The Standard Error of a Difference

Here, by the grace of Chance, we've staked a Mean,
Uncertain marker of elusive truth.
But have we caught a fact, or trapped a doubt
Within this stretching span of confidence--
A shadow world four standard errors wide,
All swollen by the stint of observation?
For recollect that once in twenty times
The phantom Truth will even lie beyond
That span, in the unending thin-drawn tails
Which point to the infinitude of Error.
 
Here stands another Mean, an unlike twin,
Another child of planless Chance,
Different, as sons are differently cast
By random sorting of the parent genes.
Yet different too, it may be, by Design,
By treatments planned to conquer Chance
And weight the rolling dice in divers ways
To part these Means, as true twins may be parted
Despite a likeness in heredity
By greater strength of circumstance.
 
which is the stronger variance? WITHIN
The scores are tumbled by unreckoned factors;
BETWEEN, there is the mirroring of these
Plus what Design has added. We make this test:
The standard error of the difference, 
Extracted from the sum of variances
WITHIN these twin-tossed congeries of Chance,
Is matched against the difference BETWEEN,
If twice outdone, Chance has lost the contest
To Design. We shout exultant, It's a Fact!
 
But still we're cautioned by those ominous tails,
which point to Error ad infinitum.
 
                            ----Anonymous