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Recent questions in Correlation And Causation

garkochenvz 2022-08-16

Why is the standard deviation important for non-normal distributions?
In the case of the normal distribution, I know that the standard deviation tells me that 78% of my sample is in the interval $[μ - σ, μ + σ]$
Suppose I have another sample which is not normally distributed. Is there any valuable information I get from knowing the standard deviation of that sample?

metodystap9 2022-08-13

If we have two non-zero correlated random variables then they are dependent.
Why then do we have the saying "Correlation does not imply Causation". A change in one variable may not cause exactly the same change in another but there is at least some 'causal' link.

Brylee Shepard 2022-08-13

What’s Wrong?
Motorcycles and Sour Cream In recent years, there has been a strong correlation between per capita consumption of sour cream and the numbers of motorcycle riders killed in noncollision accidents. Therefore, consumption of sour cream causes motorcycle fatalities.

Matonya 2022-08-12

Advantages of Mathematics competition/olympiad students in Mathematical Research
Everyone in this community I think would be familiar with International Mathematical Olympiad, which is an International Mathematics Competition held for high school students, with many countries participating from around the world.
What's interesting to note is that many of the IMO participants have gone to win the Fields Medal. Notable personalities include Terence Tao (2006), Ngo Bao Chau (2010), Grigori Perelman (2006), etc.
I would like to know: What advantages does an IMO student possess over a 'normal' student in terms of mathematical research? Does the IMO competition help the student in becoming a good research mathematician or doesn't it?

Freddy Friedman 2022-07-23

Probability (independent?) events
Hi everyone I have a question about the following problem:
Events for a family: $A_{1}$ = ski, $A_{2} =$ = does not ski, $B_{1}$ = has children but none in 8-16, $B_{2}$ = has some children in 8-16, and $B_{3}$ = has no children. Also, $P (A_{1}) = 0.4$ , $P (B_{2}) = 0.35$ , $P (B_{1}) = 0.25$ and $P (A_{1} \cap B_{1}) = 0.075$ , $P (A_{1} \cap B_{2}) = 0.245$ . Find $P (A_{1} \cap B_{1}) = 0.075$ .
Here is my solution:
Since P(A1 and B1) = 0.075, P(A2 and B1) = 0.25-0.075= 0.175. Also since P(A1 and B2) = 0.245, P(A2 and B2) = 0.35 - 0.245 = 0.105. From this we can find P(A2 and B3) which is 0.6-0.175-0.105 = 0.32. But when I use the formula for independent events formula $P (A_{2} \cap B 3) = P (A_{2}) * P (B 3)$ I get 0.24. Does this mean that the events are not independent? If so, how are these events not independent?

Israel Hale 2022-07-22

Correlation and causation data
What are some real life examples (data) in which high correlation:
1) implies causation
2) doesn't imply causation.
I know that there is a lot of data out there of weird correlations, like divorce rate and consuption of margarine, but the problem with this data is, that we don't really know if one is caused by the other, because nobody tested it, so we cannot strictly say that they're unrelated.

Lillie Pittman 2022-07-21

Causation doesn't imply correlation and correlation does not imply
causation
Let P := |corr(X,Y) > .5| let Q := exits a relation F: $X ⟹ Y$
Then the often stated line of correlation does not imply causation is simply! $Q ⟹ P$ .
It is also true that causation does not imply correlation. So! $Q ⟹ P$
But $(P ⟹ Q) \lor (Q ⟹ P)$ is a tautology.

scherezade29pc 2022-07-20

Correlation of Rolling Two Dice
If A is a random variable responsible for calculating the sum of two independent rolls of a die, and B is the result of calculating the value of first roll minus the value second roll, is is true that A and B have a $c o v (A, B) \neq 0$ ? In other words, is it true that they are correlated?
I've come to the conclusion that they must be correlated because they are not independent, that is, the event of A can have an impact on event B, but I remain stuck due to the fact that causation does not necessarily imply correlation.
I know that independence −> uncorrelation, but that the opposite isn't true.

Tamara Bryan 2022-07-20

1. In your own words, describe the difference between continuous and discrete data sets.
2. What is the difference between the independent and dependent variable? How do you determine which goes on which axis on your graph?
3. What are the four types of correlation?
4. How do they differ from one another?
5. In your own words, explain the difference between correlation and causation.

wstecznyg5 2022-07-18

What do we mean when we say that correlation does not imply causality? What are some of the ways in which an empirical analyst attempts to disentangle the two?
Provide examples.

Libby Owens 2022-07-18

Correlation: Concept to FormulaIn digital signal processing, we calculate the correlation between two discrete signals by multiplying corresponding samples of the two signals and then adding the products. Where does this process/formula for correlation come from?
I understand the concept of correlation (similarity) between two signals. But I fail to understand how it translates to the formula that it does.
All the texts I have seen so far start with this formula and explain cross correlation, auto correlation, etc. None of them attempt to explain how the formula was derived in the first place.

Shannon Andrews 2022-07-16

PCA vs Correlation
What is the relationship between (first) principal component(s) and the correlation matrix or the average correlation of the data. For example, in an empirical application I observe that the average correlation is almost the same as the ratio of the variance of the first principal component (first eigenvalue) to the total variance (sum of all eigenvalues).
Is there a mathematical relationship?

Correlation and causation are two important concepts in mathematics. Correlation is when two variables are related, meaning a change in one variable can cause a change in the other. Causation is when one variable causes a change in the other. To understand the difference between these two concepts, it is important to understand how equations can help answer questions about correlation and causation. Equations can help determine if a change in one variable will lead to a change in the other, and if so, how much. When studying correlation and causation, equations are a useful tool for determining the strength of the relationship between the two variables. If you need help understanding correlation and causation, on our site you can find the answers you need.

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