研究生: |
劉奕均 Liu, Yi-Chun |
---|---|
論文名稱: |
探討高教學生於假設檢定的統計認知 An Exploration about Undergraduate and Graduate Students' Statistical Cognition in Hypothesis Testing |
指導教授: |
楊凱琳
Yang, Kai-Lin |
口試委員: |
林素微
Lin, Su-Wei 王婷瑩 Wang, Ting-Ying 楊凱琳 Yang, Kai-Lin |
口試日期: | 2023/06/28 |
學位類別: |
碩士 Master |
系所名稱: |
數學系 Department of Mathematics |
論文出版年: | 2023 |
畢業學年度: | 111 |
語文別: | 中文 |
論文頁數: | 124 |
中文關鍵詞: | 假設檢定 、統計認知 |
研究方法: | 內容分析法 、 半結構式訪談法 |
DOI URL: | http://doi.org/10.6345/NTNU202300664 |
論文種類: | 學術論文 |
相關次數: | 點閱:123 下載:37 |
分享至: |
查詢本校圖書館目錄 查詢臺灣博碩士論文知識加值系統 勘誤回報 |
本研究藉由文獻探討形成假設檢定概念之評量架構,並據以設計試題,探討大學生與研究生在假設檢定概念試題的表現概況。研究問題包括「假設檢定測驗試題的效度、信度為何?」、「大學生與研究生在假設檢定測驗試題的表現概況為何?」
為了回答以上的研究問題,本研究以主要文獻與統計學教科書為出發點,分析假設檢定的概念,再依分析結果與文獻探討形成測驗目標,並據以進行試題設計,形成預試試題。研究者先行邀請1名數學系大學生寫預試試題,並請受試者於作答時放聲思考,以利收集受試者對試題的各種想法。為檢驗試題效度,預試試題交由2名大學統計學專家教授審查試題內容與測驗目標,並邀請2名曾經教過合理性檢定單元的高中數學教師檢驗預試測驗試題之雙向細目表。研究者根據專家審查結果修正預試試題,修正完畢後形成本研究的正式試題,收集63名大學生或研究生的回應與分析結果。
本研究的結論指出,依據假設檢定概念評量架構發展出的測驗試題,其試題內容具有專家效度,其雙向細目表具有編碼一致性;具有3題以上測驗試題之層面,其Cronbach’s 係數在0.6以上,具有可接受的信度。本研究亦針對各項子概念之試題提出受試者的表現概況,並指出以平均通過率而言,對本研究受試者由易而難的子概念依序是「樣本統計量與p值」、「統計假設」、「抽樣與抽樣分布」、「型一與型二錯誤」、「顯著水準與顯著性」、「母體比例的假設檢定」,從統計認知面向來看,本研究之思考試題對受試者而言較為困難,而知識試題的平均通過率與推理試題相近。
本研究亦針對假設檢定測驗試題設計、假設檢定於大學及高中階段的教與學提供建議,供未來的研究者參考。
李茂能(2010)。虛無假設顯著性考驗的演進、議題與迷思。測驗統計年刊,18(1),1-22。
邱婉嘉(2010)。台灣與美國高中信賴區間單元教材內容之分析比較[未出版之碩士論文]。國立臺灣師範大學。
邱皓政(2013)。量化研究法(二)、統計原理與分析技術:SPSS中文視窗版操作實務詳析(修訂版)。雙葉。
黃文璋(2004)。統計學裡無罪推定的精神。科學發展。擷取於2023年3月17日,https://ejournal.stpi.narl.org.tw/sd/view?vlId=FFB945E9-EDE3-481A-ADE6-8C248EDF5F58
黃文璋(2015)。銅板出現正面機率之檢定。國立高雄大學統計學研究所。擷取於2023年3月17日,https://www.stat.nuk.edu.tw/SouthShow.asp?myid=1539。
黃文璋(2016)。機率與統計在高中。中國統計學報,54(2),43-61。
楊壬孝、蔡天鉞、李政豐、李善文、蔡杰、洪允東(2021)。普通型高級中等學校選修數學甲下。全華圖書。
葉裕益(2011)高三學生在信賴區間與其先備知識的學習表現和錯誤認知[未出版之碩士論文]。國立臺灣師範大學。
墨爾‧諾芡(2014)。統計學的世界(鄭惟厚譯)。遠見天下。
Carver, R., Everson, M., Gabrosek, J., Horton, N., Lock, R., Mocko, M., Rossman, A., Roswell, G. H., Velleman, P., & Witmer, J. (2016). Guidelines for assessment and instruction in statistics education (GAISE) college report 2016. https://doi.org/10.52041/serj.v7i1.478
Casella, G., & Berger, R. L. (2021). Statistical inference. Cengage Learning.
Chance, B., del Mas, R., Garfield, J. (2004). Reasoning about Sampling Distribitions. In: Ben-Zvi, D., Garfield, J. (eds) The Challenge of Developing Statistical Literacy, Reasoning and Thinking. Springer, Dordrecht. 295-323 https://doi.org/10.1007/1-4020-2278-6_13
Dani, B.-Z., & Joan, G. (2004). Statistical literacy, reasoning, and thinking: Goals, definitions, and challenges. The Challenge of Developing Statistical Literacy, Reasoning and Thinking, Springer, Dordrecht. 3-15. https://doi.org/10.1007/1-4020-2278-6_13
Delmas, R., Garfield, J., Ooms, A., & Chance, B. (2007). Assessing students' conceptual understanding after a first course in statistics. Statistics Education Research Journal, 6(2), 28-58. https://doi.org/10.52041/serj.v6i2.483
DelMas, R. C. (2002). Statistical literacy, reasoning, and thinking: A commentary. Journal of Statistics Education, 10(2). https://doi.org/10.1080/10691898.2002.11910674
Dolor, J. M. A. (2017). Investigating Statistics Teachers' Knowledge of Probability in the Context of Hypothesis Testing [Unpublished doctoral dissertation] Portland State University
Eisinga, R., Grotenhuis, M. t., & Pelzer, B. (2013). The reliability of a two-item scale: Pearson, Cronbach, or Spearman-Brown? International journal of public health, 58, 637-642. https://doi.org/10.1007/s00038-012-0416-3
Fisher, R. A. (1956). Mathematics of a lady tasting tea. The world of mathematics, 3(8), 1514-1521.
Franklin, C., Kader, G., Mewborn, D., Moreno, J., Peck, R., Perry, M., & Scheaffer, R. (2007). Guidelines for assessment and instruction in statistics education (GAISE) report. In: Alexandria, VA: American Statistical Association.
Garfield, J. (2002). The challenge of developing statistical reasoning. Journal of Statistics Education, 10(3). https://doi.org/10.1080/10691898.2002.11910676
Garfield, J. B. (2003). Assessing statistical reasoning. Statistics Education Research Journal, 2(1), 22-38. https://doi.org/10.52041/serj.v2i1.557
Garfield, J. B., Ben-Zvi, D., Chance, B., Medina, E., Roseth, C., Zieffler, A., Garfield, J. B., Ben-Zvi, D., Chance, B., & Medina, E. (2008). Learning to reason about statistical inference. Developing students’ statistical reasoning: Connecting research and teaching practice, 261-288.
Goldie, S. (2012). International AS and A Level Mathematics: Statistics. Hodder Education.
Greg Attwood, Tom Begley, Ian Bettison, Alan Clegg, Gill Dyer, Jane Dyer, Kinoulty, J., Lima, G. F., & Smith, H. (2017). Further Statistics 1. Pearson Education.
Halpin, P. F., & Stam, H. J. (2006). Inductive inference or inductive behavior: Fisher and Neyman: Pearson approaches to statistical testing in psychological research (1940-1960). The American journal of psychology, 119(4), 625-653. https://doi.org/10.2307/20445367
Hawkins, A., Jolliffe, F., & Glickman, L. (2014). Teaching statistical concepts. Routledge.
Hogg, R. V., Tanis, E. A., & Zimmerman, D. L. (2015). Probability and statistical inference (Vol. 993). Macmillan New York.
Hubbard, R., & Bayarri, M. J. (2003). Confusion over measures of evidence (p's) versus errors (α's) in classical statistical testing. The American Statistician, 57(3), 171-178. https://doi.org/10.1198/0003130031856
Huberty, C. J. (1993). Historical origins of statistical testing practices: The treatment of Fisher versus Neyman-Pearson views in textbooks. The Journal of Experimental Education, 61(4), 317-333. https://doi.org/10.1080/00220973.1993.10806593
Lane-Getaz, S. J. (2007). Development and Validation of a Research-based Assessments: Reasoning about P-values and Statistical Significance [Unpublished doctoral dissertation] University of Minnesota.
Liu, Y., & Thompson, P. W. (2009). Mathematics teachers’ understandings of proto-hypothesis testing. Pedagogies: An International Journal, 4(2), 126-138. https://doi.org/10.1080/15544800902741564
Moore, D. S., & Kirkland, S. (2015). The basic practice of statistics (7 ed.). WH Freeman New York. https://doi.org/10.1080/00401706.1996.10484558
Morimoto, R. (2021). Stop and Think About p-Value Statistics: Fisher, Neyman, and E. Pearson Revisited. Annals of the Japan Association for Philosophy of Science, 30, 43-65. https://doi.org/10.4288/jafpos.30.0_43
Perezgonzalez, J. D. (2015). Fisher, Neyman-Pearson or NHST? A tutorial for teaching data testing. Frontiers in psychology, 6, 223. https://doi.org/10.3389/fpsyg.2015.00223
Shaver, J. P. (1993). What statistical significance testing is, and what it is not. The Journal of Experimental Education, 61(4), 293-316. https://doi.org/10.1080/00220973.1993.10806592
Smith, T. M. (2008). An investigation into student understanding of statistical hypothesis testing [Unpublished doctoral dissertation] University of Maryland, College Park.
Vallecillos, A. (2000). Understanding of the logic of hypothesis testing amongst university students. Journal für Mathematik-Didaktik, 21(2), 101-123. https://doi.org/10.1007/BF03338912
Ronald L. Wasserstein & Nicole A. Lazar (2016) The ASA Statement on p-Values: Context, Process, and Purpose, The American Statistician, 70(2), 129-133. https://doi.org/10.1080/00031305.2016.1154108