Formulate the fundamental concepts underlying hypothesis testing, drawing on creative thinking

Basic stochastic education, i.e. the ability to understand and critically scrutinise data and statistics in everyday life and in the context of scientific research, is becoming increasingly important (Ben-Zvi & Garfield 2004; Gal 2002).

Despite long-standing calls to shift the focus of stochastics lessons in schools towards basic stochastic education, the guiding principle of ‘data’ (cf. Krauss et al. 2020) and the teaching of inferential statistics (AK Stochastik 2003; KMK 2012), lessons still often concentrate on carrying out procedures and calculations (McNamara 2015; Garfield et al. 2015). However, this focus on calculations neglects the necessary development of statistical skills (Hidayati et al. 2020, cf. Gal 2002) and a basic understanding of statistical inference, which should be considered as early as possible. In combination, this can also contribute to scientific propaedeutics and avoid bad scientific practice and charlatanism (e.g. p-hacking) (cf. Wasserstein et al. 2019).

The core of every statistical study consists of analysing data and drawing conclusions beyond its processing. This also includes the basics of statistical inference, i.e. drawing conclusions about the population using sample information. Although this idea initially seems very obvious in terms of content, the interpretation of the results obtained is extremely complex. At the same time, the question arises as to how learners - as a result of the prevailing calculus in schools - are supposed to understand inferential statistical methods, develop inferential thinking and develop appropriate ideas without sound basic knowledge and content-related ideas about fundamental concepts of stochastics.

In order to address this complexity of inferential reasoning at an early stage in the sense of a spiral curricular approach and to initiate formal statistical reasoning, a precursor form for the early promotion of statistical reasoning and the understanding of inferential statistical methods was proposed under the term informal inferential reasoning. This involves, at an informal level, a) making statements about generalisation beyond the data but without the use of formal statistical methods, b) using the data as evidence, and c) using probabilistic language that expresses uncertainty about the generalisation (Makar and Rubin 2009).

Inferential statistical thinking using the example of hypothesis testing

If, taking this approach into account, the hypothesis test is considered as an example of such an inferential statistical method, important aspects of the step-by-step transition from informal to formal thinking can be established. At the same time, the following question also arises: What needs to be prepared so that learners can (1) develop a sound understanding of hypothesis tests, (2) grasp their possibilities and limitations, (3) reflect on their possibilities and limitations and (4) interpret them adequately? Although hypothesis tests are widely used in the empirical sciences to validate theoretical or exploratory assumptions about a subject area, there are sometimes serious misconceptions and inadequate interpretations of the content of hypothesis tests among a wide variety of groups of people (cf. Sotos et al. 2007; Krishnan & Noraini 2015; Haller & Krauss 2002). As a result, the significance of individual statistical values is often significantly overestimated (Wasserstein et al. 2019).

Research plan

With the primary aim of developing a sound understanding of the content of hypothesis testing and thus making an important contribution to basic stochastic education, the research project is divided into two interlinked phases that build on each other.

Research phase 1 deals with the research question of which core ideas are necessary to develop an understanding of the content of hypothesis tests. To identify such core ideas, a theoretical deconstruction of the hypothesis test is first carried out based on an extensive literature review. Based on an exemplary identification and a detailed conceptualisation of the term ‘core idea’, further relevant core ideas are identified and deductively derived. An expert survey will then be conducted to validate the derived core ideas and, if necessary, adapt them in order to generate a consensus among the experts, who are made up of subject didacticians, subject statisticians and teachers (or links between university and school). Finally, the core ideas identified will also be empirically confirmed by a questionnaire for students, which will be used in various courses of the teacher training programme in mathematics and other study programmes. The plan is to compile various items from existing test instruments, assign the individual items to the core ideas and use the data to demonstrate correlations between different items.

In research phase 2, items suitable for one or more of the core ideas identified are to be selected or developed as examples, which will then be combined into corresponding learning environments. A qualitative evaluation of the learning environments with small groups based on thinking-out-loud interviews and videos of the group work processes will be used to reconstruct whether the learning environments are able to address the envisaged core ideas. In the sense of a design-based research approach, the evaluated learning environments can thus be seen as part of a solution to the didactic challenge of understanding the content of hypothesis tests.

Personal motivation

From today's perspective, I have experienced too little understanding-orientated teaching myself, particularly in the subject area of stochastics. I therefore taught myself a lot on a self-taught basis. Although this meant that I was able to calculate the different types of problems - i.e. I had internalised the ‘calculus’ - I didn't understand exactly what was happening or why I was doing it until the end. At the time, I probably never really understood why I might need something like this, what a hypothesis test is or what significance it has. It was only during my studies that I was able to grasp the content much better and, above all, learnt about its importance for scientific research and understanding everyday issues. It is therefore important to me to contribute to the further development of stochastics teaching at school.

Literature

Arbeitskreis Stochastik der GDM (2003): Empfehlung zu Zielen und zur Gestaltung des Stochastikunterrichts. In: Stochastik in der Schule 23 (3), S. 21–26. Online verfügbar unter www.stochastik-in-der-schule.de/sisonline/struktur/jahrgang23- 2003/heft3/Langfassungen/2003-3_ak-empfehl.pdf, zuletzt geprüft am 26.02.2024.

Ben-Zvi, D. & Garfield, J. (2004). Statistical Literacy, Reasoning and Thinking: Goals, Definitions, and Challenges. In D. Ben-Zvi & J. Garfield (Hrsg.), The Challenge of Developing Statistical Literacy, Reasoning and Thinking . Springer Science + Business Media Inc. 3-16.

Gal, I. (2002). Adults’ Statistical Literacy: Meanings, Components, Responsibilities. International Statistical Review / Revue Internationale de Statistique, 70(1), 1–25. https://doi.org/10.2307/1403713

Garfield, J., Le, L., Zieffler, A., Ben-Zvi, D. (2015): Developing students’ reasoning about samples and sampling variability as a path to expert statistical thinking. Educ Stud Math, 88(3), 327–342. https://doi.org/10.1007/s10649-014-9541-7

Haller, Heiko; Krauss, Stefan (2002): Misinterpretations of significance: A problem students share with their teachers? In: Methods of Psychological Research 7.

Hidayati, N. A., Waluya, S. B., Rochmad; Wardono (2020): Statistics literacy: what, why and how?. Journal of Physics.: Conference Series. 1613(1), S. 12080. https://doi.org/10.1088/1742-6596/1613/1/012080

KMK (2012): Bildungsstandards im Fach Mathematik für die Allgemeine Hochschulreife: (Beschluss der Kultusministerkonferenz vom 18.10.2012).

Krauss, S., Weber, P., Binder, K., Bruckmaier, G., & Hilbert, S. (2020). Zur Propädeutik des Hypothesentestens in der gymnasialen Oberstufe – Die Diskrepanz zwischen schulischem Stochastikunterricht und tatsächlicher Anwendung. In: Weber, P. (Hrsg.), Wie gut bereitet der Stochastikunterricht auf Alltag, Studium und Berufsleben vor? (S.96-142). https://doi.org/10.5283/epub.43330

Krishnan, Saras; Idris, Noraini (2015): An Overview of Students’ Learning Problems in Hypothesis Testing. In: JPEN 40 (2), S. 193–196. DOI: 10.17576/JPEN-2015-4002-12.

Makar, K., & Rubin, A. (2009). A Framework for thinking about informal statistical inference. Statistics Education Research Journal, 8(1). 82-105

Sotos, C., Vanhoof, S., Noortgate, W., & Onghena, P. (2007). Students’ misconceptions of statistical inference: A review of the empirical evidence from research on statistics education. Educational Research Review, 2(2), 98-113. doi.org/10.1016/j.edurev.2007.04.001

Wasserstein, R. L., Schirm, A. L., & Nicole, A. L. (2019). Moving to a World Beyond “p < 0.05”, The American Statistician, 73(1), 1-19. https://doi.org/10.1080/00031305.2019.158391

[This dissertation was written and is only available in german. Our summary was translated by our website team. Possible quotations have been translated in accordance with scientific regularia.]