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send out more standard specimens and ask the labs to try again. (This may not answer the question.
What often happens when labs get feedback from quality control checks is that they improve their
performance. This is actually the desired result because the objective is to attain uniformly excellent
performance and not to single out poor performers.)
On the other hand, the measurement method might be all right and the true concentration might be
higher than 1.2 mg/L. This experiment does not tell us which interpretation is correct. It is not a simple
matter to make a standard solution for DO; dissolved oxygen can be consumed in a variety of reactions.
Also, its concentration can change upon exposure to air when the specimen bottle is opened in the
laboratory. In contrast, a substance like chloride or zinc will not be lost from the standard specimen, so
the concentration actually delivered to the chemist who makes the measurements is the same concen-
tration in the specimen that was shipped. In the case of oxygen at low levels, such as 1.2 mg/L, it is
not likely that oxygen would be lost from the specimen during handling in the laboratory. If there is a
change, the oxygen concentration is more likely to be increased by dissolution of oxygen from the air.
We cannot rule out this causing the difference between 1.4 mg/L measured and 1.2 mg/L in the original
standard specimens. Nevertheless, the chemists who arranged the test believed they had found a way to
prepare stable test specimens, and they were experienced in preparing standards for interlaboratory tests.
We have no reason to doubt them. More checking of the laboratories seems a reasonable line of action.

Comments

The classical null hypothesis is that “The difference is zero.” No scientist or engineer ever believes this
hypothesis to be strictly true. There will always be a difference, at some decimal point. Why propose a
hypothesis that we believe is not true? The answer is a philosophical one. We cannot prove equality, but
we may collect data that shows a difference so large that it is unlikely to arise from chance. The null
hypothesis therefore is an artifice for letting us conclude, at some stated level of confidence, that there
is a difference. If no difference is evident, we state, “The evidence at hand does not permit me to state
with a high degree of confidence that the measurements and the standard are different.” The null
hypothesis is tested using a t-test.
The alternate, but equivalent, approach to testing the null hypothesis is to compute the interval in which
the difference is expected to fall if the experiment were repeated many, many times. This interval is a
confidence interval. Suppose that the value of a primary standard is 7.0 and the average of several measure-
ments is 7.2, giving a difference of 0.20. Suppose further that the 95% confidence interval shows that the
true difference is between 0.12 to 0.28. This is what we want to know: the true difference is not zero.
A confidence interval is more direct and often less confusing than null hypotheses and significance
tests. In this book we prefer to compute confidence intervals instead of making significance tests.

References
ASTM (1998). Standard Practice for Derivation of Decision Point and Confidence Limit Testing of Mean
Concentrations in Waste Management Decisions, D 6250, Washington, D.C., U.S. Government Printing
Office.
Wilcock, R. J., C. D. Stevenson, and C. A. Roberts (1981). “An Interlaboratory Study of Dissolved Oxygen
in Water,” Water Res., 15, 321–325.

Exercises

16.1 Boiler Scale. A company advertises that a chemical is 90% effective in cleaning boiler scale
and cites as proof a sample of ten random applications in which an average of 81% of boiler
scale was removed. The government says this is false advertising because 81% does not
equal 90%. The company says the statistical sample is 81% but the true effectiveness may
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