Statistics is NOT mathematics

In summary, the conversation discussed the topic of probability and the assumptions made in solving problems. It was mentioned that assuming independence between two factors, such as wind and rain, can lead to incorrect conclusions. The conversation also touched on the idea of mathematics and its relationship with reality. The example of a quiz with 6 multiple choice questions was given, and the solution was explained to be a matter of chance.
  • #1
Whalstib
119
0
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 anyone 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
 
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  • #2
Whalstib said:
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.

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!"
 
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  • #3
Office_Shredder said:
Alternatively, your claim that rain and wind are independent is false.

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
Whalstib said:
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

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

The wind is calm for almost 52 per cent of all hours, but only
for approximately 25 per cent of the wet hours

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
 
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  • #5
Office_Shredder said:
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


Not even ...

W
 
  • #6
Office_Shredder said:
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


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

W
 
  • #7
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
Can you post the solution for the 6 multiple choice questions thing you mentioned in the first post. It sounds interesting.
 
  • #9
Whalstib said:
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

The problem here is that you completely misunderstand the definition of "independent". Can you tell us what you think it means?
 
  • #10
Number Nine said:
The problem here is that you completely misunderstand the definition of "independent". Can you tell us what you think it means?

EXACTLY!

I get what you are saying but I could easily illustrate weather scenarios where at anyone 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
Dmobb Jr. said:
Can you post the solution for the 6 multiple choice questions thing you mentioned in the first post. It sounds interesting.

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
 
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  • #12
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
Whalstib said:
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.
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.

In stats terms: R^2 = 0

W
 
  • #14
I get what you are saying but I could easily illustrate weather scenarios where at anyone point the wind and rain are clearly independent, from 2 separate weather fronts.

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 [itex]P(W) \cap P(R) = P(W)P(R)[/itex]. The problem is not with statistics, it's with your lack of knowledge of statistics.
 
  • #15
Number Nine said:
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 [itex]P(W) \cap P(R) = P(W)P(R)[/itex]. The problem is not with statistics, it's with your lack of knowledge of statistics.


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
Whalstib said:
I can hardly be held at fault for using the above definition of independence...

Yes you can.
 
  • #17
Just a not so random question, but have you studied linear algebra before? I really hope the answer is no.
 
  • #18
Uvohtufo said:
Yes you can.
Nope,

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

Pity..

W
 
  • #19
MarneMath said:
Just a not so random question, but have you studied linear algebra before? I really hope the answer is no.

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
Whalstib said:
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

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

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.

How about this:
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
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
MarneMath said:
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.

Thanks for seeing it my way!

W
 
  • #25
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.
 
  • #26
I don't know if this is pedantic, but the name of the topic should be 'probability...', and not 'statistics...' Once you know ; have an actual value of some population parameters, you're dealing with probabilities. Statistics goes in the opposite direction,where you try to figure out the pop.parameters from sample data.
 

What is the difference between statistics and mathematics?

Statistics is the study of collecting, organizing, analyzing, and interpreting data. It involves using mathematical methods and models to draw conclusions and make predictions about a population based on a sample. Mathematics, on the other hand, is a broad field that includes the study of numbers, quantities, and shapes, as well as their relationships and operations. While statistics uses mathematical tools, it also incorporates concepts from other fields such as probability and data analysis.

Can statistics be considered a branch of mathematics?

While statistics relies heavily on mathematical principles, it is not considered a branch of mathematics. This is because statistics involves more than just mathematical calculations; it also involves designing experiments, collecting data, and interpreting results in a real-world context. Additionally, statistics has its own set of unique principles and concepts that are not found in other branches of mathematics.

Do you need to be good at math to understand statistics?

While a basic understanding of math is necessary for statistics, you do not need to be a math genius to understand it. Many statistical concepts can be explained using everyday language and visual aids. However, having a solid foundation in math can help with understanding more complex statistical concepts and performing calculations.

Why is it important to differentiate statistics from mathematics?

Differentiating statistics from mathematics is important because it helps to avoid confusion and misunderstandings. While statistics and mathematics are closely related, they have different goals, methods, and applications. By understanding the differences between the two, we can use them effectively to solve different types of problems and make informed decisions.

What are some common misconceptions about statistics being a branch of mathematics?

One common misconception is that statistics is only about numbers and calculations. In reality, statistics also involves critical thinking, problem-solving, and communication skills. Another misconception is that statistics is only used in fields related to math, such as science and engineering. In fact, statistics is used in a wide range of disciplines, from social sciences to business and healthcare.

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