This section will cover basic statistical concepts like concept of variation, central limit theorem, hypothesis testing etc. which are essential for use of statistical tools. Proposed topics for book may be seen from the taxonomy of topic.
The term "Statistical Thinking" came in discussions with the evolution of computational power. Earlier it was a common assumption that the use of available statistical power gets limited by the horizon of computation.
This myth was broken after a lot more computational capability was achieved. It became clear that lack of statistical thinking is the main obstacle in the using statistics to its full potential. In fact, it was realized that statistical thinking provides a sound philosophical framework for using statistical methods in correct prospective.
Although term Statistical Thinking seems to be related with whatever we do in name of Statistics, but it has specific meaning which got attention in nineties. This newer meaning was discussed by Snee (1990) and Moor (1990). This manner of thinking was further promoted by the Statistics Division of the American Society for Quality (ASQ) in 1994 when they set a goal to “enable broad application of statistical thinking” see Torback (2001).
Although origin of concept of Statistical Thinking has been attributed to field of quality control (which is based on interconnected processes), now it is being used in many areas like medical, market research etc. Especially field of Teaching of Statistics gave more place to this concept.
Following are key points of Statistical Thinking
These concepts are in context of quality control. For giving it a broader meaning so that concept of Statistical Thinking may be generalized, it is reshaped by use of following concepts (see Wild and Pfannkuch)
On this site, concept of Statistical Thinking has been used in more broader sense by keeping its original spirit intact. For our purposes (to use statistical thinking in other area than engineering), concept of Statistical Thinking is based on following components
Given diagram represents how `Statistical Thinking’ may be perceived to accommodate current need.
Whenever we compare two sets of data, like income of people of two different geographical regions, generally emphasis given to comparing center of data for both area, without considering variation in data. In such situation, misleading results may be obtained. Through example and diagrams, Chris Wild and others has presented how one may get misleading view of reality and how variation should be incorporated in comparing two groups (in later part of article).
Curtsy to rktyagi
It is difficult to get feeling of variation in comparison of center of data. Even for getting feeling of center, median is more difficult to visualize in comparison of average. For giving better feeling of data, different scatter plots of data should be shown and students should identify groups in terms of `less- more’. Teacher can judge sensitivity of students towards variation for different type of tools used for Measuring Variation (see ..)
Latter on plot (scatter) mixture data of two or three type of groups and ask possible number of groups.
Five types of thinking that are considered as fundamental elements in Statistical Thinking are: recognition of the need for data, trans numeration, consideration of variation, reasoning with statistical models, and integrating the statistical with the contextual.
Are there particular ways of teaching that can elicit such thinking? How does the teacher draw students’ attention to notice and to attend to this thinking? How is such a habit of thinking communicated in a curriculum document?
Some teaching tips for Teaching of Statistical Thinking may be obtained from note by Maxine Pfannukch
Pedagogical issues concerned with Statistical Thinking is in not matured yet, a framework based on three core issue may be considered- (1) The teachers and the researcher need to come to a common consensus of what they mean by the term statistical thinking and thus be able to communicate. (2) The teachers need to reflect critically on their current teaching and identify areas which are acting as barriers to the development of their students statistical thinking. (3) The constraints that are imposed externally on teaching need to be recognized and acknowledged. In this regard, one can get help from case study by Maxine Pfannukch and Chris Wild.
It is difficult to calculate variation in categorical data (see Data Type). Tools to measure variation of Ratio Scale or Interval Scale data (see Data Type) cannot be applied for categorical data. Various type of diversity measure (see Measurement of Variation) like Entropy Measure may be used for purpose.
Snee, R. (1990). Statistical Thinking and its Contribution to Quality. The American Statistician, 44(2), 116-121
Moore, D. (1990). Uncertainty. In L. Steen (Ed.) On the shoulders of giants: new approaches to numeracy (pp. 95-137). Washington, D.C.: National Academy Press
Torback, L.D. (2001). Statistical Thinking, Pharmaceutical Technology,( Link http://pharmtech.findpharma.com/pharmtech/data/articlestandard//pharmtech/252002/22855/article.pdf )
Wild, C. and M. Pfannkuch, What Is Statistical Thinking? (Link http://icots6.haifa.ac.il/download_documents/word_documents/icots6_sample_paper_1.doc
New approach of teaching: This note tries to give a picture how course based on Statistical Thinking may be different from old one.
Using Statistical Thinking in Plant: 20 slides gives outline of statistical thinking applied to different area (managerial, sales, strategic etc.) of plant. Here it is important that such process was used by production system only. How outline presented here can be used in type of statistical is subject of discussion.
Statistical Thinking in Technological Environment: This is chapter in book Research on the Role of Teaching and Learning of Statistics. This edited book (procceddings of 1996 IASE round table conference) gives guidelines for new direction of statistics for different level of education.
Most of time for dealing with uncertainty we want to understand causality associated with some pattern. Statistical tools are used to measure it and how to discover it. Understanding causality with statistical point of view is one of biggest challenge particularly in area of social sciences where experiments are often impossible and observational studies are the norm. Yet in introductory statistics correlation and coefficient of determination are discussed for dealing causality. Most of time we use the phrase “correlation is not causality." This denial makes interpretation of results through statistical tool more complex because our causality is deep rooted way of interpretation for understanding uncertainty. To better satisfy the interests of user of statistics we must emphasize causality more in teaching statistics. There are many things that can be taught about causality that are not discipline specific. Students should be taught how to detect the causal connotations of words and phrases. Students must be taught to be proactive in seeking alternative explanations for differences, ratios and correlations in observational studies. Students must be taught the causal differences between description, prediction and explanation. Statistics should be expanded to include causality in ways that are discipline independent and professionally appropriate. For understanding causality we can see http://en.wikipedia.org/wiki/Causality