50 will change the results. A power value of 0.80 results
in a sample size of 32 and a power of 0.90 requires 43 samples.
As mentioned earlier the Z-test has very limited usefulness because it
requires that the population variance be known and this is rarely the case.
For two sample means, the t-test is more often used. Stata offers several
methods of computing a t-test for both one-sample and two-sample data-
sets with either paired or unpaired data. In addition, Stata has an imme-
diate form of the t-test that does not require a dataset for computation.
For a one-sample t-test, enter the following command:
ttest
varname
==
#
[
if
] [
in
] [,
level(
#
)
]
he
varname
is the variable in your dataset you wish to analyze
and the
#
is the arbitrary mean to compare with. The
if
,
in
, and
level(
#
)
are optional.
if
and
in
allow a selection of the observa-
tions to be used while
level(
#
)
can be used to set the confidence
level, which by default is set to 95.
In onion production, an average yield is about 500 40-lb boxes per
acre. This translates into about 55 lbs/plot (120 ft
2
). One way this
command could be used would be to compare this average yield to the
actual yield from an experiment. Open the onionyield03.dta dataset
and enter the following command:
ttest
fieldyield == 55
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