Statisticians Viewpoints

The Four Framework for Statistical Thinking in Empirical Enquiry

• This framework in figure 1 is built based on responses from statisticians on how one thinks statistically.
• It seeks to organise some of the elements of statistical thinking during data-based enquiry.
• In short, the thinking operates in all four dimensions at once.
• For instance, the thinker could be categorised as currently being in the planning stage of the Investigative Cycle (Dimension 1), dealing with some aspect of variation in Dimension 2 (Types of Thinking) by criticising a tentative plan in Dimension 3 (Interrogative Cycle) driven by scepticism in Dimension 4 (Dispositions).
• This pattern of thinking is not peculiar to statisticians, but the quality of thinking can be improved by gaining more statistical knowledge.

The four dimensional framework built by the authors of Statistical Thinking in Empirical Enquiry.

Dimension One: The Investigative Cycle

• The first dimension in Fig. 1(a) shows how one acts and thinks during a statistical investigation.
• This cycle is concerned with abstracting and solving a statistical problem grounded in a larger "real" problem which has the intention to improve current situation.
• A knowledge-based solution to the real problem requires better understanding of how a system works.
• For instance, when students are given a problem such as how to resolve the issue of wasted food in the school canteen, they will need to first define the problem such as how much food is wasted everyday by learning more about the problem. Then they would need to plan and analyse the issue based on what they learned. The cycle goes on with data collection such as finding out how many students actually buy their lunch from the school canteen, and analysing the data collected.  Then students will need to come up with a solution to solve this issue such as preparing lesser food on some days where most students would bring their own lunch or preparing more appetizing meals.

Dimension Two: Types of Thinking 

There are two major types of thinking: general types of thinking that are common to all problem solving and the thinking that are foundations in statistical thinking.

General types of thinking

Strategic thinking 

• Strategic thinking aimed at deciding upon what and how we will do it. For instance, planning how to solve a problem and anticipating problems to avoid them.
• It is important to have an awareness of the constraints one has while working to solve an issue. For example, being aware that one's perception will influence how one approach an issue which will then desensitizing some important information.
• By challenging our own perceptions during group discussions can remove an obstacles and lead to new insights.

Modelling

• Simplify the information and construct a model to represent the information
• We build statistical models to gain insights from this information ("interpret") which feed back into the mental model.
• "Statistical models" here is more general than something like logistic regression. It refers to all of our statistical conceptions of the problem that influence how we collect data about the system and analyse it.

Applying techniques

• Problem solving technique in math is to map a new problem onto a problem that has already been solved so that the previously devised solution can be applied or adapted.
• To use statistics, we first recognize elements of our context that can be usefully mapped onto a model (a process of abstraction from the particular to the generic), operate within that model, and then we map the results back to context (from the generic to the particular).

Fundamental statistical thinking

Recognition of the need for data

• The recognition of the inadequacies of personal experiences and anecdotal evidence leading to a desire to base decisions on deliberately collected data is a statistical impulse.

Transnumeration

• Think of a new way to represent data and to enhance or generate understanding.

Consideration of Variation

• Variation is an observable reality. It is present everywhere and in everything. Variability affects all aspects of life and everything we observe. Nothing is the same.
• It is variation that makes the results of actions unpredictable, that makes questions of cause and effect difficult to resolve, that makes it hard to uncover mechanisms. Eg: change the pattern of variation to something more desirable(reduce the accident rate)

Reasoning with statistical models

• The main contribution of the discipline of statistics to thinking has been its own distinctive set of models, or frameworks, for thinking about certain aspects of investigation in a generic way.
• Modelling tools aid in discovering valuable generic lessons through investigative processes.

Integrating the statistical and contextual

• One cannot be indulge in statistical thinking without some context knowledge.
• In order to arrive at a meaningful result, one has to make connections between existing context-knowledge and the results of analyses.

Dimension three: The Interrogative Cycle

The Interrogative Cycle illustrated in Fig. 1(c) is a generic thinking process in constant use in statistical problem solving. There are different components in this cycle:

Generate

• Think of the possibilities which come from the context, the data or statistical knowledge and apply to the present problem, or may be registered for future investigation

Seek

• Internal seeking which we observe people thinking and digging their memory for relevant knowledge
• External seeking such as obtaining information and ideas from sources outside the individual or team.
• Reading relevant literature.

Interpret

• Connecting new ideas and information with our existing mental models and enlarging our mental models to make connection.

Criticize

• Checking for internal consistency and against reference points (arguing with ourselves, weighing up against our context and statistical knowledge, against the constraints we are working under, and anticipate problems that are consequences of particular choices.) or against external reference points such as: (talk to clients, colleagues, experts, "workers in the system", available literature and other data sources).

Judge

• Make judgment of our decision whether what we do, what we ignore, what we want to research further.

Dimension four: Dispositions

This dimension describes personal qualities categorized in Fig. 1(d) which affect entry into a thinking mode. These elements are observed in the context of statistical problem solving.

Curiosity and Awareness

• Statistician Peter Mullins stressed the importance of "noticing variation and wondering why" for generating ideas for improving processes and service provision.
• This lead to engagement.

Engagement

• Background knowledge helps-it is hard to be interested in something one knows nothing about.

Imagination

• Imagination is viewing a situation from different perspectives, and generating possible explanations or confounding explanations for phenomena and features of data.

Scepticism

• Scepticism involves actions such as looking out for logical and factual flaws when receiving new ideas and information.
• Scepticism here was basically targeted towards, "Are the conclusions reached justified?". For example, "worry questions" concerning the appropriateness of the measurements taken, the appropriateness of the study design, the quality of the data, the suitability of the method of analysis, and whether the conclusions are really supported by the data.

Being logical

• Being logical ensure a valid conclusion. To be useful, scepticism must be supported by an ability to reason from assumptions or information to implications that can be checked against data.

A propensity to seek deeper meaning

• Always be prepared to dig a little deeper into issues by being open to new ideas as it helps to register and consider new ideas and information that conflict with our own assumptions and perseverance is self-evident.