You can use computer simulations to:
- Test your statistical intuition or demonstrate mathematical properties you cannot easily anticipate
- e.g. test whether when supposedly random data are generated, there is no more than 5% of significant effects for a variable in a model
- Understand sampling theory, probability distributions or test whether you understand the underlying processes of your system
- e.g. see whether simulated data drawn from specific distribution are comparable to real data
- Perform power analyses
- e.g. assess whether the sample size (within a replicate) is high enough to detect an effect simulated, in more than 80% of the cases
- Perform bootstrapping to get a confidence interval around a parameter estimate
- i.e. bootstrapping means to sample with replacement in an observed dataset. Doing this generates new 'simulated' datasets. With each of them, one can run the statistical analysis made on the observed dataset, saving each time the parameter estimate of interest. After doing this multiple time, you will obtain a confidence interval for the parameter of interest