Monday, October 9

Statistical Significance (hehe)

Surat Al-Baqarah, Qur'an 2:1-5.
(~translated by Yusuf Ali:)
In the Name of Allah, The Compassionate, The Merciful
1) A.L.M.
2) This is the Book; in it is guidance sure, without doubt, to those who fear Allah;
3) Who believe in the Unseen, are steadfast in prayer, and spend out of what We have provided for them;
4) And who believe in the Revelation sent to thee, and sent before thy time, and (in their hearts) have the assurance of the Hereafter.
5) They are on (true) guidance, from their Lord, and it is these who will prosper.
...

And so begins the second Surah of the Qur'an.
_________________________

Don't read this post and think I'm a nerd--because I struggle to pass my classes...to think about my classes...sort of.

So there I was in class, a starry-eyed aspiring stats-minor, mesmerized by my PhD candidate prof whose Portugese accent is undetectable until he says "column." The prof who looks right at me, as if the rest of the universe does not exist, and smiles upon hearing my questions--not because I'm a girl, but because he gets where my thoughts circle. As if he can look through my being and literally see the thoughts at which my questions originate.

And suddenly, we're studying the dilemma of ancient statisticians:

Consider a uniform distribution, where the probability of any event is as likely as every other event.


The probability of a single event occurring (on a continuous interval) = 0.This is just another way of saying that the probability of such occurrance is insignificant. For example, say you have the range of [real] numbers, 1-9. This doesn't mean there are nine possibilities; There are actually infinite possible events (1, 1.00000000034, 5.89, 4.999999999999999, etc.). In contrast, if you had a finite number of possibilities (like the discrete integers, "1, 2, 3, & 4"), and you wanted to know what the probability would be to randomly have outcome = 3, you know it'd be 1/4. In the first example, the total possible outcomes are infinite, so 1/infinite, one would imagine, is pretty insignificant, or may as well be = 0.

Pretty basic. That said:

There is another property of stats that establishes that the sum of all possible probabilities must = 1. Considering the latter example mentioned above with integers 1, 2, 3, and 4, this would mean that the total probability = (the probability of "1") + (the probability of "2") + (the probability of "3") + (the probability of "4")...And this is "1/4 + 1/4 + 1/4 + 1/4 = 1."

There is a head-aching disaster that statisticians encountered upon trying to apply this sum = 1 rule to the case of continuous intervals, where the number of total events possible is infinite instead of simply 4. As stated before, 1/infinite is basically zero. And yet the sum of these infinite event probabilities, each added, must = 1. Infinite zeroes will never add to one, yet that would be saying that there is no probability--that it is, in fact, impossible--for any of the events of the continuous interval to occur, which simply is false. The probability of the event, "4.999999999999999," is 0 or insignificant, but that cannot mean that there is no probability of any event between 1 and 9 occuring on the continuous interval, 1-9. It is the epitome of false (this is not a technical definition, ps).

AND THEN

came the use of integrals in order to find the area under curves (distributions) for continuous intervals. Suddenly the arithmetically impossible--the epitome of false--became so very possible, so very probable, so very true. The area under the curve (the total probability) is always = 1, and integration allows this to be calculated, where as the previous, non-calculus statistical laws failed at every attempt to explain this "phenomenon."

And tears nearly came to my eyes. How some human beings can count away their proofs against the existence of God, when maybe He just hasn't given us what here would be integration--in order to test, to define faith, to distinguish those who choose to believe from those who don't. And maybe it's all just that simple.

Here's to believing in The Unseen.

4 comments:

Outspoken Soul said...

Umm.

mashaAllah.

Can you help me with my stats homework? I messed it up last time and determined not to do it again.

Much appreciated,
Alia

Samira said...

Can try--call, as I have done without regard :) and we can set up a time to work on this, inshaa'Allah. mornings before 8:30am and evenings 5pm and after work best, plus anytime on weekends for now.

am everso indebted, though not worn of asking :(


Much honored,
ukhtuki fi Islam

rima said...

samira. why are you trying to confuse us. just go to sleep, ok?

haha ilu :)

Wanksta said...

i had tears in my eyes during stats once too. it was, however, unrelated to spiritual insights and mostly to the C minus on the exam.