Narrative Inference with and without Statistics

This article investigates the role played by narrative in drawing inferences from statistics before the adoption of formal inference regimes in economics. Two well-known, and exemplary, cases of informal inference provide the materials. Nikolai Kondratiev’s struggles to make inferences about the existence of his “long waves” from heaps of statistics in the 1920s contrast sharply with Thomas Robert Malthus’s confident account of demographic-economic oscillations made on the basis of the limited numbers available in the late eighteenth century. Comparison of their inferential reasoning, using detailed textual analysis, casts attention on the important role of narrative. These cases prompt the notion of “narrative inference”: where informal statistical inference depends on narrative accounts—used to make sense of the numbers by Malthus or to add sense onto the numbers by Kondratiev.

What Newman Can Give Catholic Philosophers Today

In this article I explain various points of contact between Newman and the Catholic philosophical tradition. I begin with Newman’s personalism as it is found in the Grammar of Assent, especially in the distinction between notional and real assent, and in the distinction between formal and informal inference. Then I proceed to Newman’s personalism as it is found in his teaching on conscience and on doctrinal development. I then consider Newman as proto-phenomenologist and also as an Augustinian thinker. Finally, I discuss Newman’s teaching on moral and intellectual virtue in The Idea of a University. If I had to pick one utterance of Newman that epitomizes his philosophical thought in a way that engages Catholic philosophers, I would pick the motto of the Grammar of Assent: “Non in dialectica complacuit Deo salvum facere populum tuum.”

Atividade de inferência informal para avaliar π

Resumo: Inferência é a parte da Estatística que trata de previsões, para uma população, a partir das informações de uma amostra. O assunto é discutido de maneira formal em disciplinas de Estatística de cursos superiores, pois envolve conceitos matemáticos avançados. Entretanto, fazer previsões é algo presente na vida de todos e com os estudantes da Educação Básica não é diferente. É importante que os estudantes desse nível de ensino tenham oportunidade de fazer previsões, ainda que limitadas e informais, como uma experiência inicial do uso dessa parte fundamental da Estatística. Neste artigo, aproveitamos a mística envolvendo o número π para discutir, de modo informal, aspectos da Inferência Estatística. Descrevemos uma atividade, presente no portal AtivEstat- Atividades de Estatística, que usa conceitos simples de Geometria para avaliar o valor do número irracional π. Palavras-chave: Inferência informal; Atividade; Valor de π. Informal inference activity to estimate π Abstract: Inference is the part of Statistics that deals with forecasts for a population from the information in a sample. The subject is discussed formally in higher education statistics disciplines as it involves advanced mathematical concepts. However, making predictions is something present in everyone's life and with students at theBasic Education it is not different. It is important that students, at this educational level, have the opportunity to make predictions, even if they are limited and informal, as an initial experience of using this key part of Statistics. In this article, we take advantage of the mystique involving the number π, to informally discuss aspects of Statistical Inference. We describe an activity, included in the Portal AtivEstat - Statistics Activities, that uses simple concepts of Geometry to evaluate the value of the irrational number π. Keywords: Informal inference; Activity; π value.

Inferência informal e inferência “informal”Informal and “Informal” Inference

“Inferencia Informal” es un enfoque de la inferencia estadística, que se basa en métodos de remuestreo y se vincula a bootstrap como sustituto de los intervalos de confianza y a las pruebas de aleatorización como alternativa a los contrastes estadísticos. La inferencia informal, por otro lado, es una conceptualización de la inferencia estadística mediante la simplificación de su complejidad mediante contextos que hacen que la interpretación de los conceptos desarrollados sea significativa, o mediante el establecimiento de analogías y metaconocimientos que proporcionen comprensión. Primero, ilustramos la prueba de significación mediante una prueba de rangos elemental. Segundo, construimos ideas informales sobre la inferencia, por analogía con la situación médica. En tercer lugar, destacamos el potencial de las aproximaciones informales a la inferencia estadística mediante ejemplos. En cuarto lugar, describimos el enfoque de “Inferencia Informal”. Finalmente, sacamos algunas conclusiones sobre el potencial didáctico y los inconvenientes de la “Inferencia Informal”. Nuestras consideraciones están significadas por el objetivo de facilitar la comprensión conceptual.

THE CO-EMERGENCE OF AGGREGATE AND MODELLING REASONING

This article examines how two processes – reasoning with statistical modelling of a real phenomenon and aggregate reasoning – can co-emerge. We focus in this case study on the emergent reasoning of two fifth graders (aged 10) involved in statistical data analysis, informal inference, and modelling activities using TinkerPlotsTM. We describe nine phases of the students’ articulations of aggregate and modelling reasoning as they explored a small sample, constructed a model and generated random samples from this model to examine its validity. These phases are distinguished by the students’ views toward data, variability, and models. We discuss implications and limitations of the results. Despite the idiosyncrasy of the case, the lessons are important because they open a new direction for research about reasoning with data and models. First published November 2017 at Statistics Education Research Journal Archives

Model-based Informal Inference

Following recent scholarly interest in teaching informal linear regression models, this study looks at teachers’ reasoning about informal lines of best fit and their role in pedagogy. The case results presented in this journal paper provide insights into the reasoning used when developing a simple informal linear model to best fit the available data. This study also suggests potential in specific aspects of bidirectional modelling to help foster the development of robust knowledge of the logic of inference for those investigating and coordinating relations between models developed during modelling exercises and informal inferences based on these models. These insights can inform refinement of instructional practices using simple linear models to support students’ learning of statistical inference, both formal and informal.

REACTION TIME IN GRADE 5: DATA COLLECTION WITHIN THE PRACTICE OF STATISTICS

This study reports on a classroom activity for Grade 5 students investigating their reaction times. The investigation was part of a 3-year research project introducing students to informal inference and giving them experience carrying out the practice of statistics. For this activity the focus within the practice of statistics was on introducing two different ways of collecting data to answer a statistical question, in this case, “What is the typical reaction time of Grade 5 students?” Workbook entries were used to assess students’ capacities to engage in the investigation. Results indicated that although the students were proficient with the procedures and measures introduced, they were less able to explain and apply the underlying concepts. The activity provides a suggestion and benchmarks for others wishing to follow student development of concepts related to the practice of statistics. First published May 2017 at Statistics Education Research Journal Archives

STUDENTS’ EXPRESSIONS OF UNCERTAINTY IN MAKING INFORMAL INFERENCE WHEN ENGAGED IN A STATISTICAL INVESTIGATION USING TINKERPLOTS

This paper reports on the results of a study investigating the potential to embed Informal Statistical Inference in statistical investigations, using TinkerPlots, for assisting 8th grade students’ informal inferential reasoning to emerge, particularly their articulations of uncertainty. Data collection included students’ written work on a statistical investigation as well as audio and screen records. Results show students’ ability to draw conclusions based on data, recognizing that these are constrained by uncertainty, and to use them to make inferences. However, few students used probabilistic language for describing their generalizations. These results highlight the need for working on probabilistic ideas within statistics, helping students to evolve from a deterministic perspective of inference to include uncertainty in their statements. First published November 2016 at Statistics Education Research Journal Archives

USING GUIDED REINVENTION TO DEVELOP TEACHERS’ UNDERSTANDING OF HYPOTHESIS TESTING CONCEPTS

Statistics education reform efforts emphasize the importance of informal inference in the learning of statistics. Research suggests statistics teachers experience similar difficulties understanding statistical inference concepts as students and how teacher knowledge can impact student learning. This study investigates how teachers reinvented an informal hypothesis test for categorical data through the framework of guided reinvention. We describe how notions of variability help bridge the development from informal to formal understandings of empirical sampling distributions and procedures for constructing statistics and critical values for conducting hypothesis tests. A product of this paper is a hypothetical learning trajectory that statistics educators could utilize as both a framework for research and as an instructional tool to improve the teaching of hypothesis testing. First published May 2015 at Statistics Education Research Journal Archives