Informal inferential reasoning

In statistics education, informal inferential reasoning (also called informal inference) refers to the process of making a generalization based on data (samples) about a wider universe (population/process) while taking into account uncertainty without using the formal statistical procedure or methods (e.g. P-values, t-test, hypothesis testing, significance test).
Like formal statistical inference, the purpose of informal inferential reasoning is to draw conclusions about a wider universe (population/process) from data (sample). However, in contrast with formal statistical inference, formal statistical procedure or methods are not necessarily used.
In statistics education literature, the term "informal" is used to distinguish informal inferential reasoning from a formal method of statistical inference.
Informal Inferential Reasoning and Statistical Inference.
Since everyday life involves making decisions based on data, making inferences is an important skill to have. However, a number of studies on assessments of students’ understanding statistical inference suggest that students have difficulties in reasoning about inference.
Given the importance of reasoning about statistical inference and difficulties that students have with this type of reasoning, statistics educators and researchers have been exploring alternative approaches towards teaching statistical inference. Recent research suggests that students have some sound intuitions about data and these intuitions can be refined and nudged towards prescriptive theory of inferential reasoning. More of an informal and conceptual approach that build on the previous big ideas and make connection between foundational concepts is therefore favorable.
Recently, informal inferential reasoning has been the focus of research and discussion among researchers and educators in statistics education as it is seen as having a potential to help build fundamental concepts that underlie formal statistical inference. Many advocate that underlying concepts and skills of inference should be introduced early in the course or curriculum as they can help make the formal statistical inference more accessible (see published reaction of Garfield & Zieffler to).
Three essential characteristics.
According to Statistical Reasoning, Thinking and Literacy forum, three essential principles to informal inference are:
Core Statistical Ideas.
Informal inferential reasoning involved the following related ideas
Bakker and Derry (2011) argue for using inferentialism as a philosophical foundation to develop informal inferential reasoning and therefore address three major challenges in statistics education--(1) avoiding students' inert knowledge (not being able to apply what they have learned to new problems), (2) avoiding atomistic approaches to teaching statistics, and (3) sequencing topics to create coherence in curriculum from a students' perspective.
Tasks that Involve Informal Inferential Reasoning.
Zieffler et al. (2008) suggest three types of tasks that have been used in studies of students' informal inferential reasoning and its development.
Tasks that involve "growing samples" are also fruitful for developing informal inferential reasoning