5.3.3 Simulation Experiments

The second method for obtaining information about a statistic’s sampling distribution is to perform a simulation experiment. This method is usually used when a derivation via probability rules is very difficult or even impossible. Such an experiment is virtually always done with the aid of a computer. The following characteristics of an experiment must be specified:

1. The statistic of interest ($\bar{X}$, $S$ a particular trimmed mean, etc.)
2. The population distribution (normal with $\mu =100$ and $\sigma =15$, uniform with lower limit $A=5$ and upper limit $B=10$, etc.)
3. The sample size $n$ (e.g., $n=10$ or $n=50$ )
4. The number of replications $k$ (number of samples to be obtained)

Then use appropriate software to obtain $k$ different random samples, each of size $n$, from the designated population distribution. For each sample, calculate the value of the statistic and construct a histogram of the $k$ values. This histogram gives the approximate sampling distribution of the statistic. The larger the value of $k$, the better the approximation will tend to be (the actual sampling distribution emerges as $k\to \infty$ ). In practice, $k=500$ or $1000$ is usually sufficient if the statistic is “fairly simple.”

EXAMPLE 5.23

EXAMPLE 5.24