I googled on the subject and found that a discipline that deals with this type of problems (measurements) is called the Decision theory. It uses statistics to estimate probability of certain events (results of measurements). So, everything depends on a decision that someone needs to make. A single observation may be justifiable for some decisions and not for others. The purpose should be kept in mind while discussing these types of problems.
As a matter of fact, measuring protein concentration just once is not a truly single observation, because the experimenter knows something about the sample, and s/he makes a decision based on a consistency of new observation with previous ones (the so-called model in your example). Alex On Mar 13, 2013, at 6:06 PM, <mjvdwo...@netscape.net<mailto:mjvdwo...@netscape.net>> <mjvdwo...@netscape.net<mailto:mjvdwo...@netscape.net>> wrote: I think that in statistics you can build a model that describes (and predicts) the uncertainty. So if you have done similar (!) replicate experiments, from which you can build the model, you can apply it to a single observation and provide a reasonably good guess for the value that you were measuring and its variance. Of course that guess would not be as good as the average value and variance from true replicates. With protein crystals (or solutions for that matter), the sample is often too precious to redo the experiment and it is worth thinking about doing replicate experiments with a "cheap one", build the model, and then apply it to single "expensive" observations. That would be statistically justified (provided that the model is valid for all sets of experiments). I have not built such models, but we know that pipetting isn't really as good as we believe. If you randomly dial to a particular value on your pipetteman (say 5 uL), you will get a certain pattern of "errors" (which is really not a good word for it), while if you consistently dial either from a low (1uL) or a high (10uL) value towards the value you want, you will get another pattern. Those two patterns are not representative of each other, I don't think, and you would need to understand how to do experiments consistently to stay within your error-model (bad word). Among many other things, statisticians try to come up with models that explain the uncertainty so that you know what to think, even if your set of observation is too small to say for sure, with n=1 being the ultimate too small. (Maybe not ultimate, n=0 is really too small.) Mark -----Original Message----- From: Alexander Aleshin <aales...@sanfordburnham.org<mailto:aales...@sanfordburnham.org>> To: CCP4BB <CCP4BB@JISCMAIL.AC.UK<mailto:CCP4BB@JISCMAIL.AC.UK>> Sent: Wed, Mar 13, 2013 3:05 pm Subject: Re: [ccp4bb] statistical or systematic? bias or noise? On Mar 13, 2013, at 1:36 PM, Ed Pozharski wrote: But what if I only have one measurement worth of sample? Is it proper to use statistical analysis for a single measurement? I thought statistics, by definition, means multiple measurements. Alex
