Real statistical experiments can use simulation-package software

The significance of statistical measurements depends on the sampling distributions of statistics like sample averages, sample variances, and statistical relative frequencies. In practice, sampling distributions are usually not measured but inferred from probability models. But for meaningful statistics education, and also for research, it is useful to study real sampling distributions, i.e. actual samples of hundreds or thousands of statistics each computed from hundreds or thousands of data values. That requires massive data processing, but we show that personal-computer simulation-package software can do such jobs in seconds if we reduce program-loop overhead. Specifically, we exhibit compact and readable programs that create true sampling distributions by system replication (vectorized Monte Carlo technique) and demonstrate very fast recursive and dot-product averaging. We estimate sample averages, sample variances, and probability densities of statistics. Runtime displays that plot not only statistics but also their sample averages and variances as functions of sample size provide remarkable insight into the real-world behavior of measured statistics.