Mixtures consisting of kinds having unequal seed weights present additional problems. Mr. Miles and his coworkers developed formulas and prepared tables of special tolerances for a number of different particle-weight ratios applicable to mixtures. Most of these tolerances are wider than those for unmixed seed, although under certain circumstances they may be narrower.

GERMINATION TOLERANCES have developed without the benefit of statistical theory or experimentation. The tolerance limits at the various percentage levels have been determined through practice. This has been done by comparing the results of tests on replicate samples from the same seed lot. The tolerances thus determined are somewhat larger than tolerances calculated from statistical theory alone, due to variation incidental to testing.

The tolerances applicable to the various germination percentages are: 96 percent of germination or more, 5 percent; 90 to 95, 6 percent; 80 to 89, 7 percent; 70 to 79, 8 percent; 60 to 69, 9 percent; 59 and less, 10 percent.

The tolerances of 10 percent for all germinations below 60 percent and 5 percent for germinations above 95 percent are unrealistic from the standpoint of statistical considerations.

STATISTICAL tolerances calculated by C. W. Leggatt, of the Canada Department of Agriculture, for two independent 400-seed tests at the 5-percent probability level range from 6.9 at 50 percent germination to 1.8 at 1 percent and 99 percent germination. These tolerances are smaller by about 1.7 to 3.5 for germinations of 40 to 100 percent than tolerances that were in use in 1961.

When the problems in testing are considered, there appears to be some justification for wider tolerances at the lower germinations. Low-germinating samples frequently develop rank growths of molds and bacteria during germination. The organisms interfere with the tests and make evaluation of seedlings less precise than with high-germinating samples.

TESTS FOR SEEDS of noxious weeds, such as dodder and quackgrass, aim to determine the number of dodder or quackgrass seeds per ounce or per pound in the seed lot. The test is quite different from the one that has been described for purity and germination. The number of seeds of noxious weeds usually is low. One therefore has to use a statistical theory known as the Poisson distribution.

The reliability of a test for noxious-weed seeds is related primarily to the number of noxious seeds found in a sample. However, testing procedures based on the rate of occurrence of the noxious-weed seed would not be practical. Uniform sample sizes by weight therefore have been established for the various kinds of agricultural and vegetable seeds. Except fora few large-seeded kinds, the sample size for noxious-weed tests is at least 10 times that for purity analyses.

Noxious-weed seed tolerances are calculated from the formula: Y=X+ 1 + 1.96 √x, in which X is the number of seeds labeled or represented and Y is the maximum number within tolerance of X. Thus, a table with any values of upper and lower limits can be set up. Some examples of tolerances computed by this formula are:

A farmer or seedsman preparing to market his seed would have it tested for purity, germination, and seeds of noxious weeds. If the seed is alfalfa, the seed laboratory may report that it found 10 dodder seeds in a 50-gram examination. The vendor may label the seed to show 90 dodder seeds per pound. He obtains the figure "90" by multiplying 10 by 9, because 50 grams is approximately one-ninth pound.

Suppose a seed inspector samples this seed at a later date and the control laboratory finds 16 dodder seeds in 50 grams. For a proper comparison, the seedsman's claim of 90 seeds per pound must be reduced to a 50-gram basis, the amount actually tested. Thus, 90 9=10. We now look in the tolerance table and find that 16 in Y column is within tolerance of 10 in X column. It would not be correct to compare the numbers on a per-ounce or per-pound basis because only one-ninth pound was tested.

SOME seed laws prohibit the sale of seeds containing noxious-weed seeds of certain designated species. It is not feasible to enforce such strict prohibitions. If no prohibited noxious-weed seeds are found in a sample, it cannot be assumed that there are no such noxious-weed seeds in the seed lot. Additional tests may reveal the presence of one or more prohibited noxious-weed seeds. For example, 999 samples drawn from the same lot may reveal no prohibited noxious-weed seed, but one or two such seeds may be found in the thousandth sample.

The seedsman who has his samples tested for labeling purposes faces this problem. That is why tolerances must be applied when seed is labeled to show no noxious seeds. The problem should be recognized by seed control officials when they consider the elimination of tolerances as applied to prohibited noxious-weed seeds.

OTHER TESTS make use of counted numbers of seeds or plants. Some kinds of seeds are so difficult to identify that 400 or 1 thousand seeds are counted out in the purity analysis for the identification of species or variety.

Certain special tests for species identification, such as the mottled-seed test of sweetclover and the ultraviolet test of ryegrass, make use of 400 seeds. Likewise, it is common practice to make varietal identifications on 50 to 1 thousand plants in greenhouse and field trials.

In all these situations, tolerances similar to those calculated by Dr. Leggatt for germination are used directly or in conjunction with other tolerances.

THE VARIETY tolerances have been modified slightly from his formula for convenience of application. If a regular purity analysis is made on Kentucky bluegrass seed and the sample is found to contain seeds of Merion Kentucky bluegrass, 400 bluegrass seeds will be taken at random to determine the proportion of each. The tolerance applicable to each variety of Kentucky bluegrass will be the appropriate tolerance for a 400-seed sample plus one-half the tolerance for the regular purity analysis.

For example, an analyst may find 85 percent of pure bluegrass seeds in a regular purity analysis. If, in a 400-seed examination, he finds that 65 percent of the bluegrass seeds are Merion and 35 percent are common, the tolerances for these percentages, in the Rules for Testing Seeds, are: Merion: 1.10+6-5-7.60; common: 1.10 + 6.7 = 7.80.

OREN L. JUSTICE is a seed botanist and Head of the Testing Section, Seed Branch, Grain Division, Agricultural Marketing Service. He holds advanced degrees from Ohio University and Cornell. Dr. Justice is the author of a number of articles on seed dormancy and seed testing.

EARL E. HOUSEMAN, a mathematical statistician, is Director of the Statistical Standards Division of the Agricultural Marketing Service. He received his statistical training at Iowa State University and has served as a consulting statistician in the Department of Agriculture since 1943.