# Statistics is NOT mathematics

1. May 12, 2013

### Whalstib

Hi,

I was just working on a problem based on the probability of wind or rain. The only way to solve it is to assume they are dependent factors when they clearly are not. Assuming independence will lead to the wrong conclusion.

If stats demands one ignore reality to solve a problem, to bend reality into the formula to make it accurate I contend it is nothing but game playing and puzzle solving, at least in probability.

Another great example we have been given on an exam is you have 6 multiple choice questions.. You have an 80% chance of getting any one individual question right. Create a scenario where you can get 100% correct. The solution is some bizarre random number scheme and does NOT give 100% accuracy. Anything less than KNOWING 100% would be pure chance.

I never thought I would miss vector calc but at least you could prove it without changing reality...

W

2. May 12, 2013

### Office_Shredder

Staff Emeritus
Alternatively, your claim that rain and wind are independent is false.

Furthermore, even if you were correct in the specific examples of wind and rain (which if you google you will find there is generally a nonzero correlation between them) this would be on the order of being in a physics class and complaining "But ramps always have friction! This has nothing to do with reality!"

Last edited: May 12, 2013
3. May 12, 2013

### Whalstib

It's windy here right now and not a cloud in the sky. Rained the other day and no wind, rained last week lots of wind.....If "dependent" the definition of "not independent" there would be a correlation and there is not.

In stats terms: R^2 = 0

W

4. May 12, 2013

### Office_Shredder

Staff Emeritus
In stats terms, the number of measurements you just gave does not give a statistically significant answer

http://www.cmhc-schl.gc.ca/odpub/pdf/65546.pdf

here is just one example where a strong correlation between rain and wind is discovered, with implications for how buildings should be constructed. Please realize that you just passed off "nuh uh" as mathematics while deriding statistics for not being real mathematics

Last edited: May 13, 2013
5. May 13, 2013

### Whalstib

Not even ....

W

6. May 13, 2013

### Whalstib

Sorry...just messing with you...cramming for a stats final finally got to me...:D

W

7. May 15, 2013

### Uvohtufo

Well... what makes something math?

"Mathematics" as I loosely understand the word, is used to refer to calculations and proofs, often about numbers.

Mathematics doesn't rely on the world for validity. The mathematical proposition '2+2=4' is not true because of some feature of the world we know empirically. The validity of a mathematical proposition comes from the rules of math. So, you claim that in statistics we can make assumptions which are empirically false. How does that preclude statistics from being a kind of math? All math ignores reality.

If the world and mathematics appear to bear semblance, its the viewer who makes the association. Mathematics has rightfully not been built up by empirical connection (that historically, comes after the math has been invented).

8. May 15, 2013

### Dmobb Jr.

Can you post the solution for the 6 multiple choice questions thing you mentioned in the first post. It sounds interesting.

9. May 15, 2013

### Number Nine

The problem here is that you completely misunderstand the definition of "independent". Can you tell us what you think it means?

10. May 15, 2013

### Whalstib

EXACTLY!

I get what you are saying but I could easily illustrate weather scenarios where at any one point the wind and rain are clearly independent, from 2 separate weather fronts.

It is interesting how one could be so dead wrong basing an assumption on phenomena they have experienced through their lives.

That said I still feel I can argue my way out of the dependence clause put forth unless worded much more specifically.

Thanks,

W

11. May 15, 2013

### Whalstib

OK here is is verbatim:

"You take a quiz with 6 multiple choice questions. You surmise that you have an 80% chance of getting any individual question correct. In your own words, explain how you could create a simulation in which all 6 multiple choice questions are answered correctly."

My response, for zero points BTW!, in essence was no matter what it boils down to a coin flip since I do not know with 100% certainty.

A bonus was offered on "What are the chances of getting all 6 questions correct?"

I responded .8^6 = .262144. wrong again for zero points....

A post exam discussion centered on random number schemes that did not seem to improve the chances. We were never told the solution....

W

Last edited: May 15, 2013
12. May 15, 2013

### Uvohtufo

Whalstib,

I think NumberNine was getting at something you arent appreciating. That, I suspect being, that dependent and independent have explicit statistical definitions, not conventional linguistic definitions.

Like, for example, I recently did a project at my university where I tried to estimate forest fire damage based off the dollar investment in forest fire suppression of previous years. The dependent variable was forest fire damage. But there has been plenty of research done where the reverse was held. 'dependence' is something defined within a statistical model.

When you do statistics you are just getting numbers and perhaps certain levels of predictive power. Intuitive notions about the meaning of those numbers, or whether one variable is a cause and another is an effect , is something that lies outside the mathematics.

Perhaps someone else can say it better than I can. I am not the most savvy regarding statistics.

13. May 17, 2013

### HallsofIvy

That is NOT what correlation means. It is quite possible for both of those to be true and for there to be a strong positive correlation.

14. May 17, 2013

### Number Nine

Let me state myself more clearly: You don't know what "independent" means.
The fact that it can rain in the absence of wind (and vice versa) does not mean that the two are independent. You need to show that $P(W) \cap P(R) = P(W)P(R)$. The problem is not with statistics, it's with your lack of knowledge of statistics.

15. May 17, 2013

### Whalstib

I know EXACTLY what independent means. You forgot, as did my instruction, to say "you do not understand what independence means in the context of statistics." THAT would be a valid statement. without that clarification you could not be more wrong... See what I mean..

Independent:

1. not influenced or controlled by others in matters of opinion, conduct, etc.; thinking or acting for oneself: an independent thinker.
2. not subject to another's authority or jurisdiction; autonomous; free: an independent businessman.
3. not influenced by the thought or action of others: independent research.
4. not dependent; not depending or contingent upon something else for existence, operation, etc.
5. not relying on another or others for aid or support.

while it is agreed upon that in the instance I put forth the wind and rain are dependent and must be for the solution to work I can hardly be held at fault for using the above definition of independence.....

W

16. May 17, 2013

### Uvohtufo

Yes you can.

17. May 17, 2013

### MarneMath

Just a not so random question, but have you studied linear algebra before? I really hope the answer is no.

18. May 17, 2013

### Whalstib

Nope,

This is my point... many of you are so delusional you can not see facts from theroy.

Pity..

W

19. May 17, 2013

### Whalstib

And so it continues...in place of factual proofs it is simply a war of words.

The mere fact some of you can not concede the rest of the world has a very different definition and point of view for independence is quite humorous.

Thanks to some of you I now have a better grasp on how to approach such problems.

Thanks to others I have a better grasp on how to approach statisticians... for better or worse...

W

20. May 17, 2013

### Whalstib

Oh yes I have studied a little linear algebra, not as a formal class but have been introduced to it.I do not recall having to change the English language to make it valid...

21. May 17, 2013

### MarneMath

Meh, I really wouldn't know how to prove it to you. It's a definition, a description of the interaction between sets that if true has some nice mathematical properties. If you can't get over the word independence between what you think it means in the real world versus what it means in probability, then I really don't know how to help you.

22. May 17, 2013

### Whalstib

It seems you are not actually reading my posts ...

I conceded several times it IS a valid way to approach to problem and only added it for the math to work it must be clear there is a dependence.

Are suggesting wind and rain are ALWAYS dependent? I contend not.

There is a .20 prob. rain and a .43 prob of wind and a .62 of both, what is the prob of wind and rain? Oh yea it is a .20 prob in Paris and .43 in Los Angeles....Does that make a difference? Are they dependent or independent? Does the language make a difference?

W

23. May 17, 2013

### MarneMath

If each probability assigned is representing events within a single universal set and their intersection is not null, then I can say they are dependent. The second sentence regarding the city location is one I cannot answer, mostly because I have no idea how these two events interact and have no ability to discern the intersection of events. However, i'm willing to say that I would assume that the intersection would also not be null, mostly because if I am wrong and it is null, that's an easier adjustment :)

24. May 17, 2013

### Whalstib

Thanks for seeing it my way!

W

25. May 17, 2013

### D H

Staff Emeritus
Whalstib, it appears that you are being intentionally obtuse. That is not a good way to learn any subject.

First off, every subject has its own jargon with terms that sometimes differ from the lay meaning of the same term. Some examples: "Discovery" means something rather specific to a lawyer. "Weight" is a force in physics but legally and colloquially weight is a synonym for mass. "Worm" and "bug" mean something rather different in computer science than the lay meaning of those terms. "Bug" has a specific meaning to a biologist while lay people use it as a catch-all term. You need to stop complaining about jargon.

Secondly, the statistic meaning of independence is completely consistent with the lay meaning. One of the lay meanings of independent is "not influenced by." That is exactly the meaning in statistics, only now there's a specific mathematical test how to determine whether one event is "not influenced by" another. Your complaints are ill-founded.