[rjb]

Hello,

Forgive what may seem like a frivolous question, but I would very much hope to get a range of opinions on appropriate sampling strategy based upon what may seem to be a simple but perhaps interesting problem... I chose pasta as my example as I'm working with fibres at the moment and I'm feeling quite hungry!

Let's imagine that I decide to go home tonight and cook a big batch of spaghetti - for the sake of argument 500 individual strands.
That sounds rather uncomplicated, but, the trouble is, my wife sometimes chooses to tidy the cupboards and occasionally puts what's left of nearly empty packets of spaghetti in the pasta jar contaminating the spaghetti (all of the same type with a cooking time of 15 mins) that's currently in there - In other words, when I choose to make spaghetti, there may be a single population, or several sub-populations within the same jar - I just don't know and nor does she . 

This in of itself would be fine, but each type of spaghetti has a completely different cooking time (for the sake or argument one takes 12mins, one takes 15mins and one takes 18mins), each looks identical and overcooking or under-cooking results in horrid sloppy spaghetti or crunchy spaghetti respectively...

As the water comes to the boil I add my 500 strands of pasta and I wait for 15 minutes and test a single piece which is just perfect... al dente. I try another and its perfect.

The question is how many pieces of pasta would I need to taste before I can be confident (again the level of confidence is up to whoever chooses to reply - if they do) that the samples I have taken are representative of the bulk of pasta and that therefore I am unlikely to have any sloppy or crunchy surprises so to speak? Clearly the only way to be totally sure is to eat all 500 pieces, but given that I don't like pasta that much, perhaps not the most practical!

Without any prior knowledge (i.e. no idea how many contaminating strands of pasta have been added and of which variety i.e. 12/15/18 min) would I be right in assuming that without being very lucky in my testing, I would not be able to determine with confidence whether there are 1, 2 or 3 types of pasta present? 

Kind Regards

R



 

 

[mjc123]

I think what you need is the hypergeometric distribution, which you can calculate in Excel.
Suppose of your 500 strands, M are the right type and would pass the taste test, 500-M are the wrong type(s) and would fail.
Suppose you test n strands, and all n of them pass the test. The probability of this in Excel is
Hypergeom.dist(n,n,M,500,false)
If you want a 95% confidence level you look for the first value of n for which P<0.05. for example, for M=300, P=0.0457 for n=6; i.e. there is less than 5% probability that 6 of 6 would pass if M=300, so we reject the hypothesis, and conclude M>300.
For M=350 the threshold value of n is 9; for M=400 it is 14; for M=450 it is 28. So you would have to test 28 strands, and all of them pass, to be confident that your pasta sample was at least 90% the right stuff.

[mjc123]

How are you getting on with your spaghetti? Have you caught your wife out?

[billnotgatez]

How sure are we you are doing a good random sample?

Could you have only 1 of the 18 min type in your population?

What amount of confidence do you want to have?


This sounds like an exam question where the professor is grasping at straws (spaghetti) to make the problem seem relevant to the common man/woman.

[rjb]

Dear All,

Many thanks for the replies...
Being a tactless idiot, I accidentally happened to mention my question to my wife and she has come up with a 'great solution' - I now have to do the shopping, but on the positive side, I am no longer forced to carry out complex calculations every time we cook pasta!

It does sound a bit like one of those terrible exam questions I know, but the question was really a way of repackaging a real world forensic science problem in the hope getting answers which were a little more 'generic' and were not influenced by 'the way things tend to be done' in my particular subject area - We have a habit of becoming quite institutionalized!

The question actually relates to the analysis of trace evidence within a forensic context and in particular in relation to fibres. As you can probably appreciate, an item of clothing submitted in a typical case may well be covered in many thousands of fibres. These are recovered (typically by taping) and the lifts are assessed under low power stereo microscope for the presence of particular 'target fibres' which have been found on a reference item.

Initial assessment of our tapes is typically on the basis of colour similarity to our reference/target fibres and after completion and a proportion of these are selected randomly for further analysis (i.e. Microscopy, PLM, FTIR, MSP, perhaps TLC etc.). The question was really about how many fibres would need to be selected before the analyst can be fairly certain that of the fibres selected for analysis were representative of the bulk of the population of fibres of similar colour to our reference/target fibres and that therefore the analysis of every single fibre was unnecessarily - hence my question on spaghetti!

There are several papers covering this particular topic, but I thought I would ask some non forensic scientists their opinion and hence chose to remove any forensic influence by using my spaghetti question! Contrary to popular belief, I am not that obsessed with spaghetti in real life

Kind Regards

R

 

[Irlanur]

I wait for 15 minutes

what kind of spaghetti do you have if they are al dente after 15mins

[mjc123]

I thought 500 strands was a lot to be cooking at once!