Questions and Answers about Test 2




On Thu, 12 Mar 1998, YUEN MO HIN wrote:

>
> (1) Is it true that in the Bonferroni, we will reject Ho if
>     P-value > alpha/g?

NO. REJECT IF P < ALPHA/G.

>
>
> (2a) In homework question 22.4 part (d), isn't it the reduced regression
>      model is the one without the interaction term?  If it is, then how
>      can we test for interaction effects with only factor A and factor B?
>

YOU'RE RIGHT. THE REDUCED MODEL HAS NO INTERACTION TERM. THE FULL MODEL
HAS ONE. COMPARING R-SQUARED FROM THE FULL & REDUCED CAN TELL YOU IF THE
FULL IS   * SIGNIFICANTLY *  BETTER THAN THE REDUCED. THIS WAS COVERED IN
STA 302. SEE THE INDEX OF YOUR TEXT. LOOK UNDER "FULL" AND "REDUCED."  FOR
DOING IT WITH SAS, SEE SAS LESSON 2 ON THE WEB.

>
> (2b) How can we do question 22.4 part (e)?
>      Do we use the formula of
>
>       F* = {[SSE(R) - SSE(f)]/df(R) - df(F)} / [SSE(F)/df(F)]
>
>      annd if F*<= F, we conclude Ho (that is interaction effects present)?
>

SEE THE LAST REMARK ABOVE. THIS IS EXACTLY WHAT SAS IS DOING WITH THE test
STATEMENT IN proc reg.


>
> (3a) Is it whenever the P-value > alpha, we resject Ho?
>

NO. REJECT WHEN P < ALPHA. YOU HAVE THIS BACKWARDS CONSISTENTLY, AND IT IS AN
IMPORTANT POINT.


>
> (3b) And whenever the F* <= F, we conclude Ho?
>

YES. THIS WILL HAPPEN IF AND ONLY IF P >= ALPHA.

>
> (3c) Is there any other way we can look from the SAS print out to make out
>      conclusion about rejecting or accepting Ho?
>
>


IN GENERAL, REJECT H0 IF AND ONLY IF P < ALPHA.  THIS IS THE MAIN 
ANSWER TO YOUR QUESTION; NOT THE ONLY ONE. 


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On Thu, 12 Mar 1998, FOK GARY PAK KIN wrote:

> Hi,this is Gary. Sorry for asking you this late. I have some questions to
> ask you.
> I am very confused about the defination of 'Equal importance and Unequal
> importance', I read through the book but I am still very confused between
> these two names.
> 1) Is the equal importance means the equal sample size and unequal
>    importance means unequal sample size?

I AGREE THAT THIS IS A LITTLE VAGUE IN THE BOOK. FOR THIS REASON, IN
OUR CLASS THE ONLY KIND OF "IMPORTANCE" WE WILL ONLY CONSIDER IS
IMPORTANCE PROPORTIONAL TO SIZE OF THE SUB-POPULATION CORRESPONDING TO A
TREATMENT MEAN IN AN OBSERVATIONAL STUDY (RE-READ THIS STATEMENT).

SAMPLE SIZES MAY BE UNEQUAL BY SAMPLING. IN THIS CASE, RELATIVE SAMPLE
SIZES WILL BE GOOD ESTIMATES OF RELATIVE POPULATION SIZES (IF THE TOTAL
SAMPLE SIZE IS LARGE), AND THEREFORE THEY MAY BE CONSIDERED TO REFLECT
"IMPORTANCE."

> 2) What does the word 'reflect' means in 'reflect unequal importance of
>    treatment means.

IT ALMOST SEEMS LIKE YOU READ MY LAST STATEMENT ALREADY. REFLECT MEANS
"INDICATE."

> 3) How to interprete the confidence interval? For example, in the lst file
>    of SAS Lesson 4. What should I say for the confidence intervel for
>    Middle height-Bottom height??

IF WE WERE TO TAKE MANY, MANY SAMPLES AND CONSTRUCT INTERVALS IN THIS WAY,
95% OF THE INTERVALS WOULD CONTAIN THE TRUE (POPULATION) VALUE OF THE
CONTRAST L.  IN THIS SENSE WE CAN SAY WE ARE "95% CONFIDENT" THAT THE REAL
VALUE OF L IS IN THE INTERVAL WE OBTAINED FROM THE SINGLE SET OF DATA WE
HAVE.  THE FIRST STATEMENT IS PRECISE. THE SECOND ONE IS LOOSE, BUT IT'S
THE BEST WE CAN DO WITH TRADITIONAL STATISTICAL THEORY.

ALSO, H0: L=0 WILL BE REJECTED IF AND ONLY IF THE CONFIDENCE INTERVAL DOES
NOT CONTAIN ZERO.

> Thank you for going through my questions...
>
>

YOU'RE WELCOME!