Two Sample Tests - Agricultural Statistical Data Analysis Using Stata - page 66

types of statistics. Differences between means in a statistical context
are determined by the probability of one mean occurring in the space
of another. Statisticians often refer to this concept in the context of
committing errors in favor of one mean over another. Two types of
errors can be identified and are often referred to as type I and type II
errors. A type I error, often denoted as α, is an error where the alter-
nate hypothesis is wrongly chosen over the null or current hypothesis.
This may be better understood in the context of an experiment.
Let's say a farmer is using a specific fertilizer rate and is producing his
crop in a satisfactory manner (he's making money). In a statistical con-
text, this fertilizer rate would be the null hypothesis or original mean.
As a researcher, you think that a different rate may be better. This
new rate would be considered the alternate hypothesis or new mean.
Because your farmer is successful with what he is currently doing, as
a researcher you don't want to recommend a different rate unless you
are sure it will work. If you recommended a different rate and this
was incorrect, that would be a type I error. See Figure 4.1 to see how
this is represented graphically. As a researcher you want to minimize
type I errors so the probability of committing this type of error is kept
low. By convention, 5% or 1% are often used. In Figure 4.1, the type
I error rate (or α) is shown as the area under the curve for the null

5%

µ 0 α

80%

20%

β µ 1

Figure 4.1 Original mean (μ 0 ) or null hypothesis compared to the new mean (μ 1 ) or alternate
hypothesis. α and β represent the type I and type II errors, respectively. 1- β , 80% in this case,
represents the power of the test.