COMET Admissions Examination Statistical Summaries Spring 2006
Basic Statistics
The COMET admissions examination consisted of a reading section, grammar and vocabulary section, an essay, and a math section consisting of four subsections. The basic statistics for this sections and subsections are presented in the table one below.
Statistic 
m1 
m2 
m3 
m4 
SM 
Read 
Write 
Grammar 
count 
1795 
1794 
1795 
1795 
1806 
1797 
1783 
1796 
min 
0 
0 
0 
0 
0 
1 
0 
3 
max 
10 
19 
10 
9 
37 
35 
40 
78 
range 
10 
19 
10 
9 
37 
34 
40 
75 
mode 
9 
3 
2 
2 
15 
14 
0 
33 
median 
7 
3 
3 
2 
15 
14 
22 
35 
mean 
6.6897 
3.6856 
3.5064 
2.4345 
16.2148 
14.8114 
20.6932 
37.0434 
stdev 
2.2997 
2.1324 
2.1969 
1.4336 
6.2405 
5.1457 
12.4327 
14.6300 
coef var. 
0.34 
0.58 
0.63 
0.59 
0.38 
0.35 
0.60 
0.39 
low95 
6.58 
3.59 
3.40 
2.37 
15.93 
14.57 
20.12 
36.37 
mean 
6.69 
3.69 
3.51 
2.43 
16.21 
14.81 
20.69 
37.04 
high95 
6.80 
3.78 
3.61 
2.50 
16.50 
15.05 
21.27 
37.72 
stand error 
0.05 
0.05 
0.05 
0.03 
0.15 
0.12 
0.29 
0.35 
skew 
0.45 
0.79 
0.70 
0.69 
0.52 
0.67 
0.27 
0.40 
kurtosis 
0.57 
1.29 
0.02 
0.88 
0.09 
0.77 
1.04 
0.49 
Table one.
m1 is the first math subsection and contains ten arithmetic level problems.
m2 is the second math subsection and contains ten prealgebra level problems.
m3 is the third math subsection and contains ten elementary algebra problems.
m4 is the fourth math subsection and contains ten college level algebra problems.
SM is the sum of the math subsections and is out of forty.
Reading is a reading score out of 40.
Writing (essay) is the essay score out of 40.
Grammar is the grammar and vocabulary score out of 80.
The reading section average is separated from random by less than one standard deviation. While significant due to the sample size, the low average reinforced analysis in the language and literature division that the reading section might be problematic.
Correlations
The correlations between the subsections is given in table two below.
Correlations 
SM 
Read 
Write 
Grammar 
SM 
1.00 
0.55 
0.55 
0.60 
Read 
0.55 
1.00 
0.59 
0.64 
Write 
0.55 
0.59 
1.00 
0.69 
Grammar 
0.60 
0.64 
0.69 
1.00 
Table two.
Although the first two subsections of the math test were rewritten to require less reading ability, the math subsections sum remains, given the sample size, correlated moderately to moderatelystrong with the English sections.
Writing correlated more strongly with the grammar section that with the reading section. Past experience in the language and literature division indicated that the writing section, the essay, was a trustworthy indicator of student ability. The strong correlation between the trusted writing section and the grammar section and the lower correlation of both to reading led the language and literature division to request that the reading score not be used in the final admissions decision this year. The division plans to redesign this section.
Distributions
The distribution of scores on each section is given in chart one. The score is on the horizontal axis, the vertical axis is the number of students with that score.
Chart
one.
With the exception of the writing section, the other sections distributed in a manner which is considered statistically reasonable. That is, the frequency (the number of students) rises with the score towards the mean, and then falls as the score continues to rise past the mean to the maximum possible score. If the distribution (the shape of the curve) is a symmetrical heap, the most common score is also the mean score as well as the median score. This distribution is sometimes called a "bell curve" and is mathematically described by the normal or student's tdistribution.
In the past, the writing section, the essay, has in performed in a statistically reasonable fashion except for the number of students who score a sum of zero. This was true again this year with 235 scores of zero. Yet the removal of those 235 scores would not return the distribution this year to a bell curve.
The most common score on the essay, except for zero, was the maximum possible score of 40 with seventyfour students attaining a score of 40. The frequency rises steadily from eight students with a score of 2 to fiftynine students with a score of 20. From a score of 20 to 35 the distribution is fairly flat. Then the distribution drops slightly until a score of 40.
The behavior of the essay section suggests that the section did not distinguish well among the seventyfour students with a score of 40. Bear in mind that a score of forty represents a paper with some errors and omissions of grammar, vocabulary, organization, cohesion, and content coverage. The distribution argues that the rubric should now include a score of five in each of the five areas. This should spread the seventyfour scores of 40 across the tenpoint range from 40 to 50. This might also provide enough information to potentially place students in a writing course at the college.
Rank order
With the recommendation to remove the reading section from the calculations, the admissions board approved a rankorder formula using zscores on the mathematics section, the grammar and vocabulary section, and the writing (essay) section. The formula placed a 50% weight on the essay, 25% on grammar and vocabulary, and a 25% weight on mathematics. The individual weighted zscores were added to generate a sum of zscores. The resulting zscore was linearly transformed to produced the final COMET score. The basic statistics for the zscore sum and the COMET score are given in table three.
Statistic 
zscore sum 
COMET 
count 
1806 
1806 
min 
8.46 
84.35 
max 
8.23 
997.78 
range 
16.69 
913.43 
mode 
5.56 
243.17 
median 
0.05 
549.95 
mean 
0.06 
544.34 
stdev 
3.53 
193.05 
cv 
62.51 
0.35 
Table three.
A COMET score of 700 was approved as the cutoff for regular admission to an associate degree program. A COMET score of 250 was established as the minimum score for admission to a certificate program. Students who have scored between 250 and 700 will be eligible for either the Intensive English Instruction sequence or a certificate program based on their individual position on a rank order by state. Decisions on the exact nature of the IEI admissions mechanism are still to be determined.
Bear in mind that the college now operates based on fixed resources and specific projections of the number students that the college can serve. Each site has an target enrollment number and an maximim enrollment capacity limit. Like many smaller colleges, the college opts to admit a specific number of students.
The result is that the target admissions number is a fixed number. Put another way, there is not the possibility at present of all high schools increasing the number of students attaining regular admission to the college. If one high school sees an increase in the number of students who have attained regular admission, then some other high school (or high schools) must have seen a decrease in the number of students who gained regular admission. Thus admission is competitive and is mathematically termed a zerosum game.
High schools that are using increases in regular admissions as an indicator do so at their own peril. If another high school improves by a larger amount, then that first high school could see a drop in admissions despite real improvement in their own educational processes.
Table four records the distribution by state and high school of the students into the three categories delineated above.
State 
School 
Nonadmitted 
Certificate/IEI 
Associate 
Total 
Chuuk 
(empty) 
1 


1 
Berea 
2 
19 
3 
24 

CHS 
65 
204 
5 
274 

CSC 
7 
71 
1 
79 

CSDA 

10 
1 
11 

Faichuk 
16 
30 

46 

Mizpah 

21 
1 
22 

Nukuno 
1 
10 
1 
12 

PLHA 
4 
42 
1 
47 

Saramen 

30 
25 
55 

SNHS 
5 
41 

46 

WHS 
15 
72 
2 
89 

Xavier 


35 
35 

Chuuk 

116 
550 
75 
741 
Kosrae 
KHS 

86 
55 
141 
Kosrae Result 


86 
55 
141 
Pohnpei 
(empty) 
2 


2 
? 

1 

1 

CCA PNI 


10 
10 

CCA PNI Tchrs 

4 
3 
7 

Madolehnihmw 

69 
29 
98 

OHWA 

8 
1 
9 

PICS 

269 
152 
421 

PNI campus 

82 
2 
84 

SDA PNI 

9 
28 
37 

Pohnpei 

2 
442 
225 
669 
Yap 
(empty) 

2 

2 
DOE 


1 
1 

NICHS 

45 
5 
50 

OIHS 

26 
8 
34 

YCS 

3 

3 

YHS 
4 
70 
42 
116 

YMH 

6 
1 
7 

YSC 

30 
3 
33 

YSDA 

2 
7 
9 

Yap Result 

4 
184 
67 
255 
Total 

122 
1262 
422 
1806 
Table four.
Note that the table above reports the high school name reported by those taking the test. The decision on the IEI admissions mechanism was still pending at the time this report was written.
The nonadmitted status is not equivalent to the the "limbo" status discussed in prior years. "Limbo" was an arbitrary term used to refer to students who had a zscore sum on reading, writing, and grammar which was less than negative three. The nearest equivalent this year would be students below a COMET score of 328. Bear in mind that the calculation this year involves mathematics, grammar, and a weighted essay score.
The average COMET score seen in table five represents a measure of the relative performance on the writing (essay) section, the grammar section, and the mathematics section.
School 
Mean COMET 
School 
Mean COMET 
Xavier 
878.35 
Overall 
544.34 
CCA PNI 
853.2 
Overall 
544.34 
YSDA 
775.26 
Mizpah 
536.25 
SDA PNI 
771.19 
NICHS 
534.41 
CCAP tch 
685.67 
PSC 
504.34 
Saramen 
680.05 
YCS 
503.63 
PICS 
657.22 
Berea 
488.63 
Kosrae 
650.08 
YMH 
473.03 
KHS 
650.08 
Nukuno 
442.68 
Pohnpei 
641.51 
Chuuk 
421.8 
Madol HS 
635.48 
PLHA 
417.05 
YHS 
613.82 
SNHS 
398.43 
CSDA 
601.12 
CSC 
389 
OIHS 
595.03 
WHS 
370.87 
OHWA 
591.4 
CHS 
341.51 
Yap 
587.06 
Faichuuk 
296.32 
YSC 
556.51 


Overall 
544.34 


Table five.
A COMET average below 400 is exceptionally weak and below 328 represents essentially random performance on all included subsections. As this is the first year with a nonadmission category, a conservative cutoff at 250 was established.
While the individual high school scores are of interest to individual schools, state educational leadership might consider the mean performance of all of the schools in their state. Note that Kosrae reported results from only a single school, thus the state mean is the mean for that school.
Where a performance is strong, no one effort can be credited with the success. Where a performance is weak, no one lack can be faulted as the cause of the poor performance. Education is a set of canoes with many people paddling. Students, parents, teachers, administrators, state leadership, and special programs should all share in the credit where credit is due, in the blame where performances are weak.
Table five is depicted graphically in chart two.
95% Confidence intervals for the COMET mean score by high school
Determining whether one high school is statistically significantly stronger in rank order than another high school requires determining whether the mean COMET scores are sufficiently separated. The following table provides the exact values for the 95% confidence interval for the COMET means by high school.
School 
n 
stdev 
low95% 
high95% 
mean 
Xavier 
35 
56.61 
858.91 
897.8 
878.35 
CCA PNI 
10 
85.11 
792.32 
914.09 
853.2 
YSDA 
9 
88.13 
707.51 
843 
775.26 
SDA PNI 
37 
132.17 
727.12 
815.25 
771.19 
Saramen 
55 
84.58 
657.19 
702.92 
680.05 
PICS 
421 
131.04 
644.66 
669.77 
657.22 
KHS 
141 
134.72 
627.65 
672.51 
650.08 
Madolehnihmw 
98 
114.72 
612.48 
658.48 
635.48 
YHS 
116 
176.86 
581.3 
646.35 
613.82 
CSDA 
11 
81.95 
546.06 
656.17 
601.12 
OIHS 
34 
121.71 
552.56 
637.5 
595.03 
OHWA 
9 
93.84 
519.28 
663.53 
591.4 
YSC 
33 
106.97 
518.58 
594.44 
556.51 
Overall 
1806 
193.05 
535.43 
553.25 
544.34 
Mizpah 
22 
110.9 
487.08 
585.42 
536.25 
NICHS 
50 
125.75 
498.67 
570.15 
534.41 
PNI campus 
84 
132.18 
475.65 
533.02 
504.34 
Berea 
24 
182.21 
411.69 
565.57 
488.63 
YMH 
7 
169.43 
316.34 
629.73 
473.03 
Nukuno 
12 
177.65 
329.81 
555.56 
442.68 
PLHA 
47 
124.03 
380.63 
453.46 
417.05 
SNHS 
46 
108.2 
366.3 
430.57 
398.43 
CSC 
79 
117.02 
362.79 
415.21 
389 
WHS 
89 
127.22 
344.07 
397.67 
370.87 
CHS 
274 
121.3 
327.09 
355.94 
341.51 
Faichuk 
46 
98.31 
267.13 
325.52 
296.32 
Table six.
Thus, for example, while PICS has a higher mean COMET score than KHS, KHS high school's 95% confidence interval spans 22 points on either side of the KHS mean COMET of 650.08. The PICS mean of 657.22 is only 7.14 points away. As the separation does not exceed 22 points, the two schools are in a statistical dead heat. Table six above is graphically shown in chart three on the next page.
The vertical bars show the extent of the 95% confidence interval for the mean score. Where a bar for one school overlaps the mean ("the ball") for another school, the former is not statistically separated from the mean of the later. Note that the upper limit for the possible mean for Faichuuk high school is less than 328, thus confirming that in terms of the admissions examination, Faichuuk scored no different from students randomly choosing answers.
Chart
three.
Writing (essay) section
The writing section is considered by both the language and literature division and by those from other divisions who mark this section to possibly be singularly indicative of the capacity of students to academically succeed at the college – if there is such a thing as a single indicator. The maximum possible score is a forty, and there is a general sense that a score above 32 indicates a potential to succeed at the college. Scores of twenty and under are considered to be significantly weak and raise questions as to whether these students can tackle any program that requires the ability to communicate in written English. Table six records the mean essay scores by state and by high school.
School 
essay mean 
School 
essay mean 
CCA PNI 
38.7 
Overall 
20.69 
CCAP tch 
37.43 
Mizpah 
20.64 
Xavier 
36.86 
YCS 
17.33 
SDA PNI 
34.89 
Berea 
16.79 
YSDA 
34.11 
PSC 
16.77 
Saramen 
33.56 
Nukuno 
15.5 
Kosrae 
28.48 
SNHS 
14.49 
KHS 
28.48 
Chuuk 
13.73 
OIHS 
27.12 
YMH 
13 
CSDA 
27.09 
CSC 
12.91 
YHS 
26.86 
WHS 
12.52 
OHWA 
26.11 
PLHA 
12.15 
PICS 
25.56 
CHS 
7.33 
Pohnpei 
25.06 
Faichuuk 
5.14 
Yap 
24.98 


Madol HS 
24.42 


YSC 
23.03 


NICHS 
21.63 


Overall 
20.69 


Table seven.
The data in table seven is shown in chart four on the next page.
The mean essay scores suggest that Kosrae, Pohnpei, and Yap states are, to differing degrees, accomplishing the task of instructing students in the skills necessary to compose written English essays. As a state, despite the impact of Xavier and Saramen Chuuk Academy, the Chuuk state average is abysmal. Looking at the individual public high schools in Chuuk indicates an almost complete lack of ability to accomplish a written composition in the English language.
While some fields such as science have significant support costs, English language and literature is likely the least expensive program on a per student basis. This is not likely a failure due to a lack of funding alone.
The 95% confidence interval for the mean writing (essay) score allows one to determine whether the means for two schools are statistically significantly separated.
State 
School 
n 
mean 
stdev 
95% low 
95% high 
mean 
Chuuk 
Xavier 
35 
36.86 
3.66 
35.6 
38.11 
36.86 
Chuuk 
Saramen 
55 
33.56 
5.56 
32.06 
35.07 
33.56 
Chuuk 
CSDA 
11 
27.09 
6.95 
22.42 
31.76 
27.09 
Chuuk 
Mizpah 
22 
20.64 
9.2 
16.56 
24.72 
20.64 
Chuuk 
Berea 
24 
16.79 
12.83 
11.37 
22.21 
16.79 
Chuuk 
Nukuno 
12 
15.5 
11.29 
8.33 
22.67 
15.5 
Chuuk 
SNHS 
45 
14.49 
9.46 
11.65 
17.33 
14.49 
Chuuk 
Chuuk 
728 
13.73 
12.7 
12.8 
14.65 
13.73 
Chuuk 
CSC 
79 
12.91 
10.06 
10.66 
15.16 
12.91 
Chuuk 
WHS 
86 
12.52 
9.91 
10.4 
14.65 
12.52 
Chuuk 
PLHA 
47 
12.15 
10.37 
9.1 
15.19 
12.15 
Chuuk 
CHS 
270 
7.33 
8.95 
6.26 
8.4 
7.33 
Chuuk 
Faichuuk 
42 
5.14 
8.56 
2.48 
7.81 
5.14 
Kosrae 
Kosrae 
141 
28.48 
8.09 
27.13 
29.83 
28.48 
Kosrae 
KHS 
141 
28.48 
8.09 
27.13 
29.83 
28.48 
Overall 
Overall 
1783 
20.69 
12.43 
20.12 
21.27 
20.69 
Pohnpei 
CCA PNI 
10 
38.7 
1.57 
37.58 
39.82 
38.7 
Pohnpei 
CCAP tchrs 
7 
37.43 
2.94 
34.71 
40.14 
37.43 
Pohnpei 
SDA PNI 
36 
34.89 
4.68 
33.31 
36.47 
34.89 
Pohnpei 
Ohwa 
9 
26.11 
7.69 
20.2 
32.02 
26.11 
Pohnpei 
PICS 
420 
25.56 
8.14 
24.78 
26.34 
25.56 
Pohnpei 
Pohnpei 
665 
25.06 
9.45 
24.35 
25.78 
25.06 
Pohnpei 
Madol HS 
97 
24.42 
9.1 
22.59 
26.26 
24.42 
Pohnpei 
PSC 
84 
16.77 
10.53 
14.49 
19.06 
16.77 
Yap 
YSDA 
9 
34.11 
6.07 
29.44 
38.78 
34.11 
Yap 
OIHS 
34 
27.12 
9.04 
23.96 
30.27 
27.12 
Yap 
YHS 
111 
26.86 
11.19 
24.75 
28.96 
26.86 
Yap 
Yap 
249 
24.98 
10.71 
23.64 
26.32 
24.98 
Yap 
YSC 
33 
23.03 
7.33 
20.43 
25.63 
23.03 
Yap 
NICHS 
49 
21.63 
9.43 
18.92 
24.34 
21.63 
Yap 
YMH 
7 
13 
14.71 
0.6 
26.6 
13 
Table eight.
Chart five depicts the 95% confidence interval for the mean writing (essay) scores, with the high schools sorted by state and then in descending writing score order. The vertical bars are the extent of the 95% confidence interval for the sample mean. Where a vertical line for one school overlaps the mean (the center ball) of a another school, the first school is not statistically significantly separated from the second school's mean.
Chart
five.
Changes in writing (essay) performance 2005 to 2006
During the marking process some graders noted that the essays appeared to be slightly stronger this year versus last year. Although yeartoyear comparisons are always risky due to potential differences in the grading teams and other confounding factors, showing that there was no significant change would disconfirm the possibility the essays improved.
The mean scores by high school were compared yeartoyear. The results are seen in table nine. NS indicates that the yeartoyear change is not significant.


2005 Results 
2006 results 


State 
School 
n 
mean 
stdev 
n 
mean 
stdev 
Significance 
Chuuk 
Chuuk 
620 
11.67 
11.11 
728 
13.73 
12.7 
Yes, change: 2.06 
Chuuk 
Berea Christian High School 
20 
18 
10.46 
24 
16.79 
12.83 
NS 
Chuuk 
Chuuk High School 
224 
7.71 
9.61 
270 
7.33 
8.95 
NS 
Chuuk 
Chuuk SDA 
11 
19.36 
10.81 
11 
27.09 
6.95 
NS 
Chuuk 
Chuuk State Campus 
43 
11.37 
8.56 
79 
12.91 
10.06 
NS 
Chuuk 
Mizpah Christian High School 
13 
17.15 
8.3 
22 
20.64 
9.2 
NS 
Chuuk 
Nukuno Christian High School 
10 
11.2 
6.75 
12 
15.5 
11.29 
NS 
Chuuk 
Pentecostal Lighthouse Academy 
52 
8.44 
7.61 
47 
12.15 
10.37 
Yes, change: 3.71 
Chuuk 
Saramen Chuuk Academy 
47 
22.98 
8.93 
55 
33.56 
5.56 
Yes, change: 10.58 
Chuuk 
Southern Nomwoneas HS 
59 
11.07 
8.87 
45 
14.49 
9.46 
NS 
Chuuk 
Weno High School 
117 
8.85 
8.17 
86 
12.52 
9.91 
Yes, change: 3.67 
Chuuk 
Xavier High School 
24 
37.71 
3.22 
35 
36.86 
3.66 
NS 
Kosrae 
Kosrae (KHS) 
191 
23.24 
8.13 
141 
28.48 
8.09 
Yes, change: 5.24 
Kosrae 
Kosrae High School 
191 
23.24 
8.13 
141 
28.48 
8.09 
Yes, change: 5.24 
Pohnpei 
Pohnpei 
643 
23.44 
8.48 
665 
25.06 
9.45 
Yes, change: 1.62 
Pohnpei 
Calvary Christian Academy P 
15 
32.47 
5.76 
10 
38.7 
1.57 
Yes, change: 6.23 
Pohnpei 
Ohwa Christian High School 
7 
26.86 
6.23 
9 
26.11 
7.69 
NS 
Pohnpei 
Pohnpei Islands Central School 
505 
22.63 
8.07 
420 
25.56 
8.14 
Yes, change: 2.93 
Pohnpei 
Pohnpei SDA 
32 
31.47 
6.26 
36 
34.89 
4.68 
Yes, change: 3.42 
Pohnpei 
Pohnpei State Campus 
60 
19.78 
8.64 
84 
16.77 
10.53 
NS 
Yap 
Yap 
228 
23.96 
9.76 
249 
24.98 
10.71 
NS 
Yap 
Neighboring Islands High School 
41 
19.54 
6.98 
49 
21.63 
9.43 
NS 
Yap 
Outer Islands High School 
31 
19.65 
9.18 
34 
27.12 
9.04 
Yes, change: 7.47 
Yap 
Yap High School 
121 
25.37 
10.48 
111 
26.86 
11.19 
NS 
Yap 
Yap Medical Hospital 
19 
24.05 
5.4 
7 
13 
14.71 
NS 
Yap 
Yap SDA 
12 
32.42 
5.74 
9 
34.11 
6.07 
NS 
Yap 
Yap State Campus 
4 
34 
8.16 
33 
23.03 
7.33 
NS 
Table nine.
The only changes which were large enough to attain significance were positive changes. No school dropped by a statistically significant amount.
Mathematics section
Yeartoyear mathematics subsection performance
Table ten records the yeartoyear performance from 2005 to 2006 on the mathematics subsections. The table also shows the averages for the top fourhundred rank order students on each subsection.
Column one 
2005 
4.00 
2006 
6.69 

2006 top 400 
8.57 

Column two 
2005 
3.25 
2006 
3.69 

2006 top 400 
5.74 

Column three 
2005 
3.08 
2006 
3.51 

2006 top 400 
5.74 

Column four 
2005 
2.25 
2006 
2.43 

2006 top 400 
3.27 
Table ten.
Each subsection showed a small improvement, with the largest improvement seen in the first subsection. This improvement is thought to be due to the removal of English, to the extent that it could be removed, from the first subsection. Failure by a student to succeed in the first subsection is now a strong indicator of a failure of the student to perform basic arithmetic operations correctly.
The redesign of the mathematics subsections with the accompanying improvement in scores, coupled with a curriculum realignment within developmental mathematics, led to a redesign of the mathematics placement function.
Mean Mathematics Scores by High School
The mean score by high school for the mathematics section represents the average number correct out of forty for a high school.
School 
Math 
School 
Math 
Xavier 
25.54 
Mizpah 
14.32 
CCA PNI 
23.8 
NICHS 
14.3 
SDA PNI 
21.08 
OIHS 
14.29 
PICS 
20.58 
PLHA 
14.28 
KHS 
20.06 
Berea 
13.5 
Madol HS 
19.88 
CCAP Tchrs 
12.57 
YSDA 
16.22 
YMH 
12.43 
Overall 
16.21 
CHS 
12.04 
YHS 
16.21 
SNHS 
11.28 
PSC 
16.01 
CSC 
11.11 
YSC 
15.88 
Nukuno 
10.75 
OHWA 
15.33 
WHS 
10.38 
CSDA 
15 
Faichuuk 
8.93 
Saramen 
14.6 


Table eleven.
A student blindly guessing on all forty fiveoption multiple choice questions should get at least eight correct. Given that the first few problems involve basic arithmetic, scores around twelve or under are extremely weak performances. Table eleven is depicted graphically in chart six.
The performance at Nukuno was statistically indistinguishable from a random score of eight. Weno high school and Faichuuk high school performed so poorly in both mathematics and English that there is merit to an argument which would shift all of whatever resources are being spent on mathematics education to the teaching of English. These schools will not do significantly worse by not teaching mathematics – there is no where down for them to go from the their current status.
Chuuk high school, while exceptionally weak in performance, still outperformed the other public high schools in Chuuk on the mathematics section. Given the poor performance of Faichuuk on the essay and mathematics sections, there is scant evidence at present that dispersing the students away from Weno will lead to improved academic results.
Chart seven on the next page depicts the 95% confidence interval for the mean mathematics scores, with the high schools sorted by state and then in descending mathematics score order. The vertical bars are the extent of the 95% confidence interval for the sample mean. Where a vertical line for one school overlaps the mean (the center ball) of a another school, the first school is not statistically significantly separated from the second school's mean.
Chart
seven.
Mathematics Placement Data
Incoming freshmen placement over the past three fall terms is given in the table below:
Course 
Fall 03 
Fall 05 
Fall 06 
MS 090 
162 
184 
75 
MS 095 
94 
80 
144 
MS 098 
101 
77 
34 
MS 100 
70 
105 
139 
MS 101/150 
25 
17 
30 
Table twelve.
The mathematics placement by high school is given in the table below:


Nonadmit 
Certificate/IEI 
Regular admission 
Sum 

State 
School 
90 
95 
90 
95 
98 
100 
90 
95 
98 
100 
101 


Chuuk 
(empty) 
1 










1 

Berea 
2 

18 
1 


1 
2 



24 

CHS 
65 

190 
14 


3 
1 

1 

274 

CSC 
7 

62 
8 

1 
1 




79 

CSDA 


8 
2 


1 




11 

Faichuk 
16 

30 








46 

Mizpah 


20 
1 


1 




22 

Nukuno 
1 

10 



1 




12 

PLHA 
4 

32 
8 
2 



1 


47 

Saramen 


28 
1 

1 
15 
9 

1 

55 

SNHS 
5 

39 
2 







46 

WHS 
15 

69 
3 


2 




89 

Xavier 






3 
6 
1 
24 
1 
35 

Kosrae 
KHS 


46 
36 

4 
4 
19 
1 
23 
8 
141 

Pohnpei 
(empty) 
1 
1 









2 

? 


1 








1 

CCA PNI 







6 

4 

10 

CCA PNI Tchrs 


4 



2 
1 



7 

Madolehnihmw 


19 
48 

2 
1 
20 
1 
7 

98 

OHWA 


3 
5 



1 



9 

PICS 


97 
135 
24 
13 
11 
39 
23 
60 
19 
421 

PNI campus 


43 
31 
5 
3 



1 
1 
84 

SDA PNI 


7 

1 
1 
8 
5 
3 
12 

37 

Yap 
(empty) 


2 








2 

DOE 






1 




1 

NICHS 


32 
13 


1 
1 

3 

50 

OIHS 


18 
8 


5 
3 



34 

YCS 


3 








3 

YHS 
4 

40 
29 
1 

7 
28 
4 
2 
1 
116 

YMH 


5 
1 


1 




7 

YSC 


17 
12 
1 

2 


1 

33 

YSDA 


1 
1 


4 
3 



9 

Total 

121 
1 
844 
359 
34 
25 
75 
144 
34 
139 
30 
1806 
Table thirteen.
Comments
The college admissions examination is an instrument that has been refined over the years towards the sole purpose of determining admissions at the college. The examination is not intended as either a diagnostic or summative measure of the effectiveness of high schools or state departments of education.
The admissions test can indicate, at the extreme ends, whether a school is performing strongly on these admissions measures or performing in a manner indistinguishable from random. Comments above have been made where performances are extraordinarily weak.
Diversity
The differences in the performances by state have repercussions on the makeup of the regular admissions. Table fourteen compares the composition of the regular admissions to the state shares of the national population. The table reflects the state of the high school, not the cultural identity of the individual test takers.
State 
Associate 
RF 
Pop 2000 
Pop RF 
Factor 
Chuuk 
75 
18% 
53595 
50% 
0.35 
Kosrae 
55 
13% 
7686 
7% 
1.81 
Pohnpei 
225 
53% 
34486 
32% 
1.65 
Yap 
67 
16% 
11241 
11% 
1.51 

422 
100% 
107008 
100% 
0 
Table fourteen.
Thus in terms of the high school's state share of the national population, students from high schools in Kosrae are the most overrepresented group in the regular admissions category with 1.81 times their share of the national population, while those from high schools in Chuuk are underrepresented at a factor of about a third of their share of the national population. Each high school has students from every state, however the data is still likely roughly reflective of the underlying cultural diversity the college can expect among freshmen in the fall of 2006.
Addendum: Subgroups of Interest
The college admissions examination is neither a diagnostic nor comprehensive measure of learning. The college admissions examination is designed for a single purpose: admitting students to the appropriate programs for their abilities in English and mathematics. Despite the focus of the examination, many sponsored programs utilize the admissions results and statistics in their reports. Other programs in the high schools also choose to use the college admissions examination as one of their many indicators. The following are analyses of the essay and mathematics section with some of these subgroups broken out separately.
Writing (essay) section
The following table details the performance of the high schools in descending mean essay score order, repeating an earlier table but including some of the subgroups of interest. Explanation of the various subgroups is given after the table. The writing section had a total possible of 40.
School 
n 
stdev 
low 
high 
mean 
CCA 
10 
1.57 
37.58 
39.82 
38.7 
Xavier 
35 
3.66 
35.6 
38.11 
36.86 
KHS au 
12 
2.93 
34.8 
38.53 
36.67 
KHS adv 
10 
4.64 
31.68 
38.32 
35 
PSDA 
36 
4.68 
33.31 
36.47 
34.89 
YSDA 
9 
6.07 
29.44 
38.78 
34.11 
Saramen 
55 
5.56 
32.06 
35.07 
33.56 
PICS ub 
22 
5.03 
30.95 
35.41 
33.18 
KHS ub 
6 
5.6 
22.96 
34.71 
28.83 
KHS 
141 
8.09 
27.13 
29.83 
28.48 
KHS reg 
99 
7.48 
26.03 
29.02 
27.53 
PICS tsp 
89 
6.93 
25.80 
28.72 
27.26 
OIHS 
34 
9.04 
23.96 
30.27 
27.12 
CSDA 
11 
6.95 
22.42 
31.76 
27.09 
YHS 
111 
11.19 
24.75 
28.96 
26.86 
OHWA 
9 
7.69 
20.2 
32.02 
26.11 
PICS 
420 
8.14 
24.78 
26.34 
25.56 
MHS tsp 
36 
8.41 
21.93 
27.63 
24.78 
PICS reg 
309 
8.29 
23.6 
25.46 
24.53 
Madol HS 
97 
9.1 
22.59 
26.26 
24.42 
MHS reg 
61 
9.54 
21.77 
26.65 
24.21 
KHS x 
14 
10.97 
17.09 
29.76 
23.43 
YSC 
33 
7.33 
20.43 
25.63 
23.03 
NICHS 
49 
9.43 
18.92 
24.34 
21.63 
Mean 
1783 
12.43 
20.12 
21.27 
20.69 
Mizpah 
22 
9.2 
16.56 
24.72 
20.64 
Berea 
24 
12.83 
11.37 
22.21 
16.79 
PSC 
84 
10.53 
14.49 
19.06 
16.77 
Nukuno 
12 
11.29 
8.33 
22.67 
15.5 
SNHS 
45 
9.46 
11.65 
17.33 
14.49 
CSC 
79 
10.06 
10.66 
15.16 
12.91 
WHS 
86 
9.91 
10.4 
14.65 
12.52 
PLHA 
47 
10.37 
9.1 
15.19 
12.15 
CHS 
270 
8.95 
6.26 
8.4 
7.33 
Faichuk 
42 
8.56 
2.48 
7.81 
5.14 
Table fifteen.
KHS au refers to the Kosrae Upward Bound students who were also in the KHS advanced class one.
KHS adv refers to students in the KHS advanced class one but who were not also in Upward Bound.
PICS ub refers to the Pohnpei Upward Bound students at PICS.
KHS ub refers to the KHS Upward Bound students who were not in the advanced class one.
KHS refers to all KHS students.
KHS reg refers to the "regular" students at KHS, that is, all of the nonUpward Bound, nonadvanced class students.
PICS refers to all PICS students.
PICS reg refers to the "regular" students at PICS, that is, all of the nonUpward Bound students.
KHS x refers to test takers who took the test at KHS but who were not seniors this year in KHS. These test takers were, typically, older former students of KHS.
tsp refers to Talent Search Program students at PICS and Madolehnihmw High School (MHS).
A chart of some of the table above is provided on the next page.
Chart
eight.
The mean essay score is marked by the central ball. The extent of the 95% confidence interval for the mean is given by the vertical bars. Where the 95% confidence interval for one school or subgroup overlaps the ball of another school or subgroup, then the scores are not sufficiently separated to ensure statistical significance.
Of some interest is that a class of 22 students at KHS working in an academically challenging curriculum and referred to as the advanced class performed on par with the top private schools in the nation. Of note is that while twelve of these students benefitted from the Upward Bound program, ten others were not a part of Upward Bound at the time of the admissions examination. These ten outperformed students who were in the Kosrae Upward Bound program but not in the advanced class in Kosrae. The ten also outperformed the Pohnpei Upward Bound participants.
Mathematics Section
The following table details the performance of the high schools in descending mean mathematics score order, repeating an earlier table but including some of the subgroups of interest. The mathematics score is the sum of the four subsections, the total number correct out of forty.
School 
n 
stdev 
low 
high 
math mean 
PICS ub 
22 
3.31 
28.62 
31.56 
30.09 
KHS advub 
12 
3.88 
26.37 
31.3 
28.83 
KHS ub 
6 
2.94 
25.24 
31.42 
28.33 
Xavier 
35 
4.31 
24.06 
27.02 
25.54 
KHS adv 
10 
4.24 
22.17 
28.23 
25.2 
CCA 
10 
4.54 
20.55 
27.05 
23.8 
PICS tsp 
90 
5.53 
21.75 
24.07 
22.91 
Madol HS tsp 
36 
2.71 
20.3 
22.14 
21.22 
PSDA 
37 
5.56 
19.23 
22.94 
21.08 
PICS 
421 
5.8 
20.02 
21.13 
20.58 
KHS 
141 
6 
19.06 
21.06 
20.06 
PICS reg 
309 
5.13 
18.65 
19.79 
19.22 
Madol HS reg 
62 
4.06 
18.07 
20.13 
19.10 
Madol HS 
98 
3.75 
19.13 
20.63 
19.88 
KHS reg 
99 
4.89 
17.53 
19.48 
18.51 
KHS x 
14 
4.85 
13.56 
19.15 
16.36 
YSDA 
9 
3.31 
13.68 
18.77 
16.22 
Mean 
1806 
6.24 
15.93 
16.5 
16.21 
YHS 
116 
5.61 
15.17 
17.24 
16.21 
PSC 
84 
5.01 
14.92 
17.1 
16.01 
YSC 
33 
3.79 
14.54 
17.22 
15.88 
OHWA 
9 
2.4 
13.49 
17.18 
15.33 
CSDA 
11 
2.86 
13.08 
16.92 
15 
Saramen 
55 
4.13 
13.48 
15.72 
14.6 
Mizpah 
22 
2.42 
13.25 
15.39 
14.32 
NICHS 
50 
4.05 
13.15 
15.45 
14.3 
OIHS 
34 
3.36 
13.12 
15.47 
14.29 
PLHA 
47 
4.64 
12.91 
15.64 
14.28 
Berea 
24 
4.36 
11.66 
15.34 
13.5 
YMH 
7 
4.5 
8.26 
16.59 
12.43 
CHS 
274 
3.4 
11.63 
12.44 
12.04 
SNHS 
46 
2.61 
10.51 
12.06 
11.28 
CSC 
79 
3.24 
10.39 
11.84 
11.11 
Nukuno 
12 
4.65 
7.79 
13.71 
10.75 
WHS 
89 
3.19 
9.71 
11.05 
10.38 
Faichuk 
46 
2.47 
8.2 
9.67 
8.93 
Table sixteen.
The subgroups above are explained in the previous section. Of note in the above table is that top three mean mathematics scores were attained by Upward Bound students. Both the Upward Bound students at PICS and the Upward Bound students in the advanced class at KHS were statistically significantly separated from the strongest performance by a school, which was Xavier. The Upward Bound students at KHS not in the advanced class were not statistically separated from Xavier, but in rank order they were higher.
Also of note is that the nonUpward Bound students in the Kosrae advanced class were statistically significantly stronger than the Pohnpei SDA students, and they performed on par with the Calvary Christian Academy students on Pohnpei. In mathematics and on the essay, the KHS advanced class performed competitively against the top private schools.
In mathematics, the Upward Bound students are generally as strong as or stronger than students benefitting from a private high school education.
A chart of the table above is provided on the next page.
Chart
nine.
Mathematics Placement Data
The following table shows the breakdown of placement by the subgroups. Code "r" refers to a regular, that is, nonUpward Bound, nonadvanced class student.
State 
School 
code 
90 
95 
98 
100 
101/150 
Sum 
Chuuk 
(empty) 
r 
1 




1 
Berea 
r 
21 
3 



24 

CHS 
r 
258 
15 

1 

274 

CSC 
r 
70 
8 

1 

79 

CSDA 
r 
9 
2 



11 

Faichuk 
r 
46 




46 

Mizpah 
r 
21 
1 



22 

Nukuno 
r 
12 




12 

PLHA 
r 
36 
8 
3 


47 

Saramen 
r 
43 
10 

2 

55 

SNHS 
r 
44 
2 



46 

WHS 
r 
86 
3 



89 

Xavier 
r 
3 
6 
1 
24 
1 
35 

Kosrae 
KHS 
adv 
1 
3 

5 
1 
10 

au 
1 
1 

6 
4 
12 


r 
39 
45 
1 
11 
3 
99 


ub 
1 


5 

6 


x 
8 
6 



14 

Pohnpei 
(empty) 
r 
1 
1 



2 
? 
r 
1 




1 

CCA PNI 
r 

6 

4 

10 

CCA PNI Tchrs 
r 
6 
1 



7 

Madolehnihmw 
r 
20 
68 
1 
9 

98 

OHWA 
r 
3 
6 



9 

PICS 
r 
108 
174 
44 
64 
9 
399 


ub 


3 
9 
10 
22 

PNI campus 
r 
43 
31 
5 
4 
1 
84 

SDA PNI 
r 
15 
5 
4 
13 

37 

Yap 
(empty) 
r 
2 




2 
DOE 
r 
1 




1 

NICHS 
r 
33 
14 

3 

50 

OIHS 
r 
23 
11 



34 

YCS 
r 
3 




3 

YHS 
r 
51 
57 
5 
2 
1 
116 

YMH 
r 
6 
1 



7 

YSC 
r 
19 
12 
1 
1 

33 

YSDA 
r 
5 
4 



9 

Sums 


1040 
504 
68 
164 
30 
1806 
Students who place into MS 100 or MS 101/101 are deemed college level students.