Measure of Standard deviations

[Toby]

So, -3sd on any DS means 2.4sd?

The -3sd is for a particular DS.

Sorry, I get confused with all the symbols.

[Bayes]

The larger the SD (or z-score) the smaller the probability of reaching it, so the smaller the z-score the higher the probability. The -3SD corresponds to a particular preselected DS and the -2.4SD is for ANY DS.

[Toby]

Let´s compare some scenarios.

We pick 4 neighbor numbers, such as 0 32 15 19 on a french singlezero wheel and after 1000 trials we hit 137 times, we have +3sd. The 4 numbers hit 34 34 34 and 35 times. Any of the 4 have little less than 2sd each. The event happens 27/10k, that is 1000 trials tested 10,000 times gives 137 hits for the 4 numbers we picked beforehand 27 times.

To find 3sd on any group of 4 on the wheel after 1000 trials is 27x37=1000/10000 or 1/10. The probability dropped from 27/10000 to 1/10.

Supose we have the 1000 sample and take 4 numbers that their sum is 137 hits, numbers are scattered. The sd measure drops. We need 4 numbers with +1.9sd each to get +3sd in the group. How would you know it?