
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)

Knowledge: arrange, define, duplicate, label, list, memorize,
name, order, recognize, relate, recall, repeat, reproduce, state.
 Comprehension:
classify, describe, discuss, explain, express, identify, indicate,
locate, recognize, report, restate, review, select, translate.

Application: apply, choose, demonstrate, dramatize, employ, illustrate,
interpret, operate, practice, schedule, sketch, solve, use, write.

Analysis: analyze, appraise, calculate, categorize, compare, contrast,
criticize, differentiate, discriminate, distinguish, examine,
experiment, question, test.
 Synthesis:
arrange, assemble, collect, compose, construct, create, design,
develop, formulate, manage, organize, plan, prepare, propose,
set up, write.
 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), 181185.
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),202210.
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.
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Orlandi,
L. R. (1971). Evaluation ofleaming in secondary school social studies.
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Ormell,
C. P. (1974). Bloom's taxonomy and the objectives of education.
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D. C., & Kelly, M. E. (1975). Hierarchical theories of development
in education and psychology. Harvard Educational Review, 45,351375.
Poole,
R. L. (1971). Characteristics of the taxonomy of educational objectives:
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Poole.
R. L. (1972). Characteristics of the taxonomy of educational objectives:
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Rumsey,
D. J. (2002) Statistical Literacy as a Goal for Introductory Statistics
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Sax,
G., Eilenberg, E. G., & Klockars, A. J. (1972). Achievement
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G. M. (1978). The properties of Bloom's taxonomy of educational
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