A Practical Application of the Student’s t Test
by Tim Loftus
For NPDES reporting of ammonia nitrogen, certain EPA approved test methods must be used. But before analysis the ammonia must be distilled from a sample into an absorbent (boric or sulfuric acid depending on the test method) to remove it from interferences. Then the ammonia can be determined using approved nesslerization, titration, electrode, or automated phenate procedures.
However, according to 40 CFR 136 Table 1B
footnote 6, “manual distillation is not required if compatibility data on
effluent samples are on company file to show that this preliminary distillation
step is not necessary.” If there
are no interferences before distillation, then the distillation step can be an
added source of error. It would be best not to distill if it is not needed. So
how do you do a comparability study on distillation versus nondistillation in
ammonia testing? Use the Student’s t Test. Below I have outlined the steps in
doing a t Test.
Over the course of the week ammonia was tested in the final effluent – with distilled and nondistilled results recorded. (In practice, you should use more data points.) The results are as follows:
test #
1
2 3
4
5
distilled (method 1)
2.1 1.7
3.0 2.4
1.3 Avg1
= 2.10 s1
= 0.651
nondistilled (method 2) 2.2
1.8 2.8
2.6 1.4
Avg2 = 2.16 s2
=0.573
Determine the average (Avg1 and Avg2) and the standard deviation (s1 and s2) for distilled and nondistilled samples. (The standard deviation calculation for each data group is a little lengthy to be included in this article. You should be able to figure it out easily on a scientific calculator or on a computer spreadsheet program.)
Before determining the value of t, you must perform a preliminary calculation for s.
s = 0.6132
(n1 is the number of data points in the distilled group and n2 is the number of data points in the nondistilled group.)
Now the determination of t can be made.
t
= - 0.1547
This calculated value of t must be compared to the “critical value of t.” Tables of critical values can be found in such sources as the CRC Handbook of Chemistry and Physics and Wastewater Sampling for Process and Quality Control, MOP- M-1 (or you can call the author for specific values). For our example, the critical value of t for 8 degrees of freedom (5+5-2) at a 95% confidence level is 1.860. Because our calculated t value of 0.1547 (ignore the “- ” sign) is less than the critical value, we can assume that both the distilled and the nondistilled procedures give equivalent results. If our t value was higher than the critical value, then the procedures are not equivalent and we would need to distill the samples for ammonia.
The Student’s t Test can also be used in the wastewater laboratory to determine equivalence in other methods such as AA and colorimetric procedures for copper testing. As always, check your state regulations. There may be additional requirements concerning test procedures that are used for reporting purposes.
This article was written under the auspices of the New England Water Environment Association (a chapter of the Water Environment Federation) Laboratory Practices Committee. Please visit the NEWEA website at www.newea.org for membership information and other opportunities.