In Tuesday’s class, we were given some SAS examples. One’s code is like this:

 I found that R-square = 0.028908 and F value = 9.82.

Then you put survyear  as another control variable, we got R-square = 0.033777and F value =9.88.

Next you put gender as the third control variable, we got R-square = 0.039503and F value =9.03.

After this I put Level (in the dataset) as the fourth control variable,

and also I got R-square = 0.040470 and F value =8.33.

Therefore, can we get a conclusion that in all cases when we put more control variables, we get larger SSM and smaller SSE, which make the R-square bigger?  If this is true, how does it make sense?

Also, I remembered that in last week’s class, you said that we can get F value if we know R-square and at the same time we can get R-square if we know F value. However, here, I didn’t see any trends of F values when R-square is getting larger. Then why?

The last, can you explain again why we look at the Type III error instead of Type I error in the SAS result?

Anonymous:

Specific Question:

In Tuesday’s class, we were given some SAS examples. One’s code is like this:

proc glm data=isqs6348.pgs;      class ethnic;      model facknowledge= ethnic;         lsmeans ethnic / tdiff pdiff;                    run; quit;

 

 I found that R-square = 0.028908 and F value = 9.82.

Then you put survyear  as another control variable, we got R-square = 0.033777and F value =9.88.

Next you put gender as the third control variable, we got R-square = 0.039503and F value =9.03.

After this I put Level (in the dataset) as the fourth control variable,

proc glm data=isqs6348.pgs;      class ethnic gender level;      model facknowledge= ethnic survyear gender level/solution;         lsmeans ethnic / tdiff pdiff;                    run; quit;

 

and also I got R-square = 0.040470 and F value =8.33.

Therefore, can we get a conclusion that in all cases when we put more control variables, we get larger SSM and smaller SSE, which make the R-square bigger?  If this is true, how does it make sense?

Also, I remembered that in last week’s class, you said that we can get F value if we know R-square and at the same time we can get R-square if we know F value. However, here, I didn’t see any trends of F values when R-square is getting larger. Then why?

The last, can you explain again why we look at the Type III error instead of Type I error in the SAS result?

 "Therefore, can we get a conclusion that in all cases when we put more control variables, we get larger SSM and smaller SSE, which make the R-square bigger?  If this is true, how does it make sense?"

Yes, this is true.  It's a result from regression analysis.  Thes eare just regression models.  Add more variables, you decrease the SSE, because the parameters are chosen to minimize the SSE.

"However, here, I didn’t see any trends of F values when R-square is getting larger. Then why?"

It's a nonlinear function, depending on the degrees of freedom.  Please have a look at the function.

"The last, can you explain again why we look at the Type III error instead of Type I error in the SAS result?"

It's Type III Sum of squares, not Type I error.  Please review the previous weeks posts, where I described the difference between Type II and Type I sums of squares.

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General Question:

First question, in the gun example, we were taught that P(death,10 plays)= 1-(5/6)^10=84%=FWER. In Thursday’s SAS example (given k=50, run=7 and at 0.05 level), we got the result: using Bonferroni, P(reject at least one true H₀)<=α (FWER<=α).Is the FWER here  1-(.95)^50? Also, I don’t understand why we use Bonferroni method, is that just because we got more significances (Type I error), for example, in the case above? So we use Bonferroni to reduce the significances by using the P_i<=.001?  Second, it seems that the Boferroni-Holm method is more superior than Bonferroni method because the Bonferroni method is conservative. But why we got the same result(FWER<=α) in Boferroni-Holm method? Is the α the in Bonferroni method the same as the α in Boferroni-Holm method? And when to use which in practice?

"Is the FWER here  1-(.95)^50? "  Yes if you don;t use Bonferoni.  No if you do.  If you do use Bonferroni, then FWER=1-.999^50. 

Note that these equations presume independence.  If the tests are dependent (the most common case), then the FWER calculation shown here does not apply.  Other, more complex formulae are needed.  However, the Bonferroni result thew FWER<.05 true, regardless of whether the tests are independent or dependent.

"Also, I don’t understand why we use Bonferroni method, is that just because we got more significances (Type I error), for example, in the case above? So we use Bonferroni to reduce the significances by using the P_i<=.001? "

We use Bonferroni to control the probability of making a Type I error, yes.

" Second, it seems that the Boferroni-Holm method is more superior than Bonferroni method because the Bonferroni method is conservative. But why we got the same result(FWER<=α) in Boferroni-Holm method? Is the α the in Bonferroni method the same as the α in Boferroni-Holm method? And when to use which in practice?"

Yes, Bonferroni-Holm is better than Bonferroni in terms of hypothesis testing.  The reason the straight Bonferroni might be preferred is that there is a simple confidence interval correspondence for Bonferroni (just use alpha/k for every interval) but there is no such simple confidence interval correspondence for Bonferroni-Holm.

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