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Significant Digits
st
Posted: Friday, December 18, 2009 11:50 AM
Joined: 12/18/2009
Posts: 4


I am just wondering how many significant digits are required to be reported for the TSS and BOD5 tests. We were recently dealing with a lab that reported 2 significant digits for their tests on influent that had results between 100 and 200 mg/L. They rounded their results to the nearest 10 mg/L. Is this a common practice or should they be giving an extra digit?

 

 


Perry Brake
Posted: Friday, December 18, 2009 12:23 PM
Joined: 12/16/2009
Posts: 69


Unless the regulatory agency to which the data is being sent says otherwise, it is a good laboratory practice to record/report results to three significant figures whenever the measurement system allows.  If the lab is using a modern, digital DO meter and good analytical balance, they can certainly report to three significant figures.  If the lab is using an analog DO meter (heaven forbid!) for BOD and top-loading pan balance for TSS (don't laugh...I've seen it done), two significant figures is probably the best they can do for each test.  That doesn't mean you have to accept the data, however...tell them you want three significant figures, and if they can't or won't give them to you, change labs (if the lab in questions is a supporting commercial lab).

 

Perry Brake


Anonymous
Posted: Monday, December 21, 2009 2:56 PM

A perfect example of what we lost with the new forum.  We had this discussion a while ago, now lost.

 

I don't agree completely with Perry here.  Yes, a good DO meter can read to 3 sig fig; but my feeling is that the BOD test is good to about one and a half sig fig, never to three.  So if you got two results of (say) 67 and 63 I'd say that was pretty good agreement even though they don't match to even one sig fig. 

 

Old Lag


Anonymous
Posted: Monday, December 21, 2009 3:21 PM
Anonymous wrote:

A perfect example of what we lost with the new forum.  We had this discussion a while ago, now lost.

 

I don't agree completely with Perry here.  Yes, a good DO meter can read to 3 sig fig; but my feeling is that the BOD test is good to about one and a half sig fig, never to three.  So if you got two results of (say) 67 and 63 I'd say that was pretty good agreement even though they don't match to even one sig fig. 

 

Old Lag


I agree with Old Lag.  Back in the dark ages when I used to do many, many BOD tests, the purpose of that specific test (as I understood it) was to be an "indicator" of biological waste concentration.  Somehow, as the EPA has entrenched themselves as the "know all" for everything environmental they have required so much quality control that the original intent of the test has become lost.  Now, if this forum (at least the former one) was any indication, lab folks spent most of their waking hours worrying about 1% accuracy on the QC tests.  


Calculations of results required using a slide rule, or possibly an abacus.  All results were somewhat "approximate," so that if you got two significant figures you were good.  Now, in the digital age, we can get a "theoretical" (only in the sense that the calculator reads to 89 significant figures) level or accuracy that some people think is the "real result."  I could see the problem coming 30 years ago, when the concept of significant figures was totally lost on the younger folks coming out of school.  I still think that an analog instrument can often (but not always) tell you more than a digital readout.


Anonymous No. ____

Jeff Naumann, pissing upwind



Anonymous
Posted: Monday, December 21, 2009 5:21 PM

you only have to report the number of specific figures that are in your permit limits.

 

Bob


Keith Chapman
Posted: Tuesday, December 22, 2009 11:20 AM
Joined: 10/2/2009
Posts: 35


The general rule, as I understand it, is to report no MORE significant figures than your least significant measurement.  Conversely, "use the same number of sig figs as your LEAST significant measurement".  Using TSS as an example, if 100 mls (3 sigfigs) of sample had a dry weight of 0.0126 grams (3 sigfigs), then report a TSS = 126 mg/l.  However, if 100 mls of sample had a dry weight of 0.0025 grams, then report only two sigfigs TSS=25 mg/l.

 

 


Anonymous
Posted: Tuesday, December 22, 2009 4:12 PM
Keith Chapman wrote:

The general rule, as I understand it, is to report no MORE significant figures than your least significant measurement.  Conversely, "use the same number of sig figs as your LEAST significant measurement".  Using TSS as an example, if 100 mls (3 sigfigs) of sample had a dry weight of 0.0126 grams (3 sigfigs), then report a TSS = 126 mg/l.  However, if 100 mls of sample had a dry weight of 0.0025 grams, then report only two sigfigs TSS=25 mg/l.

 

I quite agree. One needs to keep aware of what one is measuring.

 



Perry Brake
Posted: Tuesday, December 22, 2009 6:53 PM
Joined: 12/16/2009
Posts: 69


You're absolutely right, Keith.  And for TSS, one might also have to consider the measurement of sample volume.  If you are filtering 200 mL, for example, and you measure the volume in a 500 mL graduated cylinder, you can probably measure to only two significant figures.  Same with BOD.  And because of the volume measurement, I agree that BOD results should be reported to two significant figures.  But I will stand by my guns that it isn't the measurement of DO that limits you to two.  And for BOD results on PT study samples, it might be a good idea to report three figures regardless of what is scientifically correct since the PT providers use three.  It would be troubling to report "25 mg/L" when you calculated 25.4 mg/L and got a "not acceptable" because the lower acceptance limit in the PT study was 25.3 mg/L.  confused


James Royer
Posted: Wednesday, December 23, 2009 12:15 PM
Joined: 9/21/2009
Posts: 98


Kieth is correct. You need to know how many sin figures you have and report accordingly. As for PT samples they normall ask you to report one more figure than is significant if you can.


Anonymous
Posted: Thursday, December 24, 2009 12:49 PM
Perry Brake wrote:

You're absolutely right, Keith.  And for TSS, one might also have to consider the measurement of sample volume.  If you are filtering 200 mL, for example, and you measure the volume in a 500 mL graduated cylinder, you can probably measure to only two significant figures.  Same with BOD.  And because of the volume measurement, I agree that BOD results should be reported to two significant figures.  But I will stand by my guns that it isn't the measurement of DO that limits you to two.  And for BOD results on PT study samples, it might be a good idea to report three figures regardless of what is scientifically correct since the PT providers use three.  It would be troubling to report "25 mg/L" when you calculated 25.4 mg/L and got a "not acceptable" because the lower acceptance limit in the PT study was 25.3 mg/L.  confused

 

That is possible, Perry, but extremely unlikely. The acceptance window for the BOD test is generally big enough to pitch an Airedale through.

 

Dave Wichern aka Dedalus


Perry Brake
Posted: Thursday, December 24, 2009 2:15 PM
Joined: 12/16/2009
Posts: 69


 t's highly unlikely for good labs...but there are plenty of not-so-good labs out there, and I have seen many "not acceptable" results for BOD PE samples.

 

But be that as it may, I was just trying to make a point.

Luis Manriquez
Posted: Wednesday, January 6, 2010 11:23 AM
Joined: 1/6/2010
Posts: 20


It is ironic that we are using the BOD method to discuss sig. figures. Standard Methods lists several DO readings with 1, 2, and 3 significant figures. For example, when discussing initial DO it reccomends that it not exceed 9 mg/l DO. When discussing DW acceptance limits it says 0.2 mg/l and it talks about uptake of 0.05 to 0.1 mg/l in the same sentence!

Then it talks about residual DO of "at least 1 mg/l" and uptake of "at least 2 mg/l"

Finally, in the GGA section it lists control limits as 198 +/- 30.5 which would imply 4 sig figs precision!

 

When you consider that there are several sources of error in the calibrating procedure and that the the BOD bottle and the graduated cylinder both contribute errors, I dont see how we can report to more than 2 sig figs.

 

Same for the TSS and TDS tests. Samples with heavy solids would require use of a 10 ml cylinder, which would yield some number like 1234mg/l.  

 

Luis Manriquez

 

 

 


James Royer
Posted: Wednesday, January 6, 2010 12:52 PM
Joined: 9/21/2009
Posts: 98


When discussing significant digits it is important to know that the last significant digit is always in doubt. 162 or 166 would both be proper reporting to the most significant digit.

 

As far as BOD a DO of at least remaining and 2 depletion, they are both absolute numbers and getting a 1 or 2 depends on the significant figures of the DO readings that you use.

 

A GGA of 198 +/- 30.5 does not indicate 4 significant digits but that a result of 168 mg/L would be exceptable and 167 mg/L would indicate a need for some improvement to correct the analysis. 3 significant figures are appropriate if your meter works properly.

 

A result of 1234 mg/L would require a 10 ml measurement of 10.00 ml which would require a volumemetric measurement or weighing the sample. Not too many people care if it is 1230 or 1240 anyway. I have only seen Engineer's reports that print an average for BOD's at 189.125 mg/L. We all know this should have been rounded.


James Royer
Posted: Wednesday, January 6, 2010 1:25 PM
Joined: 9/21/2009
Posts: 98


An additional thought, the sample with a initial DO of 9 indicates that it can be 9.41 mg/L. The 9 was stated as 1 sig digit and would mean less than 9.50 mg/L. If you warm a sample to 20 +/- 3 C then at 17 C the saturation would be 9.41 mg/L at the average barometric pressure for our elivation. If you want it less than 9.00 then you have to warm it to at least 20 C.

 

You can still debate the 0.2 mg/l blank as to if it means 0.20 mg/L. I think that is what was intended so the method should reflect that fact.


Luis Manriquez
Posted: Thursday, January 7, 2010 3:39 PM
Joined: 1/6/2010
Posts: 20


My point was that SM was using numbers of differing significant figures that are all dependent on readings from the same DO meter.

 

As for the limits for 9 and .2, our lab long ago decided the opposite of what Mr. Royer suggested. If a sample is over 9.00 mg/l DO we have to bring it down by shaking vigorously. If a DW sample depletion is 0.25 mg/l it is acceptable but 0.26 is not.

 

No word on whether -0.20 mg/l (or any negative number, which would be due to different calibrations and analysts) would be acceptable.

 

As for the 10 ml TSS sample, I don't believe one can consistently get even 10.0 mls in a class A graduated cylinder. Even if one could use an Eppendorf pippette the temperature variations would add volume errors. The weighing step adds another set of errors, so we are left with rounding to 2 sig. figures, not 3 and the number to report should be 1200 mg/l.

 

Luis Manriquez


James Royer
Posted: Friday, January 8, 2010 9:43 AM
Joined: 9/21/2009
Posts: 98


A USEPA region 5 lab inspector told me that if can not report 3 significant figures then you are not analyzing a large enough volume of sample for any gravimetric analysis using an analytical balance. 10.0 ml sample is still 3 significant digits.

 

 


Anonymous
Posted: Friday, January 8, 2010 10:40 AM

"A USEPA region 5 lab inspector told me that if can not report 3 significant figures then you are not analyzing a large enough volume of sample for any gravimetric analysis using an analytical balance. 10.0 ml sample is still 3 significant digits."

 

Maybe, but 9.9 is only 2 sig figs. Inspectors and auditors of every government agency should think outside the 10.0 box.


James Royer
Posted: Friday, January 8, 2010 1:12 PM
Joined: 9/21/2009
Posts: 98


Obviously, if you only have 2 sig figures that is what you report. A residue weight of 0.0049 g with a 500 ml sample will yeild 9.8 mg/L and that would be 2 sig figures. I think he was concerned with reporting just a 10, 20, or 30 TSS because they did not filter enough sample to get more sig figures. We always filter a lot of sample on low samples because we have plenty of sample volume.


James Royer
Posted: Friday, January 8, 2010 2:28 PM
Joined: 9/21/2009
Posts: 98


On the sig digits for BOD. Standard Methods 21st ed. has dilution water blanks less than 0.20 mg/L and uptake of 2.0 with 1.0 mg/l DO remaining. As for sample DO it states that the sample should be warmed to 20 +/- 3 C and agitate vigorously to remove excess DO. Then if the temperature was 17 C a DO of 9.41 might be possible depending on barometric pressure at saturation. The sig digits have been increased in the latest ed. Std. Methods.


Luis Manriquez
Posted: Friday, January 8, 2010 5:22 PM
Joined: 1/6/2010
Posts: 20


James Royer: Thanks for the heads up. I do not have the 21st edition at hand.

Our permit is based on the 20th edition, so we use 0.25 mg/l depletion as the limit for DW.

Still no word on how to treat negative depletions. Would -0.26 be OK? It is, after all, less than 0.20mg/l.

 

My concerns about the inconsistent use of sig. figures in SM are still valid, though.

 

 

A pet peeve of mine is how many experienced analysts confuse significant figures with precision. To illustrate, say you filter two samples for TSS using 100 mls. One yields a weight difference of 8.5mg and the other gives you 185.5 mg/l. They both have the same precision, right? Most labs would report 85 mg/l and 1860 mg/l and leave it at that. 

Disregarding the balance error, one could say the sample volume was determinable to 1 in 100 mls. The 85 mg/l result would be close to this 1/100 precision. The 1860, even though is rounded up, is 1/186, a precision not supported by the sample volume. we would need to specify 1860 +/-20 as the true value.

If a smaller volume were needed to filter the sample, as happens with heavy solids wastes, the problem typically gets worse. In other words, reporting values such as 103 mg/l and 914 mg/l from a test does not accurately reflect precision.  They both have 3 significant figures, but one has precision of 1/100 and the other close to 1/1000.

 

 

 

Let's consider a typical BOD example too. A lab reports a BOD sample as say, 362 mg/l.

 

ID     SampleVol Initial DO Final DO Depletion Ratio  BOD    Avg BOD

Raw1 2ml         8.35      5.92       2.43      150    364.50     362

Raw1 4ml         8.31      3.42       4.89       75    366.75

Raw1 6ml         8.26      1.19       7.07       50    353.50  

 

 

 

As you can see, the limiting factor is the sample volume, not the DO reading.

Applying the same logic as for TSS, a sample volume of 2 mls might be precise to 0.1 mls using a precision pipette. Ignoring variables such as homogeneity and sample bottle volume, this works out to a 1 in 20 precision. For the 6 mls this would be 1 in 60. The reported result, however is 362, implying a 1/362 precision. At best, the result should be reported as 362 +/- 6 mg/l.

If we consider a worst case scenario, where only one bottle is valid, it would look like this: 

 

 

ID      Sample Vol Initial DO Final DO Depletion Ratio   BOD     Avg BOD

Raw2    1ml        8.35       1.19       7.16     300    2148.00    2150

 

 

 

 

 

In this case, the volume is precise to only 1 in 10 but he rounded result has 1 to 215 precision. We should only report that as 215 +/- 22 mg/l. 

 

 


James Royer
Posted: Monday, January 11, 2010 8:48 AM
Joined: 9/21/2009
Posts: 98


Luis, using a pipette to measure the sample volume of 1, 2, or 6 ml has 3 significant figures. You can read the 1 ml, the .1 ml and estimate the .01 ml which is the volume reading that is in doubt. The last digit of significant digits are always in doubt.

 

Your example of BOD calculations of 365, 367, and 354 mg/L averaged would be 362 mg/L and all the valures would be within the +/- 10 mg/L. Knowing the 1 reported digit is in doubt the all the values would be within 10 ml/L.

 

you might be right at the 914 mg/L reporting area. Values in this area might need to be rounded to the nearest 5 mg/L or something. Each lab should do their own calculations and include it in their own SOP.

 

I can not see any problem with reporting 3 significant digets in the SOP.