1997). - ERIC · DOCUMENT RESUME. ED 408 339 TM 026 592. AUTHOR Gronna, Sarah S.; And Others TITLE...

DOCUMENT RESUME

ED 408 339 TM 026 592

AUTHOR Gronna, Sarah S.; And OthersTITLE Creating Local Norms To Evaluate Students in a

Norm-Referenced Statewide Testing Program.PUB DATE Mar 97NOTE 56p.; Paper presented at the Annual Meeting of the American

Educational Research Association (Chicago, IL, March 24-28,1997).

PUB TYPE Reports Evaluative (142) Speeches/Meeting Papers (150)EDRS PRICE MF01/PC03 Plus Postage.DESCRIPTORS *Academic Achievement; Achievement Gains; Achievement Tests;

Elementary Secondary Education; Ethnic Groups; MathematicsTests; *Norm Referenced Tests; Racial Differences; ReadingTests; Scores; Standardized Tests; State Programs; TestConstruction; *Test Norms; Test Results; *Testing Programs

IDENTIFIERS *Hawaii; *Stanford Achievement Tests

ABSTRACTHawaii uses the eighth edition of the Stanford Achievement

Test (Stanford 8) to assess academic performance of the student population ingrades 3, 6, 8, and 10. Hawaii was not included in the norming for theStanford 8, neither for the national nor the Pacific norms. In this study,Hawaii norms were developed based on the Stanford 8 reading and mathematicsresults from 1992 to 1996 to supplement the national norms and provide anadditional means of comparison. Hawaii reading norms were lower at everygrade level, especially grades 3 and 8. However, local mathematics normsshowed Hawaii students exceeding national norms in the upper quartile ongrades 3, 6, and 8. Hawaiian and national grade-10 mathematics norms werevery similar. Average performance changes between grades were analyzed, andit was found that the longitudinal cohorts made greater gains in achievementfrom third to sixth and from eighth to tenth grades than nationalcounterparts, while the sixth-to-eighth grade group made lesser gains. Thesenorms provide tools to improve the understanding of Hawaii studentperformance relative to their mainland counterparts. (Contains 5 tables, 8figures, and 26 references.) (Author/SLD)

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Reproductions supplied by EDRS are the best that can be madefrom the original document.

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_.

Running head: CREATING NORMS FOR HAWAII

U.S. DE=TMENT OF EDUCATION

m:ImprovementED ATIONAL RESOiRLES INFORMATIONNCENTER (ERIC)

This document has been reproduced asreceived from the person or organizationoriginating it.

1=1 Minor changes have been made toimprove reproduction quality.

Creating Norms for Hawaii 1

Creating Local Norms to Evaluate Students

So-ro-h S G ro n vl ain a Norm-Referenced Statewide Testing Program

PERMISSION TO REPRODUCE ANDDISSEMINATE THIS MATERIAL

HAS BEEN GRANTED BY

Points of view or opinions stated in thisdocument do not necessarily represent Sarah S. Gronna and Amelia A. Jenkins TO THE EDUCATIONAL RESOURCESofficial OERI position or policy.

INFORMATION CENTER (ERIC)

M University of Hawaii at ManoaMooc=1. Selvin A. Chin-Chance

Planning and Evaluation Branch, Hawaii Department of Education, Honolulu, Hawaii

Sarah S. Gronna is a concurrent doctoral student in the Department of Educational

Psychology and the Department of Special Education at the University of Hawaii, and Amelia A.

Jenkins is an Assistant Professor in Special Education at the University of Hawaii. Selvin A.

Chin-Chance is Administrator of the Testing Office in the Hawaii Department of Education. We

would like to gratefully acknowledge the assistance provided by Patricia Ishimura for her helpful

insights, advice, and patience.

Correspondence concerning this paper should be addressed to Sarah S. Gronna, Hawaii

Department of Education, Test Development Section, 3430 Leahi Avenue, Building D, 1st Floor,

Honolulu, HI 96815. Electronic mail may be sent via Internet to [email protected].

BEST COPY AMIABLE


Abstract

Hawaii uses the Stanford Achievement Test (Stanford 8) to assess academic performance

of the student population in grades 3, 6, 8, and 10. Hawaii was not included in the norming for

the Stanford Achievement Test 8th edition (Stanford 8), neither for the national nor the pacific

norms. Hawaii norms were therefore developed based on the Stanford 8 reading and mathematics

results from 1992 to 1996 to supplement the national norms and provide an additional means of

comparison. Hawaii reading norms were lower at every grade level, especially grades 3 and 8.

However, local mathematics norms showed Hawaii students exceeding national norms in the

upper quartile in grades 3, 6, and 8. Hawaii and national grade 10 mathematics norms were very

similar. Average performance changes between tested grades were analyzed. The longitudinal

cohorts made greater gains in achievement from 3'd - 6th and 8th - 10th grades than the national

counterparts, while the 6th - 8th grade group made lesser gains. These norms provide tools to

improve the understanding of Hawaii student performance relative to their mainland

counterparts.

3


Creating Local Norms to Evaluate Students

in a Norm-Referenced Statewide Testing Program

Assessment of student achievement is required by legislation in many states.The Hawaii

Department of Education mandates annual testing for all public school students in grades 3, 6, 8,

and 10 unless specifically excluded from testing. The most widely used standardized tests are

norm-referenced ones, which were developed to compare individual student performance to a

representative national sample. The norm-referenced Stanford Achievement Test, 8th Edition

(Stanford 8), published in 1992 by the Psychological Corporation, is generally the standardized

instrument used to measure academic achievement in Hawaii. The Stanford 8 results can be

reported in a variety of normed scores (e.g., stanines, percentiles, and scaled scores) for use in

comparing students in the target group (Hawaii) with the norming group (Heim, 1994). Even

though commentators have emphasized the shortcomings and questioned the validity of

standardized tests, it is improbable that these tests will be discarded as assessment instruments

(Crouse & Trusheim, 1989; Powell & Steelman, 1996) as they appear to be the most efficient,

and relatively objective method of measuring student achievement.

There have been numerous controversies surrounding the use of norm-referenced tests in

Hawaii (Aizawa, 1994; Chin-Chance, 1994; Heim, 1994; Paris, 1994). However, in order to

consider the appropriateness of administering the Stanford 8, the purpose of the mandated

assessment must be understood: to assess the performance of students. To assess the achievement

of Hawaii public school students, their performance on the Stanford 8 is compared with the

performance of other students and schools in the nation.

\


The Stanford 8 national norms are based upon a sample (n=175,000) of students assessed

in 1991 (The Psychological Corporation, 1992). However, students in Hawaii's public schools

were not included in the sample, neither in the pilot testing nor in the development of the

national norms. The Psychological Corporation maintains that Hawaii's lack of representation in

the national norming process does not significantly affect the national norms, as Hawaii's student

population includes ethnic groups that comprise only'1-2% of the United States' student

population (J. Mayo, personal communication, September, 1994). Moreover, when Stanford 8

norms were developed for the Pacific region, students in American Samoa, Guam, and CNMI

were included but students in Hawaii were not (M. Turituri, personal communication, October

23, 1996).

It is often advantageous for a state or school district to develop special norms to

supplement the national norms, which may be inadequate for the local setting, to provide an

additional means of comparison (Nunnally, 1972; Petersen, Kolen, & Hoover, 1989; Brown &

Bryant, 1984). Brown and Bryan recommend the development of local norms when there are

significant differences in characteristics of ethnicity, gender, achievement performance, or age

between the local population and the normative group. The typical characteristics of Hawaii's

public school students warrant the development of local norms.

Rationale for Development of Local Norms in Hawaii.

Ethnicity. Unlike the rest of the contiguous states, the ethnicity of the public school

population in Hawaii is approximately 23% Caucasian, 4 % Hispanic, .4% African American,

21% Native Hawaiian and Part Hawaiian, 34% Asian, and 18% other (Chin-Chance, Gronna, &

Jenkins, 1996a). The Stanford 8 norms, however, were developed using a representative national


sample of 72% Caucasian, 7% Hispanic, 15% African American, and 5% other ethnicity (The

Psychological Corporation, 1992b). Studies have linked achievement in Hawaii to ethnicity

(Brandon, 1984; Educational Testing Service, 1993; Gallimore, Boggs, & Jordan, 1974). The

national norms therefore do not reflect Hawaii's multicultural student population and

achievement.

Gender. The achievement pattern in mathematics is atypical for boys and girls in Hawaii

(Brandon, Jordan, & Higa, 1995; Kip linger, 1996). The Total Reading and Total Mathematics

"dimensions" of the Stanford 8 are computed based on the scores of several subtests in each area.

Hawaii is the only large school district in the United States where girls outperform boys in

Stanford 8 Total Reading and Total Mathematics at all grade levels (Liskum & Chin-Chance,

1996).

Achievement. Unlike the national average (10.4%), Hawaii has a higher (19%),

proportion of students enrolled in private schools (Lai, Saka, & Chin-Chance, 1994). Research

indicates that private school students who once attended public schools in Hawaii typically score

in the above average range of achievement (Lai, et al., 1994). Furthermore, 12.9 % of the tested

student population in Hawaii is comprised of special education students (Chin-Chance, Gronna,

& Jenkins, 1996b). Studies have indicated that students with disabilities typically score in the

below average range of achievement (Gronna, Jenkins, & Chin-Chance, 1996). The Stanford 8

normative sample only includes 4.9% special education students (The Psychological

Corporation, 1992a). When Hawaii is compared to the nation, the normative sample includes

more "bright" students who are not attending private schools and fewer students with disabilities.

6


Age. Hawaii is one of eight states maintaining late entrance admission (December 1 to

January 1) cut-off dates (Liskum & Chin-Chance, 1996). Hawaii has more "younger" students

within each grade than other states. Younger children are usually at an academic disadvantage

when compared to older classmates (Crosser, 1991). Liskum and Chin-Chance found a

relationship between age and Stanford 8 test scores in Hawaii at all tested grades. Children born

in the last three months of the year, had statistically significant lower achievement scores than

their older peers. Liskum and Chin-Chance (1996) suggest that Hawaii is at relative disadvantage

in norm-referenced comparisons with other states, because the Stanford 8 normative sample was

based on an older population.

Purpose of study

This study sought to analyze the standardized test score data for students within Hawaii

in order to profile their achievement. We hypothesized that the overall test performance of

students within Hawaii is different from the mainland population. This study developed local or

state-wide norms for public school students taking the Stanford 8 in grades 3, 6, 8, and 10 based

on cross-sectional data from 1992 to 1996 in order to assess performance of these students. A

longitudinal analysis was conducted to develop a sense of typical changes in reading and

mathematics based on the Stanford 8.

Method

The Hawaii Department of Education, Test Development Section of the Planning and

Evaluation Group maintains an extensive student identity database on all public school students

that includes ethnicity, home language, age, and gender. The Stanford 8 results have been stored

in annual databases. The student identity and Stanford 8 databases for 1992 through 1996 (n =


247,817) were used for analysis. During this period, approximately 68,679 grade 3 students,

66,553 grade 6 students, 60,400 grade 8 students, and 51,185 grade 10 students were assessed

using the Stanford 8.

Procedure

Development of Hawaii Norms based on Cross-Sectional Data. Using Microsoft Access

(Microsoft, 1995) the individual student records (_N -=.1,069,500) in the 1992 to 1996

demographic databases were disaggregated into tested grades and linked by student identification

numbers to the Stanford 8 databases. The cross-sectional data from 1992 and 1996 were

combined to provide more stable benchmarks. Of these, all Total Reading student scaled scores

and Total Mathematics scaled scores in grades 3, 6, 8, and 10 were used to develop Hawaii

norms for the test dimensions at each tested grade level. The Stanford 8 scaled scores represent

approximately equal units in learning on a continuous scale from 1 to 999 and facilitate the

conversion into other score types that are suitable for studying the change in performance over

time (The Psychological Corporation, 1992a). Descriptive statistics and frequency distributions

of scores within tested grades were calculated using SPSS 7.0 for Windows 95 (SPSS, 1996).

From these data, tentative Hawaii percentile rank norms were constructed.

National normative data were compiled from the technical data reports for the Stanford 8

(The Psychological Corporation, 1992). The normative data for scaled scores and percentiles

were published in the "look-up" tables by administration data and test form. The means and

standard deviations of the scaled scores of the combined spring standardization sample and

number of students included in the sample were published in National technical reports (The

Psychological Corporation, 1992). The mean scores for the combined Spring standardization


sample may vary from specific values found in the "look-up" tables due to slight differences

between test forms. The mean scaled scores for Total Reading and Total Mathematics

dimensions were determined from the Stanford 8 technical reports and were identified as the

nationally normed scaled score at the 50th percentile rank for each grade. The arithmetic

differences between national means at sequential grades were computed to determine the national

average scaled score increases per grade level and test dimension.

Changes in Scaled Scores Between Grades Based on Longitudinal Data. To develop

longitudinal cohorts, the student identity and Stanford 8 data bases were further linked to test

results at an earlier grade. The longitudinal analysis was based on two 3rd to 6th grade cohorts (n

= 20,826). Cohort A included 3rd grade students in 1992 and 6th grade students in 1995 (na =

10,429). Cohort B included 3rd grade students in 1993 and 6th grade students in 1996 (nb =

10,397). Three 6th to 8th grade cohorts (n = 29,948) were included. Cohort C included 6th grade

students in 1992 and 8th grade students in 1994 (nc = 9,781). Cohort D included 6th grade

students in 1993 and 8th grade students in 1995 (nd = 9,980). Cohort E included 6th grade

students in 1994 and 8th grade students in 1996 (ne =10,187). Finally, three 8th to 10th grade

cohorts were included in the longitudinal analysis (n = 23,683). Cohort F included 8th grade

students in 1992 and 10th grade students in 1994 (nf = 7,886). Cohort G included 8th grade

students in 1993 and 10th grade students in 1995 (ng = 7,823). Cohort H included 8th grade

students in 1994 and 10th grade students in 1996 (nh = 7,974).

The cohorts data were aggregated by grade grouping to provide more stable benchmarks.

To study the changes between the tested grades the Psychological Corporation scaled scores were

9


used as they adequately represent approximately equal units on a continuous scale and are

equivalent across test forms and test levels (The Psychological Corporation, 1992b).

Hawaii scaled score mean increases were determined for each longitudinal cohort's Total

Reading and Total Mathematics dimensions. The associated scaled score corresponding to the

50th percentile rank of the frequency distribution was identified at each grade level and

dimension. The arithmetic difference between Hawaii means at sequential grades were computed

to determine the Hawaii average scaled score increases per cohort and test dimension.

Results

Tables 1 and 2 represents the descriptive statistics, means, and standard deviations for

Stanford 8 Total Reading and Total Mathematics scaled scores for each Hawaii grade level based

on the cross-sectional data. Hawaii means and standard deviations for test dimensions are

different from the national norms at each grade level. The Total Mathematics kurtosis (.910 to -

.145) and skewness (.817 to .390) and Total Reading kurtosis (-.405 to .116) and skewness (.293

to .468) for each Hawaii frequency distribution of scores are represented by grade in Table 3. The

distribution of scores is generally positively skewed. The distribution of the Hawaii scaled scores

does not fall along the normal distribution of the Stanford 8 scaled scores for the Total Reading

and Total Mathematics dimensions.

Tentative Hawaii percentile rank norms were constructed for grades 3, 6, 8, and 10 from

the scores of all students who took the Stanford 8 in a standardized manner. These norms include

students with disabilities and have a fairly equal representation of male and female students (e.g.,

males: 51%, 50.5%, 51.2% and 50.1% for grades 3, 6, 8, and 10, respectively). Figures 1 through

0


8 compare Hawaii percentile rank norms to national norms for reading and mathematics

dimensions.

The reading performance gap between the Hawaii and national norms is the greatest at

grades 3 (14 to 20 scaled score points) and 8 (10 to 16 scaled score points). Smaller performance

gaps are noted for grades 6 and 10. The performance gap is not consistent across all performance

levels. For grades 3, 6, and 10 the largest differences occur in the mid-range while grade 8

Hawaii students demonstrate the most severe gap in the lower half of the performance range.

Hawaii mathematics performance indicates relatively small differences (3 to 6 scaled

score points) when compared to national norms. In grades 3, 6, and 8, Hawaii students perform

better than their national counterparts in the upper quartile range and less well in the middle

quartiles. At grade 10, the national normative group performs better at almost every level, but

only at a very small amount (3 to 4 scales score points).

Average scaled score values were further analyzed to ascertain the average changes in

scaled scores between grades based on a longitudinal analysis the data. Between 3'd and 6th

grades the Hawaii group increased an average of 11 Total Reading and 14 Total Mathematics

scaled score points above the national norm. However, between 6th and 8th grades, the Hawaii

group gained 2 scaled score points less in Total Reading and 16 points less in Total Mathematics

dimensions. Between 8th and 10th grade, Hawaii students increased an average of two scaled score

points above the national group in Total Reading and exhibited equal scaled score increases in

Total Mathematics when compared to the gains made nationally (see Tables 4 and 5).

Discussion

11


The primary purpose of this study was to analyze the standardized test score data for

students within Hawaii in order to evaluate academic performance within the state. Statewide

norms for Hawaii's public school students were developed by grade level in order to provide an

indicator of Hawaii "normal" performance. By developing local norms, students in Hawaii are

being compared to the performance of amore relevant heterogeneous population.

Closer inspection of the Hawaii norms reveal that at all four grades tested, Hawaii

students do not perform on par with the national normative group. Hawaii students fail to

perform on par in reading with their national counterparts, yet are relatively equivalent in

mathematics performance. Hawaii reading norms were lower at every grade level, especially

grades 3 and 8. However, Hawaii mathematics norms showed Hawaii students exceeding

national norms in the upper quartile in grade 3, 6, and 8. Hawaii and national grade 10

mathematics norms were very similar. In mathematics, Hawaii students generally perform much

closer to their national counterparts.

The longitudinal cohorts made greater gains in achievement from 3'd - 6th and 8th -10th

grades than their national counterparts, while the 6th - 8th grade group made lesser gains. It is

interesting that while gains between grade 6 and 8 are not as substantial as the national normative

gains between these years, the grade 3 and 6 cohorts as well as grade 8 and 10 cohorts increase or

remain equivalent to national normative performance achievement. These findings are

compatible with previous research (Chin-Chance, et al., 1996a; Gronna, et al., 1996; Lai, et al.,

1994). The variables that can account for the increase or decrease in Stanford 8 reading scores

have not yet been identified nor evaluated. Perhaps the differences in scores between grades

12


could be related to school philosophies, perceived self-efficacy, students' background

characteristics, motivation, or gender.

Since the results of our study are based on the entire public school population at targeted

grades, the differences reported must be viewed in terms of educational significance rather than

statistical significance. Undoubtedly the grade 3 to 6 cohort differences are large enough to

represent relative large changes in relative rankings between Hawaii and national norms while

the two to three point differences in the grade 8 to 10 cohort would represent relative minor

changes in relative rankings. These analysis and norms provide additional tools to improve the

understanding of Hawaii student performance relative to their mainland counterparts.

Summary

There are four important features to use when examining norms: (a) the types of derived

scores that are reported, (b) the demographic representativeness of the normative sample, (c) the

size of the normative group, and (d) the recency of test standardization (Wallace, Larsen, &

Elskin, 1992). One must be wary of comparing the results of students in Hawaii, who take the

Stanford 8, to the national norm. The Hawaii "norms" developed in this study more accurately

reflect the demographic student characteristics of Hawaii's public school students than the

national or Pacific region norms. The Hawaii norms are based on a population much larger than

the Stanford 8 sample, and are more current.

The Hawaii norms can provide additional information about how well individual students

are performing in comparison to students who are similar to them on important characteristics

such as gender, ethnicity, and age. The Hawaii norms could be used to further identify the

influence of gender and age on achievement measured by the Stanford 8. The possible finding

13


could influence school entrance age requirements, curriculum, and teaching styles. The Hawaii

norms could be additionally compared to the Stanford 8 norms of the Pacific region for further

evaluation of achievement within the Pacific basin. Use of these norms do not imply that the

more traditional norms are incorrect. It should be viewed from the standpoint that these norms

provide additional interpretive tools for understanding students performance in Hawaii.

14


References

Aizawa, H. M. (1994). A view from the superintendent's office. The Kamehameha

Journal of Education, 5., 55-60.

Brandon, P. (1984). Hawaii public school students' results on the Stanford Achievement

Test: A follow= to the Native Hawaiian Educational Assessment Project Final Report. (Office

of Program Evaluation and Planning Report No. 84-85: 18). Honolulu, HI: Kamehameha

Schools/Bishop Estate, Office of Program Evaluation and Planning.

Brandon, P. R., Jordan, C., & Higa, T. A. (1995). Why Hawaii girls out perform Hawaii

boys on mathematics tests: Suggestions about the influence of immigration and native Hawaiian

peer culture. In P. Rogers & G. Kaiser (Eds.), Eauitv in mathematics education: Influences on

feminism and culture (pp. 98 -108). London: The Falmer Press.

Brown, L., & Bryant, B. R. (1984). The why and how of special norms. Remedial and

Special Education, 4, 52-61.

Chin-Chance, S. (1994). A view from the state testing office. The Kamehameha Journal

of Education, 5., 27-33.

Chin-Chance, S. A., Gronna, S. S., & Jenkins, A. A. (1996a, March). Assessing special

education students in a norm referenced statewide testing program: Hawaii State Department of

Education. Paper presented at the Council of Chief State School Officers State Collaborative on

Assessment and Student Standards Assessing Special Education Students Consortium,

Washington, DC.

15


Chin-Chance, S. A., Gronna, S. S., & Jenkins, A. A. (1996b, June). Who are we

assessing? Determining participation rates for Students with Disabilities in a norm referenced

statewide testing program: Hawaii State Department of Education. Paper presented at the

Council of Chief State School Officers State Collaborative on Assessment and Student Standards

Assessing Special Education Students Consortium, Minneapolis, MN.

Crosser, S., L. (1991). Summer birth date children: Kindergarten entrance age and

academic achievement. Journal of Educational Research, 84(3), 140-146.

Crouse, J., & Trusheim, D. (1989). Five challenges for the Scholastic Aptitude Test.

Educational Digest, 54., 26-28.

Educational Testing Service. (1993). NAEP 1992: Mathematics state report of Hawaii.,

the Trial State Assessment Program. Princeton, NJ: Author.

Gallimore, R., Boggs, J. W., & Jordan, C. (1974). Culture, behavior and education: A

study of Hawaiian-Americans. Beverly Hills, CA. Sage.

Gronna, S. S., Jenkins, A. A. , & Chin-Chance, S. A. The performance of students with

disabilities in a norm referenced standardized statewide testing program. Manuscript submitted

for publication.

Heim, M. (1994). SAT scores and what? The Kamehameha Journal of Education, 5., 83-

88.

Kiplinger, V. L. (1996). Investigation of factors affecting mathematics achievement in the

eighth grade: Academic performance in Hawaii's public schools. Unpublished doctoral

dissertation, University of Colorado, Boulder.

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Lai, M. K., Saka, T., & Chin-Chance, S. (1994). Exodus for public to private schools.

The Kamehameha Journal of Education, 5, 97-101.

Liskum, D, R., & Chin- Chance, S. A. (1996, March). A Comparison of Males and

Females SAT Scores from the 1994 Hawaii State Wide Testing. Unpublished paper presented at

the meeting of the State of Hawaii, Department of Education, Board of Education, Honolulu, HI.

Microsoft Corporation. (1995) Microsoft Office for Windows 95 (Version 7.0)

[Computer software]. Redmond, WA: Author.

Nunnally, J. C. (1972). Educational measurement and evaluation (2nd ed.). New York:

McGraw-Hill.

Overton, T. (1996). Assessment in special education: An applied approach (2nd ed.).

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The Kamehameha Journal of Education, 5., 173-187.

Petersen, N. S., Kolen, M. J., & Hoover, H. D. (1989). Scaling, norming, and equating in

educational measurement. In R. Linn (Ed.), Educational Measurement (3rd ed., pp. 221-262).

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problems: Testing for teaching. (2nd ed.). Boston: Allyn and Bacon.

18


Table 1

Total Reading Scaled Scores for Stanford Achievement Test 8: 1992- 1996

Hawaii Natio

M SD n SD

M

Third 590 38 65,866 40 611 9,617

Sixth 642 34 65,218 38 656 9,870

Eighth 661 36 58,033 36 676 8,711

Tenth 679 35 47,157 36 688 6,491

Note. The mean scores for the combined Spring standardization sample may vary from specific

values found in the "look-up" tables due to slight differences between test forms.

19


Table 2

Total Mathematics Scaled Scores for Stanford Achievement Test 8: 1992- 1996

Hawaii Natio

M SD n SD

M

Third 596 43 66,623 40 596 9,636

Sixth 657 37 64,978 39 663 9,792

Eighth 683 39 57,473 39 690 8,671

Tenth 707 44 48,028 44 705 6,440

Note. The mean scores for the combined Spring standardization sample may vary from specific

values found in the "look-up" tables due to slight differences between test forms.

20


Table 3

Kurtosis and Skewness for Frequency Distributions of Scaled Scores in Hawaii

Grade

Total Reading

Kurtosis Skewness

Total Mathematics

Kurtosis Skewness

Third -.407 .334 -.145 .390

Sixth -.193 .333 .282 .656

Eighth .116 .468 .588 .817

Tenth -.225 .293 .910 .801


Table 4

Mean Total Reading Scaled Score Differences for Selected Cohorts.

Grade 3 to 6 Grade 6 to 8 Grade 8 to 10

3 6 A 6 8 A 8 10 A

Hawaii 591 643 52 640 662 22 666 680 14

National sample (Typical) 608 649 41 649 673 24 673 685 12

22


Table 5

Mean Total Mathematics Scaled Score Differences for Selected Cohorts.

Grade 3 to 6 Grade 6 to 8 Grade 8 to 10

3 6 A 6 8 A 8 10 A

Hawaii 598 658 60 657 685 28 690 710 20

National sample (Typical) 594 640 46 640 684 44 684 704 20

23


Figure 1. Comparison of Hawaii (local) and national scaled scores of the Stanford 8 for third

grade Total Mathematics.

Figure 2. Comparison of Hawaii (local) and national scaled scores of the Stanford 8 for third

grade Total Reading.

Figure 3. Comparison of Hawaii (local) and national scaled scores of the Stanford 8 for sixth


Figure 4. Comparison of Hawaii (local) and national scaled scores of the Stanford 8 for sixth


Figure 5. Comparison of Hawaii (local) and national scaled scores of the Stanford 8 for eighth


Figure 6. Comparison of Hawaii (local) and national scaled scores of the Stanford 8 for eighth


Figure 7. Comparison of Hawaii (local) and national scaled scores of the Stanford 8 for tenth


Figure 8. Comparison of Hawaii (local) and national scaled scores of the Stanford 8 for tenth


24

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