topic What is the significance behind confidence intervals and alpha value? in Statistical Procedures

What is the significance behind confidence intervals and alpha value?

Babloo — Mon, 09 Feb 2015 08:32:36 GMT

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!

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

MichelleHomes — Mon, 09 Feb 2015 09:40:47 GMT

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

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

Ksharp — Mon, 09 Feb 2015 09:47:44 GMT

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

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

Babloo — Mon, 09 Feb 2015 10:24:37 GMT

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.

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

Babloo — Mon, 09 Feb 2015 10:28:16 GMT

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.

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

Ksharp — Mon, 09 Feb 2015 10:58:46 GMT

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

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 .....