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What is the significance behind confidence intervals and alpha value?

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Super Contributor
Posts: 426

What is the significance behind confidence intervals and alpha value?

In general modelling, we will reject the null hypothesis if P value is less than alpha value (P<0.05) and we fail to reject the null hypothesis if P value is greater than or equal (P>=0.05) to alpha value. Although I tried to understand the significance behind alpha value i could not understand it's significance.

Why we should reject the null hypothesis if P value is less than alpha value (P<0.05) for 95% CI? Can someone tell me the significance behind alpha value and confidence intervals?

Thanks!

Trusted Advisor
Posts: 1,272

Re: What is the significance behind confidence intervals and alpha value?

The SAS/STAT user guide has some definitions that may help - SAS/STAT(R) 13.1 User's Guide - Hypothesis Testing, Power, Confidence Interval as well as this old SUGI paper - http://www2.sas.com/proceedings/sugi22/STATS/PAPER270.PDF

Kind Regards,

Michelle

Super Contributor
Posts: 426

Re: What is the significance behind confidence intervals and alpha value?

Thanks for the document.

However, I'm not clear on the point, 'Another common approach is to reject the null hypothesis when the %~o confidence intervals of the means do not overlap' from the documentation. If you can explain, it would be better for me to understand.

Super User
Posts: 9,769

Re: What is the significance behind confidence intervals and alpha value?

P value is actually the probability of  (H > H0 )   (H0 is  the estimator when H0 is true) .

And keep in your mind, all the estimators whether it is Normal estimator or Chi-square  estimator , they are all the estimator of deviation of expected value.

i.e. they all contains a   X-X0     ,it is a deviation , X0 is the estimator value when H0 is ture.

Take right test as an example:  If P(H > H0 ) = 0.001 , means there is very few estimator H greater than H0 ,which means H0 is very very large ,on account of benchmark of significant degree ALPHA=0.05 . therefore X-X0   is very very large , X is differently than X0 .

Xia Keshan

Super Contributor
Posts: 426

Re: What is the significance behind confidence intervals and alpha value?

What is H and X in your comments?

And keep in your mind, all the estimators whether it is Normal estimator or Chi-square  estimator , they are all the estimator of deviation of expected value.- Any possibilities to expand this statement? I'm still not clear.

Super User
Posts: 9,769

Re: What is the significance behind confidence intervals and alpha value?

Assuming we have a variable named X which conform to Normal Distribution .

x.png

H is  hypothesis test  estimator which conform to Normal Distribution .

X is x in picture.

X0 is theta in picture . which is a value when H0 is true . e.x. H0: mu=0 , theta is 0 .

You see there is a measure of deviation ( x-theta ).

Chi-Square distribution also have such forum :  (x1- e)^2/e  +  (x2- e)^2/e   .....

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