The answer is:

=IF(OR(AND(OR(AND(Structure>=22;Reading>=27);Sum Of Structure + Reading>=49);Composition (or projected composition)>1);AND(Stucture>=16;Reading>=20;Composition (or projected Composition)>5));3;IF(AND(Structure>=16;Readng>=20;Composition>0);2;1))

Where:
S
tructure = 22 corresponds to a TOEFL structure score of 469.38
Structure = 16 corresponds to a TOEFL structure score of 399.93
Reading= 27 corresponds to a TOEFL reading score of 466.27
Reading= 20 corresponds to a TOEFL reading score of 402.22
Sum of structure + reading = 49 is equivalent to a 470 average of the reading and structure score using the function:

=10*((1.158*Structure+21.47)+(0.915*Reading+21.92))/2

Yields:
Projected destination (ProjDest) 3: National Campus: 694
2: IEP: 225
1: State Campus: 440
 
I used a projected composition (projcomp) scores for PICS using:

=ROUND(0.1258*Average of structure and reading-0.1929;0)

because the average had the highest correlation to the composition score of r = 0.7434.

The logic was as follows that drove the above work: 


Reading Structure Average Composition Destination
Case one:  470+ 470+
2+ National
Case two:

470+ 2+ National
Case three:  400+ 400+
1+ IEP

Note the lack of a case four for the IEP.  Here I was guided by the old rule that any one score under 400 automatically implies little to no skills and therefore the student should attend the pre-IEP ESL courses at the state campus.

I suppose there should be a case five which would be "everyone else goes to the state campus" or ProjDest: 1.

The "+" means "equal to or greater than."  Note that a student could get dual 600's on the structure and reading, test but if they did not get at least a two on the composition (">1") they were denied admission to the national campus.  Having read many essays I am personally comfortable with saying a one on a composition is not ready for Palikir.

We should however, advise the following students to retake the essay:
Seq HS Last First Gen Struct Read Avg Struct7r Read7r Avg7 Sum Cmp Dest ProjDest projcomp Cp Diff 90 95 98 100 MS
174 CHS Nuokus Amanda F 34 45 39.5 610 630 620 79 1 2 2 1 5 -4 6 0 2 1 95
211 CHS Robert Renwick M 28 34 31 540 530 535 62 1 2 2 1 4 -3 2 0 2 1 90
1 PATS Akeang Zilla F 25 34 29.5 500 530 517 59 1 2 2 1 4 -3 7 7 5 2 98
114 KHS Robert Dora E. F 24 33 28.5 490 520 507 57 1 2 2 1 3 -2 3 1 1 4 90
1 Mizpah Akapito Jerome M 27 28 27.5 530 480 501 55 1 2 2 1 3 -2 3 2 5 1 90
28 YHS Finigmed Francisco M 22 31 26.5 470 500 486 53 1 2 2 1 3 -2 1 3 4 3 90
161 CHS Molly Sanes M 21 31 26 460 500 480 52 1 2 2 1 3 -2 1 0 1 3 90
7 YHS Chieng Gibson Berry M 23 27 25 480 470 474 50 1 2 2 1 3 -2



90

A single point improvement in their essay would gain them admission to the national campus.

Other notes falling out of my soggy brain in absolutely no logical order:

The functions that convert raw structure and reading scores to theoretical TOEFL scores are based on a linear regression generated from a table Jonathan gave me.  Both functions have a correlation coefficient of r = 0.99 and the two functions can be "seen" in the function =10*((1.158*Structure+21.47)+(0.915*Reading+21.92))/2

I spent a lot of time staring at what I call the boundary value problems (BVPs).  These are looking at who is what side of a boundary, what scores did they get, and where did they place. 

In general the logic was that having both structure and reading greater than or equal to 470 would lead to national campus admisson. 

Studying the BVPs I found:

Seq HS Last First Gen Struct Read Avg Struct7r Read7r Avg7 Sum Cmp Dest ProjDest projcomp Cp Diff 90 95 98 100 MS
91 YHS Waayam Jubilynn T. F 28 26 27 540 460 498 54 3 2 3 3 3 0 4 5 5 3 90
189 CHS Peter Espit M 27 26 26.5 530 460 492 53 5 2 3 5 3 2 3 5 4 2 90
13 YHS Defan Derek N. G. M 26 26 26 520 460 486 52 5 2 3 5 3 2 2 2 1 5 90

These students appear to have underlying strength in English: an equivalent to 540 on grammar for Jubilynn, and compositions at a very strong 5 for Espit and Derek.  I added case two: an average of structure and reading greater than or equal to 470.  The average TOEFL is the Avg7 column.  Cmp is the composition.

With case one and two installed I went back and looked at the BVPs and found:

Seq HS Last First Gen Struct Read Avg Struct7r Read7r Avg7 Sum Cmp Dest ProjDest projcomp Cp Diff 90 95 98 100 MS
53 YHS Leebrug Josephine F 27 21 24 530 410 469 48 6 3 3 6 3 3 3 6 3 3 98

A composition of six is extraordinarily strong.  The reading score appears to aberrant. A study of the rest of the averages below 470 found no other composition rated at six.  Josephine is a singularity at this point - unless the retake at PICS creates other "Josephines."

So the portion of the equation where AND(Stucture>=16;Reading>=20;Composition (or projected Composition)>5) carves out an exception for the Josephinian situation. The exception effectively allows either or both of the structure and reading scores to fall as low as the bottom of the IEP intake (400 equivalent), but if the composition is a 6 then the student gets into the College.  I call this "valuing the composition."

Bear in mind the ">1" that knocked out Amanda, Renwick, Zora, et al, also "values" the composition.  What does a one look like?

when the Education outside a classroom by doing things. Education outside of a by doing thing. I'm Education in own may family. the Education outside in the side. I'm Education in my mine.  I was the Education a class room by doing thing.

Gladdy [Kanfin] SNHS

For reference:
Seq HS Last First Gen Struct Read Avg Struct7r Read7r Avg7 Sum Cmp Dest ProjDest projcomp Cp Diff 90 95 98 100 MS
28 SNHS Kanfin Gladdy F 11 24 17.5 340 440 390 35 1 1 1 1 2 -1 4 2 3 3 90

Amanda is probably the biggest puzzle: how can a dual 600+ rack up a one?  Two graders deemed Amanda a one, there was no disagreement:

I bick beingg educated in the classroom to study my lesson or being good to my teacher to listen to them when the explain their work. And I want to listen up to my teacher. I like to stay with my best friend. I alway want to be a teacher. I want to continue my education. I will be a teacher.

Being educated in class is good, but outside is better. Because inside class we'r just sit and write some thing, but out side we'r just playing around.

Another random note: My functions are based on the raw values. These are the "source numbers."  The linear regressions that generate pseudo-TOEFL values suffer from changing the weighting of the structure and reading.  Using the pseudo-TOEFL for admission would weight the structure more heavily than the reading (see the slope coeffiecients).

Entering the data required eight hours of work - with time off to go to Wall Mart to buy Sara Lee Chocolate Feast ice cream to treat depression and numeric insanity - on Saturday and another three hours on Sunday.  The problem was the data was neither alphabetic nor grouped by high school. We need to keep the high school bundles together, and having someone who can alphabetize the high school sets would be wonderful (I'm talking post marking, not pre). 

Another reason to alphabetize is to find the Amanda and Renwick papers faster when one is in the analysis phase.

Speaking of analysis phase, there were KHS, CHS, and YHS papers in the "set-aside" box. I now suspect that the PPSD papers (Pohnpei State Police) are in the box as well.  By the way, one of the officers is a graduated advisee of mine:
Seq HS Last First Gen Struct Read Avg Struct7r Read7r Avg7 Sum Cmp Dest ProjDest projcomp Cp Diff 90 95 98 100 MS
19 PPSD Polly Markihta F 29 22 25.5 550 420 486 51
1 3 3 3
2 5 4 1 90

She is predicted to write a 3 on an essay, I have not dug the box to see if that might be the case as I now invalidated as a first reader because I know her predicted score.  But we now have post-graduation data on a student!  Look at that math placement.  Look at the raw scores: nearly random.

Anyway, I have been poring over the numbers for five hours now - taking time off for Sunday brunch as Gregg and Dennis are aware.  I feel I have a reasonable answer that well reflects past practice and policy.  I feel we can follow these freshmen and then determine next year what needs to be changed in our scoring structure and sorting function. 

Because the BVPs are so useful, here are two sets of boundaries with ten students on either side of the boundary, one along the national/IEP boundary and the other the IEP/state boundary for others to consider (I think you need a 17" monitor runing at 1024x768 pixels to handle these tables!):

 
Seq HS Last First Gen Struct Read Avg Struct7r Read7r Avg7 Sum Cmp Dest ProjDest projcomp Cp Diff 90 95 98 100 MS
5 PPSD Augustine John M 21 28 24.5 460 480 467 49
1 3 3 3
3 3 4 0 90
61 KHS Phillip Shrue F 17 33 25 410 520 466 50 5 2 3 5 3 2 2 3 3 3 90
71 KHS Sigrah Rosania J. F 20 29 24.5 450 480 465 49 2 2 3 2 3 -1 2 3 4 2 90
25 SCA Raydawn Reckson M 20 29 24.5 450 480 465 49 4 2 3 4 3 1 3 4 5 0 90
97 KHS Jim Resler M 20 29 24.5 450 480 465 49 4 2 3 4 3 1 4 3 2 6 101
92 PICS Enicar Evangeleen F 20 29 24.5 450 480 465 49
1 3 3 3
4 2 2 4 90
71 CHS Estak Mike M 20 29 24.5 450 480 465 49 3 2 3 3 3 0 4 6 4 1 98
23 Berea Sonni Machinta F 16 34 25 400 530 465 50 2 2 3 2 3 -1 2 6 5 2 98
75 PICS Donre MagieAnn F 19 30 24.5 430 490 464 49 3 2 3 3 3 0 5 6 4 3 98
3 Mizpah Benjamin Paulyne F 18 31 24.5 420 500 463 49 2 2 3 2 3 -1 2 1 4 0 90
174 CHS Nuokus Amanda F 34 45 39.5 610 630 620 79 1 2 2 1 5 -4 6 0 2 1 95
211 CHS Robert Renwick M 28 34 31 540 530 535 62 1 2 2 1 4 -3 2 0 2 1 90
1 PATS Akeang Zilla F 25 34 29.5 500 530 517 59 1 2 2 1 4 -3 7 7 5 2 98
114 KHS Robert Dora E. F 24 33 28.5 490 520 507 57 1 2 2 1 3 -2 3 1 1 4 90
1 Mizpah Akapito Jerome M 27 28 27.5 530 480 501 55 1 2 2 1 3 -2 3 2 5 1 90
28 YHS Finigmed Francisco M 22 31 26.5 470 500 486 53 1 2 2 1 3 -2 1 3 4 3 90
161 CHS Molly Sanes M 21 31 26 460 500 480 52 1 2 2 1 3 -2 1 0 1 3 90
7 YHS Chieng Gibson Berry M 23 27 25 480 470 474 50 1 2 2 1 3 -2



90
24 OIHS Tefahoydep Melinda F 24 24 24 490 440 466 48 3 2 2 3 3 0 1 2 4 4 90
139 PICS Jackson Elizabeth F 24 24 24 490 440 466 48
1 2 3 3
5 6 4 1 98
96 PICS Eperiam Geitchy M 24 24 24 490 440 466 48
1 2 3 3
1 3 6 3 100
Seq HS Last First Gen Struct Read Avg Struct7r Read7r Avg7 Sum Cmp Dest ProjDest projcomp Cp Diff 90 95 98 100 MS
19 YHS Falanruw Jesse M 17 20 18.5 410 400 407 37 3 2 2 3 2 1 4 1 4 1 90
202 CHS Raymond Tarlyn M. F 16 21 18.5 400 410 406 37 1 2 2 1 2 -1 1 1 4 0 90
199 CHS Raymond Andrea F 16 21 18.5 400 410 406 37 1 2 2 1 2 -1 2 1 2 2 90
37 Weno JohnMark Patricia F 16 21 18.5 400 410 406 37 2 2 2 2 2 0 0 3 4 2 90
88 Weno Sakate Sarty M 16 20 18 400 400 401 36 3 2 2 3 2 1 3 4 5 2 90
33 PLHA Reuney T.K. M 16 20 18 400 400 401 36 2 2 2 2 2 0 2 2 2 2 90
167 CHS Mwarelick Jayleen F 16 20 18 400 400 401 36 1 2 2 1 2 -1 2 3 1 3 90
93 CHS Ikap Rosealinta R. F 16 20 18 400 400 401 36 1 2 2 1 2 -1 0 2 1 4 90
4 NCHS Erwan Herna F 16 20 18 400 400 401 36 1 2 2 1 2 -1 5 4 3 1 90
12 CHS Aliwech Levy M 16 20 18 400 400 401 36 2 2 2 2 2 0 5 4 0 2 90
17 KHS Benjamin Junior W. M 28 19 23.5 540 390 466 47 4 1 1 4 3 1 0 0 2 2 90
55 CHS Daunny Misia M 13 37 25 370 560 461 50 1 1 1 1 3 -2 1 1 4 1 90
293 PICS Suldan Jesse M 28 18 23 540 380 461 46 5 1 1 5 3 2 6 7 4 4 98
6 CHS Aisek Ratson M 15 34 24.5 390 530 459 49 1 1 1 1 3 -2 5 3 2 1 90
103 YHS Yuwun Nicole Goomith F 27 17 22 530 370 451 44 4 1 1 4 3 1 3 5 1 0 90
9 CSDA Luke Luwisa S. F 27 17 22 530 370 451 44 5 1 1 5 3 2 3 2 4 2 90
46 CHS Choniong Danny M 28 15 21.5 540 360 448 43 3 1 1 3 3 0 4 2 1 1 90
12 CSDA Tom Thomas M 15 31 23 390 500 446 46 3 1 1 3 3 0 2 0 4 2 90
259 PICS Sackryas Jackey M 15 31 23 390 500 446 46 3 1 1 3 3 0 8 5 7 3 100
107 Weno Umwech Padrick M 15 31 23 390 500 446 46 3 1 1 3 3 0 2 2 1 3 90
28 PLHA Maipi Lillian P. F 15 30 22.5 390 490 441 45 2 1 1 2 3 -1 2 2 0 2 90


Odd ends

There were some blank essays that bore scores of zero. I left them zero. This would automatically place a student in a state campus certificate.  One had to have at least a one to get into IEP.

I have six essays that are names not in Bastora's database:
Repat Komaki 1
Hady Adler 4
Rebecca Ruwetinan 4
Keiky Wily 1
Sina Saimon 2
Sandra 1
 
I had five essays with no name whatsoever.  I think the name was on the other answer sheet and was lost at separation.
 
I have seven essays that need a second or third reader.  I figure we can handle those Monday, hence I did not disturb Patty Kelly.
 
I did have a look at whether I could use a projected composition score to identify unexpected results, but the project bore no useful fruit.  The high school averages looked to be well within and 95% confidence interval.  It did appear that the relationship between structure, reading, and composition scores was slightly nonlinear: the weak high schools did worse than predicted by the function and the strong schools did better than predicted.
 
The following cross-tab looks at the mean of the difference between the actual composition score and the predicted composition score, crossed by high school and gender.  Since n is hidden there is no way to know whether results are significant.  But you can see that Saramen and Xavier compositions outperformed their predicted performance based on a linear regression off of the structure and reading score.
 
Mizpah, on the other hand, must teach only reading and grammar to the exclusion of essay writing as their students underperformed what their reading and structure skills suggest they should have been able to do.
 
With KHS and PICS having similar academic profiles, is the PICS outperformance of 0.52 an indication of the practice effect?  I actually do not believe so: we did not mark the bulk of the PICS papers.  There are PICS comp scores in the data: I left in the ones marked previously.  We will replace them with the new essay scores. I did this for two reasons: one, the earlier essays did not look coached, two, external information is that only some sections of business and vocational "practiced" the test.
 
Average - Diff Gen

HS F M Total Result
Berea 0.13 0.33 0.21
CCA -0.63 1 -0.44
CHS -0.3 -0.49 -0.4
CSDA 0.14 0.33 0.23
KHS 0.16 0.41 0.3
KSC 0.17 -1 -0.22
Mizpah -0.5 -0.83 -0.59
NCHS -0.25 -0.43 -0.36
NICHS 0.09 -0.28 -0.14
Ohwa 2 -0.89 -0.6
OIHS 0.33 0.05 0.14
PATS -0.75 -0.25 -0.33
PICS 0.55 0.5 0.52
PLHA -0.36 -0.38 -0.37
PPSD


PSDA 0.08 -0.1 0
SCA 0.68 0.57 0.64
SNHS -0.02 -0.18 -0.09
Weno 0.12 -0.24 -0.1
Xavier 1 0.81 0.88
YHS 0.53 -0.17 0.2
YSDA 1 0.5 0.75
Total Result 0.08 -0.09 -0.01
 
I am sure that there is much I am forgetting, but I am dizzy from the numbers and the analysis. 
 
I have yet to do my traditional TOEFL comparison analysis that I do each year.  I will probably do such as a part of the work I do in statistics class, but my own druthers would be to start a tradition of only reporting the composition averages from year to year and then only as a z-score in rank order...  maybe I start that tonight, although I really ought to plan for my classes this week. 
 
Oh, I will forward the whole spreadsheet to Bastora for printing, but I would suggest we print a minimal number of copies as I show it to be 43 copies in its current OpenOffice format.
 
Dana