We have a procedure for testing samples by assigning numbers and then testing the sample number randomly generated.
Now the process for assigning and generating numbers is very long for each number. If we have 20 samples we end up testing 16. So to save 5 minutes I randomly generate the numbers for the 4 I’m not testing. My boss hates when I do this since it isn’t SOP, but doesn’t make me change the way I do it, rather just complains.
Is the probability math different by negatively selecting instead of positively selecting the random numbers?
Do you mean that you have samples numbered 1 thru 20, then pick 4 of those numbers at random as the ones to exclude, rather than picking 16 of those 20 as the ones to include? If so, there is no difference; the 16 tested samples are just as random for each method.
Now, if the random number generator is slightly biased–say, for example, it produces the number X at a higher-than-expected rate than pure chance–I wonder which method would be better? My instinct says choosing only four numbers would be better because it’s fewer opportunities for the bias to occur, but that’s just a guess
To amplify a bit, “Number of ways Y objects can be chosen from X objects”–written here as “(X choose Y)”–can be shown to be X!/[Y!(X-Y)!] (X! = “X factorial” = 123*…*(X-1)*X). With that formula, it’s easy to see the equality.
I meant that as there was no human bias to choosing the numbers, but re-reading CJJ* that is not what they were talking about.
Nothing complicated, it is more like internally generated paperwork that must be filled out each time we use the generator, which ensures a quality control. We use an company-wide program (kinda a beefed up Excel) with an equation probably similar to Random.org (only no one really has access to it for me to verify). The annoying part is filling out the paperwork to go along with it. It easily takes five minutes per sample to finish.
So thanks to you wonderful people, I now have an extra hour of my day not filling in boxes with control numbers. Thank-you!
If you’re worried about bias or the effects of covariance from your random number generator, you can choose your entire sample with a single random number. Take your random number between 0 and 1, multiply by (20 choose 4 = ) 4845 and take the floor (or ceiling). Now you just have to transform this integer into a set of 4 numbers. The first (19 choose 3 = ) 969 will contain 1. The next (18 choose 3 = ) 816 will contain 2, but not 1. Of those that contain 2 but not 1, the first (17 choose 2 = ) 136 will contain 3, and the next (16 choose 2 = )120 will contain 4 but not 3, and so on.
I’d be willing to bet a lot of money that this is not a good random number generator. You’d almost certainly be better off using something that contains open source random number generation algorithms.
I didn’t know that, but i was just using them as an example.
I not have access to the equation/ algorithm so I can’t speak to it. Whatever we use it meets standards for my company, which is a fairly large multi-national corporation, so I’m in no position to change it (no matter how stupid it is )
It’s easier to understand the equality just from the observation in the OP… if you choose a set of objects to include, that amounts to a corresponding choice of objects to exclude.
Oho … but he only needs to get 4 unique results in a row, which is much easier!
Assuming that the Official Corporate Random Number Generator can be set to spit out a number between 1 and 4845, the OP could create a look-up table with all the ways to pick 16 things from 20, and ask the OCRNG to generate an index into the table. Then he only needs to file the paperwork for one random number instead of four.
Of course his boss’s head would probably explode … .
It wouldn’t take much. You should’ve seen the emails that went back and forth between department heads when it was discovered that I was helping an intern with homework by doing Bradford assays (for those that never took a biochemistry class, its a method that is probably only done in classrooms now, and has been around forever) in our lab. His problem wasn’t me actually fucking around on-the-clock, but that we were following the professors procedure, instead of the company dictated way to do things.
Other then that he is a really nice guy, but very old school with how he does stuff.
Just curious - what is the rationale behind excluding 4 samples out of 20 from the test, as opposed to excluding 10 or 15? It does not seem like you save that much time compared to just testing all of them, nor gain all that much certainty compared to testing a smaller subset.
I have no clue. We always keep 80% of the prepared batch, and the other four in this case go off to various QC departments. I don’t know the reasoning behind why those numbers are chosen.
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