Tolerance

 

tolerate it

I wait by the door like I'm just a kid
Use my best colors for your portrait
Lay the table with the fancy shit
And watch you tolerate it
If it's all in my head tell me now
Tell me I've got it wrong somehow
I know my love should be celebrated
But you tolerate it

Tolerance is uncertainty, NOT error!

I learned statistics as an Engineer, and what statisticians call Standard Deviation, SD, I was trained to call Tolerance.  The problem is that in this case deviation does NOT mean error, so it is IMHO bad branding. 

Let’s use a fair game of craps as an example.  The Mean/Median/Mode is a roll of 7, but the possible rolls are from 2 to 12.  The tolerance is the highest roll minus the mean roll divided by 3 or (12-7)/3= 1.67. The variance is 1.67 squared, or 2.77.

The error and the tolerance, SD, have NOTHING to do with each other.  The error is 0 because it is a fair game.  The standard deviation is NOT zero because while it is a fair game it is an uncertain game, a game of chance. 

·       The mean plus one tolerance is 8.67.  To be a "normal" distribution  it should have 68% of the outcomes.  It has rolls of 2, 3, 4, 5, 6, 7 or 8  which are 31 of the 36 outcomes or 86%.

·        The mean plus two tolerances is 10.33. To be a "normal" distribution it  should have 95% of the outcomes. That means rolls of 2, 3, 4, 5, 6, 7, 8, 9, 10 which are 33 of the 36 outcomes or 92%. 

·        The means plus three tolerances is 12.To be a "normal" distribution it should have 99% of the outcomes. That means 2, 3, 4, 5, 6, 7, 8, 9,10,11,12  which are 36 of the 36 outcomes or 100%.

Only if there is no chance, is there no error.  So a sample can be correct, in that it is certain, but that does not mean that its standard error is zero. Tolerance and error are as different as INtolerance and no error.   Don’t mistake error with uncertainty.  What is next? Mistaking median for mean? Are you trying to prove Disraeli's attribution by Twain: Lies, Damn Lies, and Statistics? Marginal tax rates for effective tax rates? Are you Reaganomics?   End of Life discussions for Death Panels.  Are you MAGA?  Bribes for gratuities? Are you the Supreme Court?