Agriculture Reference
In-Depth Information
based on experimental error. In the preface to this handbook, Miles stated that “the tolerances for compar-
ing tests made in different laboratories allow for variation due to the amount of inter-laboratory bias which
existed in the 1950s.” He continued to say that “when the laboratories reduce the inter-laboratory bias (or
variation), the tolerances may be reduced.” He stated that “if the bias is eliminated, the inter-laboratory tol-
erances (e.g., for germination) should be computed from the binomial distribution model based on random
sampling variation only.
The signiicance level is simply deined as the probability of making a wrong decision to reject a good
sample (Type I error or false positive determination); the decision is often made using a speciic probability
value. If the probability value (p-value) is less than the signiicance level, then a Type I error will be made.
The signiicance level is usually represented by the Greek symbol alpha (α). Common signiicance levels
are 5%, 1%, and 0.1%. In general, a person with the authority to establish seed law policies chooses the
probability level. Miles (1963) emphasized that when deciding a probability level, the lower the probability
of type I error, the higher the probability of type II error. That is, decreasing the probability of rejecting a
good seed lot, increases the probability of accepting a poor seed lot.
A one-sided test (also called one-tailed test or one-way test) is a statistical hypothesis in which the
values we can reject are located entirely in one side of the probability distribution curve (Fig. 13.1). Null
hypothesis is the base argument of theory to be tested. For example, in a seed treatment study, we assumed
that our hypothesis was “no difference in germination between treated and non-treated seeds”. The null
hypothesis (H0) was that the mean germination of untreated seed (µ1) is equal to the mean germination of
treated seed (µ2). The alternative hypothesis was that they are not equal (µ1≠ µ2). The one and two-tailed
tests determine whether or not the H0 should be rejected. If we perform the test at 5% level of probability,
it means that there is a 5% chance of rejecting the null hypothesis wrongly.
A two-sided (also called a two-tailed or two-way test) is a statistical hypothesis test in which the
values we can reject the null hypothesis (H0) are located in both sides of the probability distribution curve
(Fig. 13.1). In other words, the critical region for a two-tailed test is the set of values less than a “small”
critical value of the test and the set of values “greater” than a second critical value of the test. For example,
a one-sided test would be appropriate for “Noxious weed seed tolerance” since no argument would be made
if a second test found the number of noxious weed seeds is less than the number stated on the label or found
in a irst test. However, for a proiciency or quality control test, a two-tailed test would be appropriate for we
would like to know whether laboratories reported signiicantly “lower” or “higher” results than a particular
value.
Miles developed both one-sided and two-sided tolerance tables for purity, adulteration by foreign
seeds (noxious weed seed), germination, pure-live seed, and trueness to variety. These remain as milestones
in the history of seed testing and constitute the foundations for most AOSA and ISTA tolerances today. He
suggested that the following nine questions must be answered before the proper tolerance table or column
in a table can be selected:
1. What is the attribute under consideration? I.e., purity, germination, etc.
2. Is the seed chaffy or nonchaffy, when the attribute is purity or pure-live seed?
3. Is the lot a mixture of seeds of different sizes by weight when the attribute is purity?
4. Are both values to be compared as estimates or is only one an estimate and the other a speciication?
5. Should a one-sided test or a two-sided test be used?
6. For each estimate, what size was the sample? (a) For purity, how many working samples and how
many submitted samples were used for an estimate? (b) For foreign seed, what was the weight of
seed examined? (c) For germination, how many seeds were tested?
7. Were germination estimates made in the same or in different laboratories?
8. What probability of error is to be used?
9. What do the samples represent?
