Random sampling and random allocation are essential processes in the practice of inferential statistics. These processes ensure that all members of a population are equally likely to be selected, and that all possible allocations in an experiment are equally likely. It is these characteristics that allow the validity of the subsequent calculations…

It is well known that students of inferential statistics find the hypothetical, probabilistic reasoning used in hypothesis tests difficult to understand. Consequently, they will also have difficulties in understanding "p"-values. It is not unusual for these students to hold misconceptions about "p"-values that are difficult to…

Peter Dunn and Margaret Marshman present the second of their data files articles in which they discuss the statistical investigation cycle which describes the whole process of conducting a statistical research study. [For "The Data Files: A Series of Articles to Support Mathematics Teachers to Teach Statistics," see EJ1259108.]

Teaching from an informal statistical inference perspective can address the challenge of teaching statistics in a coherent way. We argue that activities that promote model-based reasoning address two additional challenges: providing a coherent sequence of topics and promoting the application of knowledge to novel situations. We take a models and…

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…

Multiple imputation (MI), a two-stage process whereby missing data are imputed multiple times and the resulting estimates of the parameter(s) of interest are combined across the completed datasets, is becoming increasingly popular for handling missing data. However, MI can result in biased inference if not carried out appropriately or if the…

Online purposive samples have unknown biases and may not strictly be used to make inferences about wider populations, yet such inferences continue to occur. We compared the demographic and drug use characteristics of Australian ecstasy users from a probability (National Drug Strategy Household Survey, n = 726) and purposive sample (online survey…

Students recognise and analyse data and draw inferences. They represent, summarise and interpret data and undertake purposeful investigations involving the collection and interpretation of data… They develop an increasingly sophisticated ability to critically evaluate chance and data concepts and make reasoned judgments and decisions, as well as…

People frequently continue to use inaccurate information in their reasoning even after a credible retraction has been presented. This phenomenon is often referred to as the continued influence effect of misinformation. The repetition of the original misconception within a retraction could contribute to this phenomenon, as it could inadvertently…

An understanding of conditional probability is essential for students of inferential statistics as it is used in Null Hypothesis Tests. Conditional probability is also used in Bayes' theorem, in the interpretation of medical screening tests and in quality control procedures. This study examines the understanding of conditional probability of…

The term "data snooping" refers to the practice of choosing which statistical analyses to apply to a set of data after having first looked at those data. Data snooping contradicts a fundamental precept of applied statistics, that the scheme of analysis is to be planned in advance. In this column, the authors shall elucidate the…

Statistics is one of the most widely used topics for everyday life in the school mathematics curriculum. Unfortunately, the statistics taught in schools focuses on calculations and procedures before students have a chance to see it as a useful and powerful tool. Researchers have found that a dominant view of statistics is as an assortment of tools…

The area of statistics is one in which teachers may be encouraged to make important links to other curriculum areas and social issues. Statistical literacy is a key component of being numerate and living as an informed citizen. The teaching of statistics provides an opportunity to inform and educate students about social issues and moral…

Formal inference, which makes theoretical assumptions about distributions and applies hypothesis testing procedures with null and alternative hypotheses, is notoriously difficult for tertiary students to master. The debate about whether this content should appear in Years 11 and 12 of the "Australian Curriculum: Mathematics" has gone on…

A consistent body of research shows that large classes have been perceived by teachers as an obstacle to deliver quality teaching. This large-scale study sought to investigate further those differential effects by asking 1,119 teachers from 321 K-12 schools in New South Wales (Australia) their perceptions of ideal class size for a variety of…