I have read several simulation studies to control for statistical assumptions, but very often, the chosen values are 50, 100, 250, 500, 1000 and 2500 as sample sizes. Is there any reason why these exact values are chosen? Why not use 49, 121, 225, 529 (7**2, 11**2, 15**2 and 23**2) as values for simulation studies. All of the normally chosen values are even. It means for each data-point one other data-point can compensate for it. If the sample sizes are unequal, at least one data-point will not have a mirror to compensate for any harm it can do.
Some simulations take a very long time and require enormous computer power. If one simulation takes a couple of weeks, then 50 simulations might be all that can be done within existing budget and time constraints.
Sometimes the simulation that took weeks several years ago, now takes but a few moments.
Some simulations converge. Running too many simulations is pointless.
Sometimes people do not understand the nature of variability. For something like a randomization test, 50 randomizations is insufficient by about three orders of magnitude.
In terms of the number of simulations, there will be little difference between 987 and 1000. Using 987 simulations becomes distracting. If the simulation is influenced by the number of simulations, then one might be justified in using other values.
Evenness is not really an issue. If you end up with a result that has a 1 in a 10,000 chance of happening and you have done 50 simulations, are you really happy with any outcome? Fifty simulation is just not appropriate for estimating any rare event. If I am interested in events that happen 1 in X, I will plan on doing at least 100X simulations.
@Timothy, please read my question carefully. I do not ask about the amount of simulations, but about the values of n that are used when people perform simulations. They are always even numbered sample sizes. Why not use different values or use a random table to select the sample sizes used. In an even sized sample values can be compensated one-by-one. The highest value can be compensated by the lowest value. This is not completely possible with uneven sized samples. Why are the sample sizes used in simulation studies not randomized?
@Peter, Sometimes it takes a bit of thinking to get at the question, and not everyone on RG is precise in how they ask questions. So it is sometimes useful to have answers that broaden a topic a bit in an effort to get at the real problem.
The last paragraph answers the question as asked. Evenness is not an issue. The issue is whether or not the tails of the distribution are of interest, and whether the number of simulations are sufficient for that purpose.
In simulation you are sampling some random distribution, just as you would sample any population. If you draw one high value that occurs with a probability of 0.00004, what is the probability of drawing an equivalent sample that is at the other extreme of the distribution? If the simulations are independent, then the probability is 0.00004, but there is no guarantee that it will be at the other side of the distribution. If this is a random process, then the only thing that matters is the number of simulations: 500,000 is more likely to have an outcome close to the population mean than 50 simulations, but if you must do 50 simulations it makes little difference if you use 48, 49, 50, 51, or 52. The difference between 48 and 51 will likely be too small to make a measurable difference in the accuracy of the output.
There is no "mirror effect" in a random process. Randomness does not work that way. Mostly in simulations you want each run of the simulation to be independent and identically distributed.
There is nothing magical about using 500 simulations. If you want to use 499, feel free to do so. Just make a note that you stopped at 499. The risk is that someone will expect 500, and will then ask question. Did the computer die? Did you find one simulation that failed? Did you make a mistake in processing the results? Did a simulation end up with a missing value? Some of these options would suggest that the program (or the person) needs to be fixed to eliminate the errors. With errors, why should I trust the output?
What would be the point in randomly selecting the number of simulations?
Is there a specific type of simulation that you focus on?
- Badges
- Science topic
- Similar topics
- Mathematics
- Statistics
- Sampling Design
- Sample Size