If I make three replicate measurements of a system, what is the best rejection criteria for throwing one out ?

Question

I am an analytical chemist generating data from a titration. It is not uncommon to have one of the three measurements be quite different from the other two. Also, the precision (repeatability and reproducibility) of the analysis is known. THANKS

Answer 1

This is a good question even for a statistician.
The problem is your set is small and I do not know what the deviation between samples is, however the repeatability and reproducibility information can bind the window
through which the third value will fall through or perhaps even remain in.

Let me know.

Answer 2

I would not discard an outlier from only three measurements, I don't think there is a sound mathematical or scientific reason to do so. If you make five measurements and one is different than the other four, there is some logical reason to reject the outlier. But out of three measurements, you would be using pure chance to choose the one to discard. If you were an analytical chemist in a regulated environment (FDA or EPA), you might actually be breaking the law to do so!

And you can't possibly know what the precision of the analysis is if you discard data!

Answer 3

1. To echo one answer, unless you have a reason for one being off, throwing one out will be difficult.

2. You say you often have an "outlier". Is it always in the same direction, or of roughly the same magnitude? You may have a systemic error that is causing inconsistent data.

3. Does your measure of precision include all data or just that which you think you should keep? If it is just "good" data, you do not have a measure of error.

4. Assuming you have included "bad" data in your measure, figure out your distribution. Is it "normal" in the statistical sense? If not, seek a statistics text to find your distribution shape.

5. Assuming it is normal, calculate a standard deviation and 95% confidence interval. If your "outlier" is within this interval, you should keep it. It is reasonable to believe this result was due to random error. If it is outside 95%, throw it out.

Answer 4

II have learned that in science. (as a whole ) someitmes the answers are the most unlikely. So keep track of all your data Putting the unlikely in a " side file " for further reveiw . never throw out any research data (unless there was a definate human error occered in the production of the experiment.) .

Answer 5

I would suggest flushing #2.