For each seed (1-1000, for this analysis), I took the mean and standard deviation of the first 1,000 random numbers. Then I get the percent of the density function that intersects with the normal curve as well as a distance from the origin function (0,1 in this case).

With the resulting points, I find the most interesting ones based on min/max mean, min/max sd, max distance from shifted origin for points in each of the quadrants, overall max distance, and the point closest to the center.

Below is the summary of interesting points.

## type seed mu sd dist intersect

## 1 mu_min 85 -0.110 1.008 0.110 0.956

## 2 mu_max 501 0.104 1.002 0.104 0.959

## 3 sd_min 180 -0.005 0.921 0.079 0.960

## 4 sd_max 168 0.002 1.065 0.065 0.969

## 5 q1 501 0.104 1.002 0.104 0.959

## 6 q2 85 -0.110 1.008 0.110 0.956

## 7 q3 713 -0.075 0.935 0.100 0.957

## 8 q4 394 0.090 0.988 0.091 0.964

## 9 out 85 -0.110 1.008 0.110 0.956

## 10 in 548 0.000 1.000 0.000 1.000

## 11 sim 548 0.000 1.000 0.000 1.000

## 12 diff 85 -0.110 1.008 0.110 0.956

Below is a chart showing the overlap of the most similar point and a chart showing the overlap of the least similar point. Thanks again to Wolfgang for this code chunk.

Top: Seed 548; Bottom: Seed 85 |

I believe the only reason to allow an externally selected seed is to allow the user to verify results (or errors) with the identical input data set. I would never manually select a seed when running actual pseudo-random statistical analyses. Also, keep in mind that a relatively small sample such as you used in fact should not have perfect moments. The statistical probability works out that it won't.

ReplyDeleteInteresting analysis. Would you expect them to all have a mean of 0 and variance of 1?

ReplyDeleteWould a better test be to check that the means and variances for each given seed correspond to their appropriate sampling distributions?

Both good points and food for thought. I don't see any issues for the honest analyst; however, there could be opportunity to "bias" an analysis in marginal cases if so disposed.

ReplyDelete