第五章 結論與建議
第二節 建議
本研究係使用模擬資料進行探討，變項設定為：二種等化設計（NEAT 與 BIB）；二種施測人數（10920 人與 16128 人）；二種施測題數（18 題與 36 題）
進行不同估計方法下對於個體能力與群體參數估計之比較。而其中 PV 法及 EAP_AV 法因納入了背景變項做為輔助變數計算，使得不管是群體能力平均數或 是標準差，在各種情形下之估計結果皆比其它 3 種未納入背景變項的估計方法為 佳。茲就本研究結果提出下列研究建議及未來研究建議。
壹、本次研究建議
一、 本研究發現，納入背景變項的估計法在垂直等化的試題設計上，不管是個 體能力估計或是群體能力參數的估計上，均優於傳統的點估計方法；尤其 是 PV 法在群體能力標準差的估計上，更是遠優於各種估計法。建議大型 測驗要進行跨年級連結的垂直等化時，應使用 PV 或其它納入背景變項的 估計法來進行個體能力或群體參數估計。
二、 本研究發現，受試者施測題數愈多、估計愈精準，建議在大型測驗在進行 跨年級連結的垂直等化時，能在適度的範圍內增加施測題數，以增加估計 精確度。
三、 本研究發現，錯誤的 PV 使用方式，在垂直等化設計上亦會造成估計上的 嚴重偏誤，是以在使用 PV 進行次級資料分析時，必須依據正確方式來使 用，否則將造成估計上的偏誤。
貳、未來研究建議
一、 有關於 BIB 設計估計結果優於 NEAT 設計的情形，可能是因為 BIB 垂直等 化設計係由低年級組的每個試題區塊中各挑選出難度最高的題目做為高低 年級間的定錨題。而 NEAT 垂直等化設計卻是完全由低年級組中的定錨試 題區塊直接挑選出難度最高的數題做為高低年級的定錨題。建議以後可用 其它等化方式進行研究。
二、 本研究的人數及題數的設定上，係參考 TASA 及其它學者之研究結果而制 定，於是設定了二種超過 10000 人以上模擬人數及 18 與 36 二種試題數量 來進行研究。建議爾後可參考其它資料來進行不同人數及不同題數的研究 比較。
三、 本研究僅探討一種受試者能力分布及一種試題參數分布，未來建議可針對 不同能力分布及不同試題參數分布設定進行估計方法與等化設計之比較。
四、 本研究僅依據單參數試題反應理論進行研究，未來可針對其它試題反應理 論（雙參數、三參數、多點計分、多元計分等）進行相關研究。
參考文獻
中文部分
王敏嫻（2011）。不同水平等化設計於可能值方法之探討。未出版之碩士論文，
臺中教育大學教育測驗統計研究所，臺中市。
王暄博（2006）。BIB 與 NEAT 設計之水平及垂直等化效果比較。未出版之碩士 論文，臺中教育大學教育測驗統計研究所，臺中市。
余民寧（2009），試題反應理論（IRT）及其應用（一版）。臺北市，心理出版社 股份有限公司。
洪碧霞、林素微、林娟如（2006）。認知複雜度分析架構對 TASA-MAT 六年級線 上測驗試題難度的解釋力。教育研究與發展期刊，2（4），69-86。
郭伯臣、曾建銘、吳慧珉主編(2012)。大型標準化測驗建置流程應用於 TASA 之 研究。新北市：國家教育研究院。
曾玉琳、王暄博、郭伯臣、許天維（2006）。不同 BIB 設計對測驗等化的影響。
測驗統計年刊，13（2），209-229。臺中市：國立臺中教育大學。
英文部分
Adams, R. J., Wilson, M., & Wu, M. (1997). Multilevel item response models: An approach to errors in variables regression. Journal of Educational and Behavioral Statistics, 22, 47-76.
Allen, N. L., Carlson J. E., Johnson E. G. ,& Mislevy, R. J. (1999) The NAEP 1998 technical report. Educational Testing Service.
Allen, N. L., Donoghue, J. R., & Schoeps, T. L. (2001). The NAEP 1998 technical report. Washington, DC: National Center for Educational Statistics.
Andrew, R. W. & Terry, L. S., (2001). The NAEP 1998 Technical Report (NCES 2001-509). National Assessment Governing Board, U.S. Department of Education.
Baker, F. B., & Kim, S. H. (2004). Item Response Theory : Parameter Estimation Techniques. Basel, N. Y. : Marcel Dekker, Inc.
Bock, R. D. & Mislevy, R. J. (1982). Adaptive EAP estimation of ability in a microcomputer environment. Applied Psychological Measurement, 6, 431-444.
Cox, D. R., & Hinkley, D. V. (1974). Theoretical statistics. New York: Chapman &
Hall. (Distributed by Halsted Press, New York)
Dorans, N. J. & Holland, P. W. (2000). Linking Scores from Multiple Instruments.
Foy, P., Galia, J., & Li, L. (2008). Scaling the data from the TIMSS 2007 Mathematics and Science assessments. In John F. Olson,Michael O. Martin ,Ina V.S. Mullis.
(Eds). TIMSS 2007 Technical Report.TIMSS & PIRLS International Study Center, Lynch School of Education, Boston College.
Glas, C. A. W., & Geerlings, H. (2009). Psychometric aspects of pupil monitoring systems. Studies in Educational Evaluation, 35, 83–88.
Graham J. R., Christine, Y. O’S., Alka, A., & Ebru, E. (2008). TIMSS 2007 Technical Report. Chestnut Hill, MA: TIMSS & PIRLS International Study Center, Boston College.
Klein, L. W., & Jarjoura, D. (1985). The importance of content representation for common-item equating with non-random groups. Journal of Educational Measurement, 22, 197-206.
Kolen, M. J. & Brennan, R. J. (1995). Test Equating: Methods and Practices. New York: Springer-Verlag.
Lee, J., Grigg, W., & Dion, G. (2007). The Nation’s Report Card: Mathematics 2007.
National Center for Education Statistics, Institute of Education Sciences, U. S.
Department of Education, Washington, D. C.
Lord, F. M. (1980). Applications of Item Response Theory to Practical Testing Problems. Hillsdale, NJ: Lawrence Erlbaum.
Lord, F. M. (1983). Unbiased estimators of ability parameters, of their variance, and of their parallel-forms reliability. Psychometrika, 48, 233-245
Lord, F.M. (1984). Maximum likelihood and Bayesian parameter estimation in item response theory (Research Report No. RR-84-30-ONR). Princeton, NJ:
Educational Testing Service.
Martin, M. O., Mullis, I. V. S., & Kennedy, A. M. (2007). PIRLS 2006 Technical Report. TIMSS & PIRLS International Study Center, Lynch School of Education, Boston College.
Mislevy, R. J. (1991). Randomization-based inference about latent variable from complex samples. Psychometrika, 56(2), 177-196.
Mislevy, R. J. (1984). Estimating latent distributions. Psychometrika, 49, 359-381.
Mislevy, R. J., & Sheehan, K. M. (1989). Information matrices in latent-variable
models. Journal of Educational Statistics, 14, 335-350.
Mislevy, R. J., Beaton, A. E., Kaplan, B., & Sheehan, K. M. (1992). Estimating population characteristics form sparse matrix samples of item response. Journal of Educational Measurement, 29, 133-161.
Mullis, I. V. S., Martin, M. O., & Foy, P. (with Olson, J. F., Preuschoff, C., Erberber, E., Arora, A., & Galia, J. ) . (2008). TIMSS 2007 International Mathematics Report.
Finding from IEA’s Trends in International Mathematics and Science Study at the Fourth and Eighth Grades. Chestnut Hill, MA: TIMSS & PIRLS International Study Center, Boston College.
Nancy, L. A., James, E. C., & John, R. D. (2001). The NAEP 1998 Technical Report (NCES 2001-509). National Assessment Governing Board, U.S. Department of Education.
Nemhauser, G. L., & Wolsey, L. A. (1999). Integer and Combinatorial Optimization.
New York: John Wiley.
OECD (2005). PISA 2003 Technical Report. OCED, Paris.
OECD (2009). PISA 2006 Technical Report. OCED, Paris.
Petersen, N. S., Kolen, M. J., & Hoover, H. D. (1993). Scaling, Norming, and Equating. In R.L. Linn (Ed.), Educational Measurement (3rd ed., pp221-262).
New York: Macmillan.
Rasch, G. (1960). Probabilistic models for some Intelligence and attainment tests.
Chicago: University of Chicago Press.
Tianyou, W. (2005). An Alternative Continuization Method to the Kernel Method in von Davier, Holland and Thayer's (2004) Test Equating Framework.
van der Linden, W. J., Veldkamp, B. P., & Carlson, J. E. (2004).Optimizing Balanced Incomplete Block Designs for Educational Assessments. Applied Psychological
Measurement, 28, 317-331.
von Davier M., Gonzalez, E., & Mislevy, R. J. (2009).What are plausible values and why are they useful? IERA Monograph Series:Issues and Methodologies in Large-Scale Assessment,2,.9-36.
von Davier, A. A., Holland, P. W., & Thayer, D. T. (2004). The kernel method of test equating. New York: Springer.
Warm, T.A. (1989). Weighted likelihood estimation of ability in item response models.
Psychometrika , 54 , 427–450
Wu, M. (2005). The role of plausible values in large-scale surveys. Studies in Educational Evaluation, 31 (2-3), 114-128.
Yates, F. (1936). A new method of arranging variety trials involving a large number of varieties. J. Agric. Sci. 26, 424-455
附錄一
NEAT 設計個體能力值不同估計方法之 RMSE 人數:10920 受測題數:18年級 SES 校別 PV_W EAP AV EAP MLE WLE
G-L S-L A 0.509 0.468 1.198 1.060 1.063
(0.025) (0.026) (0.339) (0.285) (0.296)
G-L S-L B 0.506 0.466 1.196 1.060 1.062
(0.023) (0.027) (0.340) (0.287) (0.298)
G-L S-H A 0.507 0.468 0.985 1.112 1.045
(0.031) (0.033) (0.323) (0.328) (0.317)
G-L S-H B 0.506 0.467 0.982 1.110 1.043
(0.035) (0.037) (0.325) (0.328) (0.317)
G-H S-L A 0.488 0.447 0.592 0.698 0.656
(0.014) (0.015) (0.142) (0.143) (0.137)
G-H S-L B 0.488 0.448 0.592 0.698 0.656
(0.018) (0.019) (0.142) (0.142) (0.135)
G-H S-H A 0.502 0.460 0.679 0.736 0.695
(0.019) (0.018) (0.209) (0.122) (0.134)
G-H S-H B 0.501 0.460 0.679 0.736 0.695
(0.021) (0.021) (0.207) (0.124) (0.134) G-L summary 0.507 0.467 1.096 1.086 1.054
(0.027) (0.029) (0.330) (0.307) (0.307) G-H summary 0.495 0.454 0.640 0.718 0.676
(0.016) (0.017) (0.167) (0.130) (0.134)
附錄一(續)
NEAT 設計個體能力值不同估計方法之 RMSE 人數:10920 受測題數:36年級 SES 校別 PV_W EAP AV EAP MLE WLE
G-L S-L A 0.397 0.365 1.019 0.944 0.949
(0.020) (0.022) (0.529) (0.498) (0.504)
G-L S-L B 0.398 0.366 1.021 0.945 0.950
(0.021) (0.022) (0.531) (0.500) (0.507)
G-L S-H A 0.394 0.363 0.928 0.957 0.931
(0.027) (0.028) (0.521) (0.515) (0.512)
G-L S-H B 0.395 0.364 0.932 0.960 0.935
(0.025) (0.027) (0.522) (0.517) (0.513)
G-H S-L A 0.381 0.350 0.642 0.669 0.658
(0.015) (0.015) (0.373) (0.364) (0.368)
G-H S-L B 0.386 0.354 0.648 0.677 0.665
(0.015) (0.016) (0.374) (0.365) (0.369)
G-H S-H A 0.393 0.361 0.650 0.689 0.672
(0.016) (0.017) (0.349) (0.365) (0.361)
G-H S-H B 0.391 0.359 0.649 0.690 0.672
(0.016) (0.017) (0.349) (0.364) (0.361) G-L summary 0.396 0.365 0.976 0.952 0.942
(0.022) (0.024) (0.525) (0.507) (0.509) G-H summary 0.388 0.356 0.649 0.681 0.667
(0.014) (0.015) (0.359) (0.364) (0.365)
附錄一(續)
NEAT 設計個體能力值不同估計方法之 RMSE 人數:16128 受測題數:18年級 SES 校別 PV_W EAP AV EAP MLE WLE
G-L S-L A 0.512 0.474 1.265 1.119 1.124
(0.028) (0.030) (0.342) (0.288) (0.299)
G-L S-L B 0.511 0.472 1.263 1.118 1.123
(0.026) (0.029) (0.340) (0.288) (0.299)
G-L S-H A 0.510 0.472 1.049 1.177 1.108
(0.033) (0.035) (0.322) (0.324) (0.314)
G-L S-H B 0.513 0.474 1.053 1.182 1.113
(0.034) (0.036) (0.323) (0.326) (0.316)
G-H S-L A 0.489 0.450 0.583 0.685 0.645
(0.019) (0.019) (0.134) (0.136) (0.128)
G-H S-L B 0.490 0.450 0.583 0.686 0.645
(0.017) (0.018) (0.134) (0.135) (0.127)
G-H S-H A 0.504 0.464 0.640 0.729 0.680
(0.020) (0.020) (0.202) (0.108) (0.121)
G-H S-H B 0.505 0.463 0.640 0.729 0.680
(0.020) (0.021) (0.202) (0.110) (0.123)
G-L summary 0.512 0.473 1.163 1.150 1.117
(0.029) (0.032) (0.331) (0.306) (0.307)
G-H summary 0.497 0.457 0.615 0.708 0.663
(0.017) (0.018) (0.160) (0.119) (0.124)
附錄一(續)
NEAT 設計個體能力值不同估計方法之 RMSE 人數:16128 受測題數:36年級 SES 校別 PV_W EAP AV EAP MLE WLE
G-L S-L A 0.406 0.375 1.246 1.150 1.159
(0.023) (0.024) (0.636) (0.610) (0.614)
G-L S-L B 0.403 0.373 1.243 1.148 1.156
(0.022) (0.024) (0.635) (0.608) (0.613)
G-L S-H A 0.404 0.374 1.146 1.173 1.146
(0.026) (0.028) (0.627) (0.622) (0.620)
G-L S-H B 0.404 0.373 1.145 1.172 1.145
(0.026) (0.028) (0.628) (0.622) (0.620)
G-H S-L A 0.386 0.355 0.720 0.744 0.737
(0.015) (0.016) (0.453) (0.443) (0.449)
G-H S-L B 0.386 0.355 0.721 0.746 0.739
(0.014) (0.016) (0.455) (0.444) (0.450)
G-H S-H A 0.397 0.364 0.689 0.768 0.744
(0.018) (0.018) (0.406) (0.444) (0.437)
G-H S-H B 0.398 0.365 0.690 0.766 0.743
(0.016) (0.016) (0.403) (0.441) (0.434)
G-L summary 0.404 0.374 1.196 1.161 1.152
(0.024) (0.025) (0.631) (0.615) (0.617)
G-H summary 0.392 0.360 0.706 0.756 0.741
(0.014) (0.015) (0.428) (0.443) (0.442)
附錄二
BIB 設計個體能力值不同估計方法之 RMSE 人數:10920 受測題數:18年級 SES 校別 PV_W EAP AV EAP MLE WLE
G-L S-L A 0.493 0.452 1.051 0.928 0.930
(0.014) (0.015) (0.230) (0.186) (0.197)
G-L S-L B 0.494 0.453 1.053 0.929 0.931
(0.014) (0.016) (0.233) (0.187) (0.198)
G-L S-H A 0.491 0.451 0.827 0.945 0.881
(0.019) (0.018) (0.212) (0.210) (0.203)
G-L S-H B 0.489 0.450 0.828 0.946 0.882
(0.018) (0.019) (0.209) (0.205) (0.199)
G-H S-L A 0.477 0.436 0.589 0.720 0.664
(0.012) (0.011) (0.122) (0.125) (0.118)
G-H S-L B 0.477 0.436 0.588 0.719 0.663
(0.014) (0.013) (0.123) (0.125) (0.118)
G-H S-H A 0.488 0.446 0.725 0.722 0.692
(0.013) (0.012) (0.175) (0.093) (0.111)
G-H S-H B 0.487 0.445 0.724 0.721 0.691
(0.012) (0.012) (0.176) (0.095) (0.112) G-L summary 0.492 0.452 0.947 0.937 0.907
(0.014) (0.015) (0.220) (0.197) (0.199) G-H summary 0.482 0.441 0.661 0.721 0.678
(0.009) (0.009) (0.148) (0.107) (0.114)
附錄二(續)
BIB 設計個體能力值不同估計方法之 RMSE 人數:10920 受測題數:36年級 SES 校別 PV_W EAP AV EAP MLE WLE
G-L S-L A 0.396 0.365 1.054 0.970 0.977
(0.017) (0.019) (0.539) (0.508) (0.515)
G-L S-L B 0.394 0.362 1.051 0.968 0.975
(0.018) (0.019) (0.537) (0.505) (0.512)
G-L S-H A 0.395 0.363 0.944 0.968 0.943
(0.024) (0.023) (0.520) (0.513) (0.510)
G-L S-H B 0.395 0.365 0.946 0.972 0.946
(0.022) (0.024) (0.520) (0.513) (0.510)
G-H S-L A 0.381 0.349 0.630 0.662 0.650
(0.012) (0.012) (0.337) (0.327) (0.334)
G-H S-L B 0.380 0.349 0.632 0.664 0.652
(0.011) (0.011) (0.338) (0.328) (0.335)
G-H S-H A 0.388 0.355 0.625 0.678 0.658
(0.013) (0.012) (0.307) (0.331) (0.327)
G-H S-H B 0.391 0.358 0.627 0.682 0.662
(0.014) (0.014) (0.311) (0.336) (0.331) G-L summary 0.395 0.364 1.000 0.970 0.960
(0.019) (0.020) (0.529) (0.510) (0.512) G-H summary 0.385 0.353 0.629 0.672 0.655
(0.010) (0.011) (0.322) (0.330) (0.332)
附錄二(續)
BIB 設計個體能力值不同估計方法之 RMSE 人數:16128 受測題數:18年級 SES 校別 PV_W EAP AV EAP MLE WLE
G-L S-L A 0.504 0.463 1.168 1.035 1.038
(0.021) (0.023) (0.325) (0.275) (0.287)
G-L S-L B 0.502 0.463 1.167 1.034 1.038
(0.024) (0.025) (0.327) (0.278) (0.290)
G-L S-H A 0.504 0.463 0.944 1.063 0.996
(0.027) (0.027) (0.305) (0.301) (0.292)
G-L S-H B 0.502 0.463 0.943 1.060 0.993
(0.030) (0.031) (0.308) (0.304) (0.295)
G-H S-L A 0.483 0.443 0.604 0.724 0.675
(0.016) (0.017) (0.130) (0.132) (0.125)
G-H S-L B 0.484 0.444 0.604 0.722 0.674
(0.015) (0.015) (0.127) (0.126) (0.120)
G-H S-H A 0.495 0.453 0.690 0.742 0.700
(0.015) (0.017) (0.199) (0.104) (0.116)
G-H S-H B 0.496 0.455 0.689 0.745 0.703
(0.018) (0.018) (0.198) (0.104) (0.115)
G-L summary 0.503 0.463 1.062 1.048 1.017
(0.024) (0.026) (0.315) (0.289) (0.291)
G-H summary 0.490 0.449 0.651 0.734 0.688
(0.014) (0.015) (0.157) (0.112) (0.118)
附錄二(續)
BIB 設計個體能力值不同估計方法之 RMSE 人數:16128 受測題數:36年級 SES 校別 PV_W EAP AV EAP MLE WLE
G-L S-L A 0.395 0.364 1.020 0.937 0.944
(0.017) (0.018) (0.556) (0.529) (0.534)
G-L S-L B 0.394 0.362 1.019 0.937 0.943
(0.015) (0.017) (0.556) (0.528) (0.533)
G-L S-H A 0.395 0.363 0.915 0.941 0.915
(0.023) (0.023) (0.545) (0.539) (0.535)
G-L S-H B 0.395 0.363 0.913 0.940 0.913
(0.022) (0.023) (0.546) (0.539) (0.535)
G-H S-L A 0.380 0.348 0.611 0.645 0.632
(0.015) (0.015) (0.398) (0.389) (0.395)
G-H S-L B 0.381 0.349 0.613 0.648 0.635
(0.015) (0.015) (0.399) (0.389) (0.396)
G-H S-H A 0.388 0.355 0.613 0.660 0.640
(0.016) (0.016) (0.375) (0.392) (0.389)
G-H S-H B 0.388 0.355 0.612 0.658 0.639
(0.016) (0.016) (0.374) (0.391) (0.389)
G-L summary 0.395 0.363 0.968 0.939 0.929
(0.018) (0.019) (0.550) (0.534) (0.534)
G-H summary 0.384 0.352 0.613 0.653 0.637
(0.014) (0.014) (0.385) (0.390) (0.392)
附錄三
NEAT 設計群體能力平均數不同估計方法之 RMSE 人數:10920 受測題數:18年級 SES 校別 PV PV_W EAP AV EAP MLE WLE
G-L S-L A 0.148 0.143 0.143 1.089 0.831 0.874
(0.087) (0.085) (0.084) (0.381) (0.381) (0.376)
G-L S-L B 0.145 0.139 0.141 1.088 0.830 0.873
(0.084) (0.083) (0.084) (0.381) (0.381) (0.375)
G-L S-H A 0.140 0.137 0.139 0.839 0.900 0.853
(0.087) (0.086) (0.087) (0.381) (0.397) (0.383)
G-L S-H B 0.142 0.137 0.137 0.835 0.897 0.850
(0.091) (0.089) (0.089) (0.383) (0.397) (0.384)
G-H S-L A 0.077 0.078 0.079 0.321 0.333 0.321
(0.063) (0.062) (0.062) (0.222) (0.236) (0.224)
G-H S-L B 0.081 0.082 0.082 0.322 0.335 0.323
(0.061) (0.065) (0.064) (0.221) (0.235) (0.223)
G-H S-H A 0.082 0.083 0.081 0.436 0.318 0.327
(0.059) (0.062) (0.063) (0.305) (0.225) (0.237)
G-H S-H B 0.082 0.083 0.082 0.434 0.318 0.328
(0.064) (0.062) (0.063) (0.306) (0.223) (0.234) G-L summary 0.143 0.139 0.140 0.960 0.865 0.862
(0.086) (0.085) (0.086) (0.386) (0.388) (0.379) G-H summary 0.079 0.081 0.080 0.359 0.325 0.324
(0.061) (0.062) (0.063) (0.262) (0.229) (0.229)
附錄三(續)
NEAT 設計群體能力平均數不同估計方法之 RMSE 人數:10920 受測題數:36年級 SES 校別 PV PV_W EAP AV EAP MLE WLE
G-L S-L A 0.102 0.098 0.098 0.922 0.796 0.817 (0.069) (0.068) (0.069) (0.579) (0.575) (0.574) G-L S-L B 0.107 0.100 0.100 0.924 0.797 0.818
(0.074) (0.072) (0.072) (0.582) (0.578) (0.577) G-L S-H A 0.100 0.096 0.097 0.813 0.819 0.800
(0.070) (0.071) (0.070) (0.582) (0.583) (0.578) G-L S-H B 0.102 0.099 0.100 0.817 0.824 0.806
(0.072) (0.071) (0.071) (0.582) (0.583) (0.578) G-H S-L A 0.062 0.062 0.061 0.469 0.469 0.468
(0.051) (0.051) (0.051) (0.450) (0.449) (0.450) G-H S-L B 0.061 0.064 0.064 0.473 0.474 0.471
(0.051) (0.053) (0.052) (0.452) (0.452) (0.454) G-H S-H A 0.056 0.058 0.057 0.481 0.467 0.465
(0.052) (0.053) (0.052) (0.423) (0.455) (0.447) G-H S-H B 0.061 0.059 0.060 0.483 0.470 0.467
(0.052) (0.051) (0.052) (0.423) (0.453) (0.445) G-L summary 0.102 0.098 0.098 0.869 0.809 0.810
(0.071) (0.071) (0.071) (0.581) (0.580) (0.577) G-H summary 0.059 0.060 0.060 0.472 0.470 0.468
(0.051) (0.052) (0.052) (0.437) (0.452) (0.449)
附錄三(續)
NEAT 設計群體能力平均數不同估計方法之 RMSE 人數:16128 受測題數:18年級 SES 校別 PV PV_W EAP AV EAP MLE WLE
G-L S-L A 0.168 0.161 0.162 1.163 0.901 0.945
(0.092) (0.090) (0.090) (0.383) (0.392) (0.383)
G-L S-L B 0.161 0.157 0.158 1.161 0.904 0.946
(0.090) (0.089) (0.089) (0.381) (0.386) (0.379)
G-L S-H A 0.158 0.155 0.155 0.910 0.976 0.926
(0.089) (0.088) (0.088) (0.388) (0.399) (0.388)
G-L S-H B 0.164 0.161 0.160 0.914 0.980 0.930
(0.091) (0.089) (0.089) (0.390) (0.401) (0.390)
G-H S-L A 0.095 0.097 0.097 0.307 0.312 0.302
(0.061) (0.063) (0.064) (0.217) (0.228) (0.217)
G-H S-L B 0.095 0.098 0.097 0.305 0.311 0.301
(0.064) (0.063) (0.063) (0.217) (0.230) (0.218)
G-H S-H A 0.093 0.095 0.094 0.367 0.304 0.298
(0.062) (0.063) (0.064) (0.304) (0.211) (0.223)
G-H S-H B 0.093 0.093 0.092 0.367 0.300 0.296
(0.059) (0.061) (0.062) (0.305) (0.214) (0.223)
G-L summary 0.162 0.158 0.159 1.037 0.940 0.937
(0.090) (0.089) (0.089) (0.385) (0.395) (0.385)
G-H summary 0.092 0.095 0.095 0.311 0.307 0.299
(0.062) (0.063) (0.063) (0.259) (0.219) (0.219)
附錄三(續)
NEAT 設計群體能力平均數不同估計方法之 RMSE 人數:16128 受測題數:36年級 SES 校別 PV PV_W EAP AV EAP MLE WLE
G-L S-L A 0.131 0.128 0.128 1.170 1.038 1.057
(0.072) (0.071) (0.071) (0.675) (0.669) (0.668)
G-L S-L B 0.130 0.123 0.125 1.166 1.034 1.053
(0.071) (0.071) (0.071) (0.675) (0.670) (0.668)
G-L S-H A 0.131 0.126 0.127 1.058 1.066 1.044
(0.069) (0.069) (0.069) (0.672) (0.674) (0.670)
G-L S-H B 0.127 0.125 0.125 1.056 1.064 1.042
(0.075) (0.072) (0.072) (0.674) (0.676) (0.672)
G-H S-L A 0.077 0.075 0.076 0.557 0.556 0.559
(0.052) (0.053) (0.053) (0.533) (0.532) (0.535)
G-H S-L B 0.074 0.076 0.076 0.557 0.557 0.559
(0.053) (0.056) (0.055) (0.535) (0.534) (0.538)
G-H S-H A 0.073 0.076 0.075 0.519 0.561 0.550
(0.051) (0.054) (0.053) (0.486) (0.536) (0.524)
G-H S-H B 0.070 0.075 0.074 0.521 0.562 0.550
(0.053) (0.052) (0.052) (0.483) (0.533) (0.521)
G-L summary 0.130 0.125 0.126 1.112 1.050 1.049
(0.071) (0.070) (0.071) (0.674) (0.672) (0.669)
G-H summary 0.073 0.075 0.075 0.536 0.559 0.554
(0.052) (0.054) (0.053) (0.509) (0.534) (0.529)
附錄四
BIB 設計群體能力平均數不同估計方法之 RMSE 人數:10920 受測題數:18年級 SES 校別 PV PV_W EAP AV EAP MLE WLE
G-L S-L A 0.099 0.095 0.096 0.934 0.673 0.723
(0.060) (0.059) (0.059) (0.262) (0.269) (0.261)
G-L S-L B 0.103 0.099 0.100 0.937 0.676 0.727
(0.064) (0.060) (0.061) (0.265) (0.271) (0.263)
G-L S-H A 0.095 0.091 0.092 0.662 0.717 0.673
(0.062) (0.060) (0.060) (0.267) (0.271) (0.264)
G-L S-H B 0.099 0.094 0.094 0.664 0.719 0.675
(0.057) (0.057) (0.057) (0.264) (0.267) (0.260)
G-H S-L A 0.047 0.046 0.047 0.319 0.360 0.331
(0.041) (0.040) (0.040) (0.200) (0.216) (0.204)
G-H S-L B 0.049 0.048 0.048 0.319 0.358 0.330
(0.042) (0.042) (0.043) (0.200) (0.217) (0.204)
G-H S-H A 0.051 0.050 0.050 0.524 0.308 0.345
(0.042) (0.041) (0.042) (0.253) (0.194) (0.209)
G-H S-H B 0.051 0.049 0.048 0.524 0.307 0.345
(0.039) (0.042) (0.042) (0.252) (0.193) (0.207) G-L summary 0.099 0.095 0.095 0.799 0.696 0.700
(0.059) (0.058) (0.058) (0.264) (0.269) (0.262) G-H summary 0.047 0.046 0.047 0.414 0.333 0.338
(0.041) (0.041) (0.042) (0.229) (0.203) (0.206)
附錄四(續)
BIB 設計群體能力平均數不同估計方法之 RMSE 人數:10920 受測題數:36年級 SES 校別 PV PV_W EAP AV EAP MLE WLE
G-L S-L A 0.101 0.098 0.099 0.960 0.829 0.849
(0.066) (0.066) (0.067) (0.590) (0.587) (0.587)
G-L S-L B 0.101 0.098 0.098 0.958 0.827 0.846
(0.067) (0.063) (0.063) (0.587) (0.583) (0.584)
G-L S-H A 0.101 0.094 0.095 0.830 0.835 0.815
(0.065) (0.062) (0.062) (0.582) (0.583) (0.578)
G-L S-H B 0.103 0.095 0.097 0.831 0.837 0.817
(0.061) (0.063) (0.063) (0.583) (0.584) (0.579)
G-H S-L A 0.062 0.060 0.061 0.456 0.457 0.456
(0.043) (0.042) (0.042) (0.412) (0.411) (0.414)
G-H S-L B 0.061 0.061 0.061 0.458 0.459 0.458
(0.041) (0.045) (0.044) (0.414) (0.414) (0.417)
G-H S-H A 0.056 0.059 0.059 0.453 0.460 0.455
(0.040) (0.041) (0.041) (0.385) (0.419) (0.411)
G-H S-H B 0.064 0.064 0.064 0.454 0.464 0.458
(0.045) (0.043) (0.043) (0.390) (0.423) (0.415) G-L summary 0.101 0.096 0.097 0.893 0.832 0.832
(0.064) (0.063) (0.063) (0.588) (0.584) (0.582) G-H summary 0.059 0.061 0.061 0.452 0.460 0.457
(0.042) (0.042) (0.043) (0.399) (0.417) (0.414)
附錄四(續)
BIB 設計群體能力平均數不同估計方法之 RMSE 人數:16128 受測題數:18年級 SES 校別 PV PV_W EAP AV EAP MLE WLE
G-L S-L A 0.136 0.129 0.131 1.059 0.803 0.848
(0.085) (0.083) (0.082) (0.363) (0.367) (0.364)
G-L S-L B 0.132 0.127 0.129 1.058 0.803 0.848
(0.082) (0.085) (0.085) (0.366) (0.370) (0.368)
G-L S-H A 0.130 0.128 0.128 0.794 0.850 0.803
(0.080) (0.081) (0.080) (0.364) (0.373) (0.361)
G-L S-H B 0.132 0.127 0.126 0.793 0.848 0.801
(0.088) (0.087) (0.085) (0.366) (0.374) (0.363)
G-H S-L A 0.078 0.079 0.079 0.343 0.365 0.348
(0.054) (0.055) (0.056) (0.213) (0.229) (0.216)
G-H S-L B 0.080 0.079 0.079 0.342 0.362 0.345
(0.055) (0.057) (0.056) (0.210) (0.225) (0.213)
G-H S-H A 0.077 0.078 0.079 0.456 0.340 0.351
(0.054) (0.053) (0.054) (0.299) (0.213) (0.221)
G-H S-H B 0.076 0.079 0.078 0.453 0.342 0.352
(0.054) (0.056) (0.056) (0.298) (0.210) (0.218)
G-L summary 0.132 0.127 0.128 0.925 0.826 0.825
(0.083) (0.084) (0.083) (0.368) (0.371) (0.365)
G-H summary 0.077 0.078 0.078 0.386 0.352 0.349
(0.054) (0.055) (0.056) (0.252) (0.217) (0.216)
附錄四(續)
BIB 設計群體能力平均數不同估計方法之 RMSE 人數:16128 受測題數:36年級 SES 校別 PV PV_W EAP AV EAP MLE WLE
G-L S-L A 0.100 0.096 0.096 0.923 0.799 0.817
(0.065) (0.061) (0.061) (0.606) (0.593) (0.594)
G-L S-L B 0.100 0.095 0.095 0.922 0.798 0.816
(0.063) (0.061) (0.061) (0.605) (0.592) (0.593)
G-L S-H A 0.098 0.095 0.095 0.803 0.809 0.789
(0.061) (0.061) (0.061) (0.596) (0.597) (0.590)
G-L S-H B 0.096 0.094 0.093 0.801 0.807 0.787
(0.062) (0.061) (0.061) (0.598) (0.598) (0.591)
G-H S-L A 0.058 0.059 0.059 0.428 0.429 0.431
(0.048) (0.049) (0.049) (0.467) (0.468) (0.468)
G-H S-L B 0.056 0.058 0.059 0.428 0.429 0.430
(0.048) (0.049) (0.049) (0.468) (0.469) (0.469)
G-H S-H A 0.058 0.059 0.059 0.424 0.435 0.428
(0.046) (0.048) (0.048) (0.454) (0.469) (0.466)
G-H S-H B 0.061 0.057 0.058 0.422 0.432 0.425
(0.047) (0.048) (0.048) (0.454) (0.469) (0.465)
G-L summary 0.098 0.095 0.095 0.860 0.803 0.802
(0.062) (0.061) (0.061) (0.604) (0.595) (0.592)
G-H summary 0.057 0.058 0.058 0.421 0.431 0.428
(0.047) (0.048) (0.048) (0.461) (0.469) (0.467)
附錄五
NEAT 設計群體能力標準差不同估計方法之 RMSE 人數:10920 受測題數:18年級 SES 校別 PV PV_W EAP AV EAP MLE WLE
G-L S-L A 0.012 0.124 0.158 0.015 0.253 0.182
(0.009) (0.014) (0.014) (0.010) (0.026) (0.022)
G-L S-L B 0.010 0.119 0.154 0.016 0.259 0.188
(0.007) (0.014) (0.013) (0.013) (0.024) (0.019)
G-L S-H A 0.011 0.124 0.158 0.026 0.258 0.187
(0.007) (0.014) (0.012) (0.013) (0.029) (0.023)
G-L S-H B 0.013 0.123 0.156 0.029 0.262 0.191
(0.010) (0.017) (0.016) (0.015) (0.028) (0.023)
G-H S-L A 0.012 0.122 0.154 0.018 0.226 0.166
(0.010) (0.014) (0.014) (0.013) (0.024) (0.021)
G-H S-L B 0.011 0.121 0.153 0.021 0.227 0.167
(0.008) (0.014) (0.012) (0.011) (0.022) (0.018)
G-H S-H A 0.012 0.128 0.164 0.017 0.271 0.194
(0.008) (0.014) (0.013) (0.011) (0.024) (0.017)
G-H S-H B 0.012 0.129 0.165 0.018 0.272 0.196
(0.008) (0.014) (0.013) (0.009) (0.027) (0.022) G-L summary 0.008 0.084 0.106 0.072 0.217 0.133
(0.006) (0.009) (0.009) (0.015) (0.019) (0.017) G-H summary 0.008 0.086 0.107 0.092 0.204 0.123
(0.006) (0.008) (0.008) (0.013) (0.019) (0.014)
附錄五(續)
NEAT 設計群體能力標準差不同估計方法之 RMSE 人數:10920 受測題數:36年級 SES 校別 PV PV_W EAP AV EAP MLE WLE
G-L S-L A 0.009 0.071 0.090 0.023 0.133 0.101
(0.007) (0.012) (0.011) (0.011) (0.017) (0.014)
G-L S-L B 0.009 0.069 0.089 0.024 0.133 0.101
(0.006) (0.011) (0.011) (0.012) (0.017) (0.015)
G-L S-H A 0.008 0.071 0.090 0.041 0.128 0.098
(0.006) (0.011) (0.011) (0.012) (0.016) (0.014)
G-L S-H B 0.010 0.070 0.090 0.040 0.128 0.097
(0.007) (0.012) (0.011) (0.013) (0.016) (0.014)
G-H S-L A 0.007 0.071 0.089 0.031 0.112 0.086
(0.006) (0.009) (0.008) (0.012) (0.015) (0.013)
G-H S-L B 0.008 0.075 0.093 0.029 0.113 0.086
(0.006) (0.010) (0.009) (0.011) (0.014) (0.011)
G-H S-H A 0.008 0.076 0.097 0.010 0.133 0.100
(0.007) (0.011) (0.010) (0.008) (0.018) (0.015)
G-H S-H B 0.007 0.076 0.095 0.010 0.138 0.104
(0.006) (0.010) (0.009) (0.007) (0.014) (0.011) G-L summary 0.004 0.049 0.062 0.018 0.105 0.067
(0.003) (0.005) (0.005) (0.009) (0.009) (0.008) G-H summary 0.005 0.053 0.065 0.031 0.096 0.060
(0.003) (0.005) (0.005) (0.008) (0.009) (0.008)
附錄五(續)
NEAT 設計群體能力標準差不同估計方法之 RMSE 人數:16128 受測題數:18年級 SES 校別 PV PV_W EAP AV EAP MLE WLE
G-L S-L A 0.010 0.122 0.155 0.014 0.255 0.185
(0.007) (0.012) (0.011) (0.009) (0.021) (0.017)
G-L S-L B 0.009 0.119 0.154 0.016 0.254 0.185
(0.007) (0.012) (0.012) (0.011) (0.017) (0.014)
G-L S-H A 0.009 0.123 0.158 0.027 0.262 0.190
(0.007) (0.012) (0.012) (0.013) (0.028) (0.023)
G-L S-H B 0.009 0.120 0.155 0.030 0.266 0.194
(0.007) (0.013) (0.012) (0.013) (0.028) (0.023)
G-H S-L A 0.009 0.119 0.151 0.021 0.226 0.166
(0.006) (0.012) (0.011) (0.013) (0.028) (0.022)
G-H S-L B 0.009 0.120 0.154 0.019 0.225 0.165
(0.006) (0.012) (0.011) (0.012) (0.025) (0.020)
G-H S-H A 0.012 0.133 0.166 0.019 0.269 0.192
(0.007) (0.014) (0.013) (0.012) (0.018) (0.013)
G-H S-H B 0.009 0.129 0.164 0.018 0.272 0.195
(0.008) (0.012) (0.012) (0.011) (0.023) (0.017)
G-L summary 0.006 0.082 0.104 0.069 0.221 0.136
(0.005) (0.007) (0.007) (0.013) (0.019) (0.016)
G-H summary 0.006 0.085 0.107 0.094 0.203 0.121
(0.005) (0.007) (0.007) (0.016) (0.017) (0.014)
附錄五(續)
NEAT 設計群體能力標準差不同估計方法之 RMSE 人數:16128 受測題數:36年級 SES 校別 PV PV_W EAP AV EAP MLE WLE
G-L S-L A 0.008 0.074 0.094 0.020 0.124 0.094
(0.005) (0.010) (0.010) (0.011) (0.012) (0.011)
G-L S-L B 0.006 0.072 0.091 0.024 0.129 0.098
(0.004) (0.008) (0.007) (0.009) (0.012) (0.010)
G-L S-H A 0.008 0.073 0.093 0.040 0.131 0.100
(0.006) (0.010) (0.009) (0.011) (0.016) (0.015)
G-L S-H B 0.006 0.073 0.092 0.040 0.130 0.100
(0.005) (0.008) (0.007) (0.009) (0.014) (0.013)
G-H S-L A 0.007 0.074 0.092 0.027 0.108 0.082
(0.006) (0.008) (0.009) (0.012) (0.013) (0.012)
G-H S-L B 0.007 0.071 0.090 0.029 0.111 0.086
(0.005) (0.009) (0.008) (0.010) (0.011) (0.010)
G-H S-H A 0.007 0.077 0.097 0.010 0.136 0.101
(0.006) (0.010) (0.010) (0.006) (0.015) (0.012)
G-H S-H B 0.007 0.077 0.098 0.008 0.133 0.099
(0.005) (0.009) (0.009) (0.006) (0.015) (0.012)
G-L summary 0.004 0.050 0.063 0.017 0.104 0.067
(0.004) (0.006) (0.005) (0.009) (0.010) (0.010)
G-H summary 0.004 0.052 0.065 0.033 0.094 0.058
(0.004) (0.006) (0.005) (0.010) (0.011) (0.009)
附錄六
BIB 設計群體能力標準差不同估計方法之 RMSE 人數:10920 受測題數:18年級 SES 校別 PV PV_W EAP AV EAP MLE WLE
G-L S-L A 0.011 0.121 0.154 0.012 0.251 0.179
(0.007) (0.014) (0.013) (0.008) (0.024) (0.017)
G-L S-L B 0.012 0.123 0.157 0.012 0.248 0.175
(0.009) (0.015) (0.014) (0.009) (0.023) (0.018)
G-L S-H A 0.013 0.124 0.159 0.017 0.231 0.159
(0.010) (0.015) (0.014) (0.012) (0.025) (0.020)
G-L S-H B 0.012 0.122 0.155 0.019 0.233 0.162
(0.009) (0.016) (0.014) (0.012) (0.022) (0.017)
G-H S-L A 0.011 0.114 0.147 0.033 0.252 0.185
(0.007) (0.014) (0.012) (0.013) (0.021) (0.019)
G-H S-L B 0.011 0.118 0.149 0.033 0.253 0.185
(0.008) (0.014) (0.014) (0.013) (0.019) (0.016)
G-H S-H A 0.010 0.121 0.157 0.012 0.276 0.196
(0.007) (0.013) (0.014) (0.009) (0.027) (0.021)
G-H S-H B 0.012 0.124 0.157 0.013 0.276 0.196
(0.009) (0.016) (0.015) (0.011) (0.027) (0.021) G-L summary 0.008 0.085 0.106 0.085 0.196 0.110
(0.007) (0.009) (0.008) (0.012) (0.014) (0.009) G-H summary 0.007 0.083 0.102 0.073 0.225 0.137
(0.005) (0.009) (0.008) (0.011) (0.016) (0.013)
附錄六(續)
BIB 設計群體能力標準差不同估計方法之 RMSE 人數:10920 受測題數:36年級 SES 校別 PV PV_W EAP AV EAP MLE WLE
G-L S-L A 0.009 0.072 0.091 0.018 0.122 0.091
(0.007) (0.012) (0.011) (0.010) (0.015) (0.014)
G-L S-L B 0.008 0.070 0.089 0.020 0.126 0.095
(0.006) (0.010) (0.009) (0.010) (0.016) (0.013)
G-L S-H A 0.007 0.073 0.092 0.028 0.113 0.082
(0.007) (0.010) (0.010) (0.011) (0.014) (0.013)
G-L S-H B 0.008 0.072 0.091 0.029 0.114 0.083
(0.006) (0.012) (0.010) (0.011) (0.014) (0.012)
G-H S-L A 0.009 0.069 0.088 0.043 0.130 0.101
(0.006) (0.011) (0.010) (0.011) (0.013) (0.012)
G-H S-L B 0.007 0.067 0.085 0.044 0.129 0.101
(0.006) (0.009) (0.008) (0.008) (0.010) (0.009)
G-H S-H A 0.010 0.073 0.092 0.015 0.140 0.106
(0.007) (0.012) (0.011) (0.010) (0.017) (0.014)
G-H S-H B 0.008 0.073 0.093 0.014 0.140 0.106
(0.007) (0.011) (0.010) (0.008) (0.016) (0.013) G-L summary 0.005 0.050 0.063 0.028 0.090 0.053
(0.003) (0.006) (0.006) (0.007) (0.008) (0.007) G-H summary 0.005 0.050 0.062 0.017 0.111 0.073
(0.004) (0.006) (0.006) (0.006) (0.008) (0.007)
附錄六(續)
BIB 設計群體能力標準差不同估計方法之 RMSE 人數:16128 受測題數:18年級 SES 校別 PV PV_W EAP AV EAP MLE WLE
G-L S-L A 0.011 0.121 0.154 0.013 0.251 0.179
(0.007) (0.013) (0.014) (0.009) (0.022) (0.017)
G-L S-L B 0.009 0.121 0.156 0.009 0.246 0.175
(0.006) (0.011) (0.010) (0.006) (0.023) (0.017)
G-L S-H A 0.009 0.121 0.156 0.017 0.239 0.166
(0.006) (0.011) (0.010) (0.011) (0.019) (0.013)
G-L S-H B 0.009 0.123 0.156 0.018 0.237 0.164
(0.007) (0.011) (0.011) (0.011) (0.024) (0.018)
G-H S-L A 0.009 0.119 0.152 0.030 0.250 0.185
(0.007) (0.012) (0.010) (0.012) (0.019) (0.016)
G-H S-L B 0.008 0.120 0.152 0.030 0.249 0.184
(0.006) (0.010) (0.010) (0.011) (0.017) (0.014)
G-H S-H A 0.010 0.130 0.161 0.012 0.275 0.196
(0.009) (0.011) (0.012) (0.008) (0.024) (0.019)
G-H S-H B 0.008 0.125 0.160 0.010 0.277 0.198
(0.007) (0.012) (0.011) (0.009) (0.028) (0.021)
G-L summary 0.006 0.083 0.104 0.082 0.199 0.113
(0.005) (0.007) (0.007) (0.011) (0.013) (0.010)
G-H summary 0.006 0.085 0.105 0.077 0.224 0.137
(0.004) (0.005) (0.006) (0.008) (0.014) (0.011)
附錄六(續)
BIB 設計群體能力標準差不同估計方法之 RMSE 人數:16128 受測題數:36年級 SES 校別 PV PV_W EAP AV EAP MLE WLE
G-L S-L A 0.006 0.072 0.092 0.016 0.121 0.091
(0.005) (0.008) (0.007) (0.008) (0.012) (0.010)
G-L S-L B 0.007 0.071 0.091 0.018 0.123 0.093
(0.006) (0.009) (0.009) (0.009) (0.012) (0.010)
G-L S-H A 0.006 0.073 0.092 0.029 0.114 0.083
(0.005) (0.008) (0.008) (0.010) (0.015) (0.012)
G-L S-H B 0.008 0.075 0.093 0.027 0.113 0.081
(0.006) (0.010) (0.009) (0.010) (0.014) (0.012)
G-H S-L A 0.007 0.072 0.089 0.040 0.127 0.098
(0.005) (0.009) (0.008) (0.009) (0.013) (0.012)
G-H S-L B 0.007 0.067 0.087 0.043 0.131 0.101
(0.004) (0.008) (0.007) (0.008) (0.011) (0.009)
G-H S-H A 0.007 0.074 0.094 0.012 0.137 0.102
(0.005) (0.008) (0.008) (0.007) (0.014) (0.012)
G-H S-H B 0.007 0.070 0.090 0.015 0.140 0.105
(0.006) (0.009) (0.010) (0.009) (0.013) (0.011)
G-L summary 0.005 0.051 0.063 0.029 0.090 0.052
(0.004) (0.006) (0.005) (0.008) (0.008) (0.007)
G-H summary 0.004 0.050 0.062 0.018 0.110 0.071
(0.003) (0.005) (0.005) (0.006) (0.008) (0.007)