Random Number Generation Question

[RetroVertigo]

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?

[CJJ*]

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

[RetroVertigo]

Originally Posted by CJJ*

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.

Yes.

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

There is no bias. Purely random.

Thanks this is what I thought, and once I do the math for my boss, I get a free lunch. I just wanted to double check before opening my mouth.

[zoid]

Originally Posted by RetroVertigo

Yes.



There is no bias. Purely random.

Thanks this is what I thought, and once I do the math for my boss, I get a free lunch. I just wanted to double check before opening my mouth.

Purely random is probably not true, that's almost impossible to accieve.

[Chronos]

If you want to express it mathematically, the statement you're looking for is that (20 choose 4) = (20 choose 16).

[The Hamster King]

Originally Posted by RetroVertigo

Now the process for assigning and generating numbers is very long for each number.

Now I'm curious what this process is.

Something tells me you're not rolling a 20-sided die.

[CJJ*]

Originally Posted by Chronos

If you want to express it mathematically, the statement you're looking for is that (20 choose 4) = (20 choose 16).

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" = 1*2*3*...*(X-1)*X). With that formula, it's easy to see the equality.

[RetroVertigo]

Originally Posted by zoid

Purely random is probably not true, that's almost impossible to accieve.

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.

Originally Posted by The Hamster King

Now I'm curious what this process is.

Something tells me you're not rolling a 20-sided die.

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!

[The Hamster King]

Originally Posted by RetroVertigo

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.

LOL ... you should just roll a D20. It would be faster and more random than whatever numbers the official pseudo-random generator is spitting out.

(FWIW ... random.org doesn't use an equation. Their numbers come from sampling noisy physical systems.)

[Dr. Love]

Originally Posted by CJJ*

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

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.

[Dr. Love]

Originally Posted by The Hamster King

LOL ... you should just roll a D20. It would be faster and more random than whatever numbers the official pseudo-random generator is spitting out.

That depends on how you're generating numbers. Trying to get 16 unique results in a row with a D20 might take a while.

[ultrafilter]

Originally Posted by RetroVertigo

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.

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.

[RetroVertigo]

Originally Posted by The Hamster King

LOL ... you should just roll a D20. It would be faster and more random than whatever numbers the official pseudo-random generator is spitting out.

(FWIW ... random.org doesn't use an equation. Their numbers come from sampling noisy physical systems.)

I didn't know that, but i was just using them as an example.

Originally Posted by ultrafilter

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 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 )

[Indistinguishable]

Originally Posted by CJJ*

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" = 1*2*3*...*(X-1)*X). With that formula, it's easy to see the equality.

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.

[The Hamster King]

Originally Posted by Dr. Love

That depends on how you're generating numbers. Trying to get 16 unique results in a row with a D20 might take a while.

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 ... .

[RetroVertigo]

Originally Posted by The Hamster King

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.

[Absolute]

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.

[RetroVertigo]

Originally Posted by Absolute

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.

[Chronos]

LOL ... you should just roll a D20. It would be faster and more random than whatever numbers the official pseudo-random generator is spitting out.

Yes, if it's a good-quality d20. Many polyhedral dice are horribly biased.

[D18]

Relevant Dilbert.

[szabrocki]

All random generators need a seed number. I use the voltage coming into the power supply on a server.

Say it is 230 volts. It is really 230.XXXXXX volts. That XXXXXX constantly changes in microseconds.

Use the decimal ( or part of it) as the seed number and that is about as random as you can get as it changes every moment.

[septimus]

Originally Posted by szabrocki

All random generators need a seed number. I use the voltage coming into the power supply on a server.

To each his own. My great-uncle used the U.S. Treasury daily balance.

[Chronos]

It depends on how much entropy you need, and how quickly you burn through it. You can also get entropy from user input devices like keyboards and mice, or from a microphone, or from the least-significant bits of the processor temperature, all things which the typical computer has access to. If you really want to get serious about it, you get a special piece of hardware that has a sample of some radioactive material in it, and use the timing of the decays to generate entropy.