Beta coefficient vs. Significance coefficient

[Kontilera]

Hello Physicsforums!
I've stumbeld on a problem in statistics (which is one of my weaknesses when it comes to math).

I´m currently trying to analyze data from a study and using multiple regression analysis.
From regression analysis with one independent variable I´m used to mainly focus on the significance values. When there are more independent variables however I understand that it is the beta and tolerance values that are of importance.

I am now wondering if anybody could help me understand why the significance value isn't relevant?

+ what determines wheater it is the standardized or not standardized coefficients that are relevant for my study?

Thanks in advance!

 

[FactChecker]

The statistical significance of a variable in a model addresses a different issue from it's standardized coefficient (aka beta). If a variable has a large beta, changing it tends to lead to a large change of the estimated variable, but it doesn't say how statistically strong that relationship is. A variable can have a large beta and a small statistical significance (or visa versa). When deciding if a variable should statistically be in the linear model, the statistical significance is important. Once the model is determined and the statistically best variables are in it, beta helps you characterize that linear model.

 

[jim mcnamara]

Traditional use of the terms alpha and beta in statistics:
Beta is the probability of Type II error in any hypothesis test. It tells us if we are
incorrectly concluding no statistical significance.
Alpha is the probability of Type I error in any hypothesis test - wrongly claiming
statistical significance.

Tiger chow:
This dumb but essentially correct story helped a lot of my students to get Type I and Type II.

Have you ever seen faces in clouds? Are there really faces up there or is this a construct
of some hard-wiring of neurons in the brain?
Long time ago, two people are walking home. They see a bush way up ahead. Person A says:
It kinda looks like there is a tiger behind that bush. Person B says: I dunno, but that is
the shortest way home. Person A and B go their chosen ways. Most of the time B gets home,
but sometimes winds up as tiger chow. Long term people behaving like Person A contributed
more offspring to the gene pool. Person B is committing Type II errors long term. And hence not
around to have and raise kids.

Type II == tiger chow! Type I is more harmless. Why we often see faces when there are none there
most times. Or get that creepy uneasy feeling in some places.

Note: some texts and lots of software unfortunately use "beta" for population regression
coefficients.

Do not confuse the two concepts. I cannot tell if that is what is going on here.

 

[FactChecker]

Traditional use of the terms alpha and beta in statistics:
Beta is the probability of Type II error in any hypothesis test. It tells us if we are
incorrectly concluding no statistical significance.

That is not the same beta that the OP is referring to. The OP beta refers "to how many standard deviations a dependent variable will change, per standard deviation increase in the predictor variable." (see https://en.wikipedia.org/wiki/Standardized_coefficient )

 

[jim mcnamara]

@FactChecker - Wasn't clear to me. Thanks for the correction. And as you know there are several meanings for beta, so instead of the OP
being confused, I was.