Tolerances in the Testing of Seeds

OREN L. JUSTICE AND EARL E. HOUSEMAN.

NO TWO samples taken from the same seed bag or same seed lot are likely to be identical. In well-mixed seeds, the particles that make up the lot are randomly distributed, and the variation from sample to sample is limited. Inadequate mixing interferes with random distribution and so lowers the chances of getting a representative sample from the lot.

The size of a lot of seeds may vary from a pound or two of cauliflower or other expensive seed to one or more carloads of alfalfa or wheat. A carload lot of alfalfa seeds contains more than a billion seeds.

Can the germination of this carload lot be determined by testing only 400 seeds or the percentage of pure seeds by testing 3 thousand seeds, or the number of noxious-weed seeds by testing 30 thousand seeds?

By testing all the seeds in the lot, the actual quality can be determined. For obvious reasons, we must content ourselves with testing a relatively small sample to determine within calculated limits the quality of the lot. By "quality of the lot" we mean the average of the entire lot for each quality factor, such as the percentage of pure seed and germination.

Actual percentages of germination, pure seed, or other quality factors cannot be determined. The application of appropriate statistical methods to test results enables us to determine the quality of the lot within a calculated range of limits. In testing seeds, the amount of this range is called the tolerance. It is the expected variation resulting from incomplete mixing of the seed, variations in sampling, and uncontrolled differences in the application of testing procedures.

A TOLERANCE, or expected variation, is expressed in terms of a probability and the amount of the tolerance. We are all familiar with games involving chance and frequently speak of odds. Probability, or probability level, carries the same connotation as odds.

Probabilities are expressed as odds (100 to 1), as percentages (1-percent level), or as decimals (0.01).

The figures in parentheses mean that the result of a subsequent test has a chance of about 1 out of 100 of exceeding the tolerance. In some kinds of work, tolerances that may be exceeded as often as once in 20 trials, the 5-percent level, may be satisfactory. Other types of work require a greater degree of confidence. Tolerances computed at the 1 -percent level are greater than those computed at the 5-percent level.

If a representative sample from a well-mixed lot of alfalfa seeds germinates 88 percent in a properly conducted test, the average germination for the entire lot is not necessarily 88 percent. If a second sample is drawn from the lot and properly tested, however, the chances are approximately 20 to 1, according to statistical tolerances calculated by C. W. Leggatt, that the result of the second test will not go below 83.1 percent. The chances are also approximately 40 to 1 that the result of the second test will not fall below 82.4 percent, and approximately 100 to 1 that it will not fall below 80.8 percent. Any sample drawn from this seed lot would be expected to yield results which would fall into this statistical pattern.

The magnitude of tolerances at any given probability level will depend on the percentage of the seed component in the sample for which the tolerance is desired, the variations associated with testing procedures, the characteristics of the seed, and the size of sample tested. It also will depend on whether tolerances are intended to cover the difference between a test and a predetermined standard.

The minimum germination standards that have been established for vegetable seeds are an example of the latter. Because the standard is a fixed figure, only one test can vary.

In the other situation, a seedsman labels his seeds on the basis of a single test. A seed control agency later samples and tests the seeds. In this instance, results of two independent tests are being compared, both of which are subject to variation.

CERTAIN BASIC PRINCIPLES Must prevail if the tolerances are to be used properly.

The seed lot from which the sample is drawn should be relatively homogeneous. The sample must be drawn in a random manner from a sufficient number of containers or locations in the lot. Bias must be avoided insofar as possible in conducting tests. Random sampling assumes that each seed or particle in the seed lot has an equal chance of being drawn and that no selection of any type is exercised.

If we assume that a seed lot has been reasonably well mixed, a sample was drawn at random, and a proper test was made, a single test will indicate that in a specified number of cases, say, 95 in 100 or 99 in 100, the true value of the lot is no more than one tolerance range removed from the result of the test. This value may be either higher or lower than the test result. If the seedsman labels his seeds with the result obtained by a proper test, results of later tests should be within tolerance of his statement.

The probability statement allows for an occasional test result to exceed the tolerance range. The number of these exceptions is indicated in the probability statement. When results do exceed the tolerance range, additional tests should be made to determine the cause of the excessive variation.

The purity tolerances were used as early as 1889, only 20 years after the first seed-testing station was established. At this time H. Rodewald, a German, showed that the variation in results of purity and germination tests of red clover agreed well with theoretical expectations.

He recognized several sources of error that led to variation in test results. They included difference in technique, change in the material being tested, accidents, and personal factors. The errors were classified as systematic errors or accidental errors. In testing seeds of orchardgrass for purity, he found the total error to be twice the accidental error, whereas the total error was only 1.4 times as great as the accidental error for red clover.

C. P. Smith, of the University of Maryland, in 1917 proposed arbitrary tolerances for percentages of pure seed.

His formula was based on the premise that the sample was composed of the component under consideration and the sum of all other components. His original formula was simplified to: T (tolerance) =0.2+20 percent of the lesser part divided by 100, the lesser part meaning the component under consideration or the sum of all other components, whichever is smaller. It was adopted by the Association of Official Seed Analysts in 1917 and used until 1938.

G. N. Collins, of the Department of Agriculture, published a circular in 1929 under the title, "The Application of Statistical Methods to Seed Testing." He proposed formulas for calculating purity and germination tolerances on the basis of the binomial distribution and for calculating noxious-weed seed tolerances on the basis of the Poisson distribution. Although Dr. Collins' formulas were evidently sounder, they were not adopted by seed analysts' organizations.

The International Seed Testing Association adopted in 1932 for the pure seed component the formula:

T=0.6+ ( 0.2 axb/100 ), where a equals the percentage of the component under consideration and b equals 100 a. The tolerances for other crop seeds, weed-seeds, and inert matter were calculated by the same formula, except that 0.2 was substituted for 0.6. These formulas were used in the Rules and Regulations under the Federal Seed Act from 1940 and in the Rules for Testing Seeds of the Association of Official Seed Analysts from 1944. Apparently the first term in the formula was intended to cover or compensate for errors incident to testing and the second term to take care of variations associated with random sampling. Tolerances calculated by these formulas have been used for nonchaffy seeds.

Wider tolerances are required for chaffy grass seeds which do not blend so well. These tolerances are obtained by adding to the tolerances calculated by the above formulas an additional tolerance. It is obtained by multiplying the lesser of a and b by the regular tolerance and dividing by 100.

Completely new purity tolerances were accepted by the Association of Official Seed Analysts in 1960. They were based on studies on variations associated with sampling and testing procedures begun in 1953 by S. R. Miles, A. S. Carter, and L. C. Shenberger, of Purdue University. Through cooperative research with 21 seed-testing laboratories, they measured the variations between different seed bags, different probes from the same bag, different test samples from the submitted sample, different analysts, and day-to-day variation of one analyst.

Mr. Miles and his coworkers used the following for calculating tolerances:

T= 1.414t[(B²/_n) (N n) / N+ C²/_n + W²/_n +A² /_n +1²/_n]^1/2

In the formula; t = A factor corresponding to the desired probability level. (The actual factors used were: 5 percent probability level; 1.65; 1 percent level-2.33; 0.1 percent level-3.09.)

B=Component of variation due to differences among bags.

C= Component of variation due to differences among cores or probes within bags.

W= Variations among working samples taken from the same submitted sample.

A=Component of variation due to the fact that different analysts may test samples differently.

I=A component of variation arising from the fact that the same analyst may test the same sample differently from day to day.

N=Number of bags in lot sampled.

n=Number of units of source of variation shown in same term of the equation.

Appropriate values for the different components of variance are inserted in the formula for the computation of regular tolerances for either nonchaffy seeds or chaffy seeds. The same tolerance is applied to a given percentage, regardless of whether it is pure seed, other crop seeds, weed seeds, or inert matter.

THE NEW tolerances for pure seed of both nonchaffy and chaffy kinds are narrower than the former tolerances. If the pure seed of alfalfa, a nonchaffy kind, is 98 percent, the new tolerance is 0.82 percent, but the old tolerance is 1.00 percent. When the pure seed percentage drops to 95, the old tolerance is 1.55, and the new is 1.21 percent.

The same pattern holds true for tolerances on pure seed of chaffy kinds, but the differences are not very great if the seed is 85 to 100 percent pure. The tolerances for chaffy kinds are slightly greater than for the nonchaffy kinds.