Defining and Distinguishing Statistical Literacy,
Statistical
Reasoning, and Statistical Thinking

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Definitions of Statistical Literacy, Statistical Reasoning, and Statistical Thinking
Examples of Assessment Items coded as Statistical Literacy, Reasoning, and Thinking
How Statistical Literacy, Reasoning, and Thinking are Related
How Statistical Literacy, Reasoning, and Thinking relate to Bloom’s and other taxonomies
Words that characterize assessment items for Statistical Literacy, Reasoning, and Thinking
   
Definitions of Statistical Literacy, Statistical Reasoning, and Statistical Thinking
  Statistical literacy
  Statistical literacy involves understanding and using the basic language and tools of statistics: knowing what statistical terms mean, understanding the use of statistical symbols, and recognizing and being able to interpret representations of data.
To read more about statistical literacy see Rumsey (2002).
   
  Statistical reasoning
 

Statistical reasoning is the way people reason with statistical ideas and make sense of statistical information. Statistical reasoning may involve connecting one concept to another (e.g., center and spread) or may combine ideas about data and chance. Reasoning means understanding and being able to explain statistical processes, and being able to fully interpret statistical results.
To read more about statistical reasoning see Garfield (2002).

   
  Statistical thinking
  Statistical thinking involves an understanding of why and how statistical investigations are conducted. This includes recognizing and understanding the entire investigative process (from question posing to data collection to choosing analyses to testing assumptions, etc.), understanding how models are used to simulate random phenomena, understanding how data are produced to estimate probabilities, recognizing how, when, and why existing inferential tools can be used, and being able to understand and utilize the context of a problem to plan and evaluate investigations and to draw conclusions.
To read more about statistical thinking see Chance (2002).
   
Examples of Assessment Items coded as Statistical Literacy, Reasoning, and Thinking
  Example of an item designed to measure statistical literacy:
  A random sample of 30 first year students was selected at a public university to estimate the average score on a mathematics placement test that the state mandates for all freshmen. The average score for the sample was found to be 81.7 with a sample standard deviation of 11.45. Explain to someone who has not studied statistics what the standard deviation tells you about the variability of placement scores for this sample.
   
  Example of an item designed to measure statistical reasoning:
 

The following stemplot displays the average annual snowfall amounts (in inches, with the stems being tens and leaves being ones) for a random sample of 25 American cities:

Without doing any calculations, would you expect the mean of the snowfall amounts to be larger, smaller, or about the same as the median? Why?

   
  Example of an item designed to measure statistical thinking:
 

A random sample of 30 first year students was selected at a public university to estimate the average score on a mathematics placement test that the state mandates for all freshmen. The average score for the sample was found to be 81.7 with a sample standard deviation of 11.45.

A psychology professor at a state college has read the results of the university study. The professor wants to know if students at his college are similar to students at the university with respect to their mathematics placement exam scores. This professor collects information for all 53 first year students enrolled this semester in a large section (321 students) of his "Introduction to Psychology" course. Based on this sample, he calculates a 95% confidence interval for the average mathematics placement scores exam to be 69.47 to 75.72. Below are two possible conclusions that the psychology professor might draw. For each conclusion, state whether it is valid or invalid. Explain your choice for both statements. Note that it is possible that neither conclusion is valid.


a. The average mathematics placement exam score for first year students at the state college is lower than the average mathematics placement exam score of first year students at the university.


b. The average mathematics placement exam score for the 53 students in this section is lower than the average mathematics placement exam score of first year students at the university.

   

How Statistical Literacy, Reasoning, and Thinking are Related
 

Although we define Statistical Literacy, Reasoning, and Thinking as three separate learning outcomes, we think they is some overlap between them. Figure 1, modified from delMas (2002), represents each domain as representing cognitive outcomes that are unique from the other two, although there is some overlap. This diagram also shows a type of hierarchy, with Statistical Literacy providing the foundation for Reasoning and Thinking.


FIGURE 1

   
How do Statistical Literary, Reasoning and Thinking compare to Bloom’s and other Taxonomies?
  This is a question we are often asked, along with, why didn’t we categorize our items according to the six levels of Bloom’s Taxonomy. Here’s our response.
   
  In order to help categorize different types of responses, both for research purposes and for assessment design, taxonomies have been created to describe hierarchies of cognitive learning outcomes. For example, Bloom's taxonomy (Table 1) has been utilized by assessment writers to help write items to assess a variety of levels of cognitive objectives. Despite its reputation and recognition, writers using this guide are often faced with the ambiguity of figuring out exactly how to use the taxonomy as they contextualize the cognitive objectives they want to assess. In addition, Bloom's taxonomy is fairly general, and several articles have pointed out problems and limitations (e.g. Stanley & Bolton, 1957; Cox, 1965, Poole, 1971, 1972; Fairbrother, 1975, Phillips & Kelly, 1975; Orlandi, 1971; Ormell, 1974, Sax, Eilenberg, & Klockars, 1972; Seddon, 1978).
   
  Specific guidelines within a discipline appear to be more useful then the six general categories in Bloom’s taxonomy. We have found that using statistical literacy, reasoning, and thinking to distinguish between desired learning outcomes in statistics is extremely helpful both in thinking about instructional goals as well as in writing assessment items.
These three statistics learning outcomes also seem to coincide somewhat with Bloom's more general categories. In particular, some current measurement experts feel that Bloom's taxonomy is best used if it is collapsed into three general levels (Knowing, Comprehending, and Applying). We see statistical literacy as consistent with the "knowing" category, statistical reasoning as consistent with the "comprehending” category (with perhaps some aspects of application and analysis) and statistical thinking as encompassing many elements of the top three levels of Bloom's taxonomy.
   
  We encourage statistics instructors to read our definitions of statistical literacy, reasoning, and thinking, read the related papers on this topic, and review our classification of items according to these categories. We have found these definitions to be very useful as we think about desired student learning outcomes and how to assess them, and we hope others will find them useful as well.
   
 

Table 1
Bloom’s Taxonomy (Bloom, 1956)

  1. Knowledge: arrange, define, duplicate, label, list, memorize, name, order, recognize, relate, recall, repeat, reproduce, state.
  2. Comprehension: classify, describe, discuss, explain, express, identify, indicate, locate, recognize, report, restate, review, select, translate.
  3. Application: apply, choose, demonstrate, dramatize, employ, illustrate, interpret, operate, practice, schedule, sketch, solve, use, write.
  4. Analysis: analyze, appraise, calculate, categorize, compare, contrast, criticize, differentiate, discriminate, distinguish, examine, experiment, question, test.
  5. Synthesis: arrange, assemble, collect, compose, construct, create, design, develop, formulate, manage, organize, plan, prepare, propose, set up, write.
  6. Evaluation: appraise, argue, assess, attach, choose compare, defend estimate, judge, predict, rate, score, select, support, value, evaluate.
   
Words that characterize assessment items for Statistical Literacy, Reasoning, and Thinking
  One way to distinguish between these related outcomes is by examining the types of words used in assessment of each outcome.
Table 2 (modified from delMas, 2002) lists words associated with different assessment items or tasks.
  Table 2
Words associated with assessment tasks
 
BASIC LITERACY
REASONING
THINKING

IDENTIFY
DESCRIBE
TRANSLATE
INTERPRET
READ
COMPUTE

EXPLAIN WHY
EXPLAIN HOW
APPLY
CRITIQUE
EVALUATE
GENERALIZE
   
References
 

Bloom B. S. (1956). Taxonomy of Educational Objectives, Handbook I: The Cognitive Domain. New York: David McKay Co Inc.

Chance, B. L. (2002) Components of Statistical Thinking and Implications for Instruction and Assessment" Journal of Statistics Education [Online], 10(3)
www.amstat.org/publications/jse/v10n3/chance.html

Cox, R. C. (1965). Item selection techniques and evaluation of instructional objectives. Journal of Educational Measurement, 2(2), 181-185.

delMas, Robert C. (2002). Statistical Literacy, Reasoning, and Learning: A Commentary. Journal of Statistics Education Volume 10, Number 3 (2002)
http://www.amstat.org/publications/jse/v10n3/delmas_discussion.html

Fairbrother, R. W. (1975). The reliability of teachers' judgment of the abilities being tested by multiple choice items. Educational Research, 17(3),202-210.

Garfield, J. (2002) The Challenge of Developing Statistical Reasoning" Journal of Statistics Education [Online], 10(3). www.amstat.org/publications/jse/v10n3/garfield.html

Guttman, L. (1953). Image theory for the structure of quantitative variates. Psychometrika, 18(4),277-296.

Orlandi, L. R. (1971). Evaluation ofleaming in secondary school social studies. In B. S. Bloom, J. T. Hastings, & G. Madaus (Eds.), Handbook onformative and summative evaluation of student learning. New York: McGraw Hill.

Ormell, C. P. (1974). Bloom's taxonomy and the objectives of education. Educational Research, 17,3-18.

Phillips, D. C., & Kelly, M. E. (1975). Hierarchical theories of development in education and psychology. Harvard Educational Review, 45,351-375.

Poole, R. L. (1971). Characteristics of the taxonomy of educational objectives: Cognitive domain. Psychology in the Schools, 8,379-385.

Poole. R. L. (1972). Characteristics of the taxonomy of educational objectives: Cognitive domain--A replication. Psychology in the Schools, 9, 83-88.

Rumsey, D. J. (2002) Statistical Literacy as a Goal for Introductory Statistics Courses" Journal of Statistics Education [Online], 10(3). www.amstat.org/publications/jse/v10n3/rumsey2.html

Sax, G., Eilenberg, E. G., & Klockars, A. J. (1972). Achievement as a function of test item complexity and difficulty. Journal of Educational Psychology, J 6, 89-103.

Seddon, G. M. (1978). The properties of Bloom's taxonomy of educational objectives for the cognitive domain. Review of Educational Research, 48(2),303-323.

Stanley, J. C., & Bolton, D. T. (1957). A review of Bloom's "Taxonomy of educational objectives" and J. R. Gerberick's "Specimen objective test items, a guide to achievement test construction." Educational and Psychological Measurement, J 7, 631-634.

Copyright 2006 by the Regents of the University of Minnesota. The University of Minnesota is an equal opportunity educator and employer. This page is subject to change without notice. Last modified: June 9, 2006. For questions or comments, contact Bob delMas at delma001@umn.edu