I am happy that you will become a teacher in mathematics and I would like to inform you of the way I destroyed mathematics, by mathematics themselves…
(Poor orphan girl, we try to help you for these studies, and don’t resist your own teachers with my arguments: just obey, get the diploma and get the job, then in 5 years maybe, read what I proved…)
- estimated standard deviation : the (FDA etc.) calculation is false
- proof of normality : the (FDA etc.) principle is false
- validation by non-significance : the (FDA etc.) principle is false
- most probable number : the (ISO etc.) principle is false
I wrote 4 web-sites about that, but almost all of them in French language, sorry. (http://www.kristofmeunier.fr/varians.htm ; http://www.kristofmeunier.fr/Normal_sin.htm ; http://www.kristofmeunier.fr/NonSignificatif.htm ; http://www.kristofmeunier.fr/npp_plus.htm ). Here I faced mainly anger, pretending I am insulting the teachers and celebrities of the past centuries… Now this bad Western World makes war with Islam, and I know you are a Muslim girl, so maybe I try in the other side if there would be more comprehensiveness/honnesty.
As a first glance I tell you simply the standard deviation problem: The standard deviation S is the quadratic average “distance from average”. There is no problem on a population of N items, but the problem occurs when you select just a sample of n items (n smaller than N) and want to estimate S on the population, this estimation being written s, because there is a bias: the calculation of S refers to the average inside the sample, m, which is best centered, the true average in the population M being worse centered, thus S simply calculated against m is underestimated. There is a correction into s, but I deny that its value is the good one. I have proven my correction with n=2 and N=3 (no matter what are the values x), and confirmed it with dozens of other cases.
University law:
Population: S² = sum(x-M)² /N = average(x-M)²
Sample: no matter N, s² = sum(x-m)² /(n-1) = average(x-m)² * n/(n-1)
Meunier-Malcor formula : (unchanged for Population; Sample:)
- Sampling without replacement (if each selected item is removed from the population before taking the next one):
s² = average(x-m)² *[n/(n-1)] * [(N-1)/N]
- Sampling with replacement (if each selected item is put back in the population before taking the next one):
s² = average(x-m)² *[n/(n-1)] * [(N+1)/N]
- If N is infinite:
s² = average(x-m)² * n/(n-1)
--------------------- Addition 02/24/2018 ---------------------
I enclose here the way to proove what I say (the official law is proven wrong), what nobody dares to verify:
