Content Standards and Rubrics for Introductory Statistics

Introduction to Statistical Analysis is an introduction to techniques used in descriptive and inferential statistics. Our section emphasizes starting with the data and context, and learning to choose and use appropriate techniques as needed within that context. Writing, communication and critical thinking are also stressed. The Content Standards for the course are integrated into the tasks (and accompanying assessment rubrics) and supported by appropriate technology, all described below.

Content Standards

    STANDARD 1: Students will be able to critically evaluate statistics in the media and in their major field of interest.
    Indicators for Standard 1 include:

           Indicator 1.1: Locating several sources of introductory-level statistics in the media and in one's
           major field of interest.

           Indicator 1.2: Identifying and critiquing ambiguous or misleading statistical language.

           Indicator 1.3: Making appropriate inferences from numerical and graphical summaries, and
           identifying when they are ambiguous, misleading, or impossible.

           Indicator 1.4: Assessing soundness of reported results or methodology, and recognizing the
           extent to which this can be done with the information provided.

           Indicator 1.5: Identifying results as statistically significant and/or practically significant.

           Indicator 1.6: Demonstrating awareness of popular misconceptions involving concepts such as
           variability, aggregation, causation, correlation, sampling, independence, bias, randomness,
           probabilities and regression to the mean.

    STANDARD 2: Students will be able to plan, implement and communicate the results of a real-world data analysis to investigate an appropriate hypothesis they have generated.
    Indicators for Standard 2 include:

            Indicator 2.1: Selecting a problem or question of interest and identifying an appropriate procedure,
            hypothesis, sampling procedure, sample size, instrument, statistical test.
     
            Indicator 2.2: Identifying and applying any applicable ethical considerations BEFORE data are collected.

            Indicator 2.3: Appropriately collecting, "cleaning up", coding/transforming, and summarizing the data
            collected.

            Indicator 2.4: Analyzing the data collected with appropriate tools and computing relevant descriptive
            and inferential statistics.

            Indicator 2.5: Interpreting the results in both statistical and practical terms, discussing any statistical and
            nonstatistical sources of error.

            Indicator 2.6: Communicating the results professionally (primarily in self-contained write-ups with tables
            and graphs, but ideally also including small-group and whole-class oral presentations).

    NOTE: Standard 2 is similar to #3 of Colorado Model Mathematics Content Standards; Standards 1 and 2 turned out to be very similar to standards articulated on p. 39 of in the 1997 IOS Press publication (I.Gal and J.Garfield, Eds.)The Assessment Challenge in Statistics Education)

Tasks (and their connections to the Standards):
QUIZZES: Quizzes are periodically given in class to reinforce material from the textbook or class activities and support various elements of Content Standard #1 and Content Standard #2. They are not always announced in advance, so be in the habit of bringing your calculator, book and notes to each class. Quizzes are designed to be assessment tools, not high pressure grade competitions, and are structured so that they can only help your grade in the course. Many quizzes will be designated to be completed by teams.

LABS: After an ungraded "introduction to the technology" lab, we are currently scheduled to have a lab on each of several topics.  These labs incorporate teamwork and technology to develop understanding of statistical concepts and to develop tools for realizing Content Standard #2.

PROJECT #1 (STATISTICS IN THE MEDIA): This project strongly supports course Content Standard #1 as it provides you a variety of opportunities to find, analyze and critique examples of statistics that are common in the mass media and/or your field of interest.

PROJECT #2 (ANALYSIS OF SELF-COLLECTED DATA): This project supports Course Standard #2 and allows you to put together most of the tools you have learned throughout the course as you identify an appropriate question of interest to you, formulate a testable hypothesis, plan and implement a data collection procedure, analyze the results and complete a full writeup. There will be checkpoints long before the project deadline to ensure you are on pace with a project that is manageable and within stated ethics guidelines.

FINAL: The 2.5 hour final exam will be held on the day and time scheduled by the Schedule of Classes (see short syllabus). Like life, it is cumulative, and has questions on it that support Standard #1 and Standard #2. Questions will reflect the diversity of types of assessments (labs, quizzes, projects) from the course, emphasizing real-life contextual interpretation and conceptual understanding over mathematical derivations, long calculations or reciting definitions. You will be allowed to use your textbook, class notes, returned assignments, calculator. The extent to which computers will be available will be announced well in advance. So, memorization should not be a factor and the length of the test will be such that time should not be a factor either!

Grading percentages specified in POLICIES; specific combination or application of assessment rubrics are specified when the assignment is passed out.The instructor reserves the right to modify the assignments, or number of assignments if necessary, but would announce any such changes well in advance.

RUBRICS

The following are Analytic Rubric Families that will be applied in various combinations to score certain assignments or writeups. Rubrics not only are a more dimensional, more meaningful, and less instructor-dependent description of student work than a letter grade, but also allow for specific areas of improvement to be identified and tracked over future work.(Even if time constraints force a less detailed application of these rubrics, it is still helpful to know what explicit criteria are being considered to assess overall quality of work.)

The exact combination of rubrics that will be used will be specified at the time the assignment is made as well as the method used to convert ratings of "Exceeds (expectations)", "Meets (expectations)" and "In Progress" into points, so that students will also be able to calculate "traditional grade equivalents". (Sample combinations appear below, however.) A very rough rule of thumb is to equate Exceeds with outstanding high A work, Meets with acceptably competent middle B work, and In Progress with work that might range from low C to F. N/A means "not applicable," as not all criteria have three levels.

Work Ethic/Ethics

Communication

Tool Usage

Interpretation and Critical Evaluation

WORK ETHIC / ETHICS Rubric:
CRITERION In Progress Meets Exceeds
punctuality not turned in by deadline, but not late by more than 3 calendar days (see Policies on LateWork) on time N/A
completeness no more than 10% of assignment omitted, incomplete or filled with answers to unassigned questions (if more than 10%, the total score for the assignment will be multiplied by the proportion of work completed) all parts completed N/A
ethics one or more of the following (serious violations may incur additional consequences):

stated ethics guidelines on data collection not followed;

data are "mined" (analyzed selectively) in misleading manner;

nonrandom data collection is represented as random;

missing reference citations

 data collected with no more than a superficial deviation from stated ethics guidelines

AND

references are cited, but perhaps not fully

 data collected according to ethics guidelines; AND

data collected and/or analyzed in reasonably objective and open fashion AND

appropriate citation of any references
COMMUNICATION Rubric:
CRITERION In Progress Meets Exceeds
clarity imprecise distinction between lay & statistical usage

AND/OR

misleading, unlabeled or inappropriately sized tables/graphs/axes/units; or unidentified variables in formulas

 no major instances and no more than two minor instances of "In Progress" items procedures, writing & visuals are clear and could be understood by someone not in our class
professional appearance one or more of the following:

writeup appears disorganized or sloppy;

seriously distracting spelling, diction, grammar; tone inapproprate tone or level of formality for reader

inappropriate inclusion, omission or appending of output

 neatly done, but reads like list of HW answers

AND/OR

some errors in spelling, diction, grammar; flow of paper may be choppy at times

 "camera-ready", well-integrated, self-contained writeup with solid writing that "flows";

judicious inclusion and integration of output; detail and balance of prose, tables, graphs appropriate for reader
oral communication
 one or more of the following: distracting posture; not enough vocal projection or inflection; talk "read" to us; undue minimization or maximization of findings; poor sense of time awareness handouts or A/V materials are easy to read, time limits followed; talk is not "read"; background info provided appropriately; body position appropriate in relation to visuals creative and effective use of any handouts, A/V materials or equipment; awareness of and connection with audience; encourages/handles questions from audience
TOOL USAGE Rubric:
CRITERION In Progress Meets Exceeds
appropriate choices (of technology, formula, table, protocol, etc.) for task several ineffective choices made nearly all choices effective; some may be inefficient all choices effective and efficient; perhaps some elegant or innovative, too!
reasonable answers obtained and explained includes one or more unrealistic, irrelevant, omitted, inconsistent or impossible answers without awareness that they are such answers

AND/OR

insufficient or no attempt at explaining answers or resolving known inconsistencies

 reasonable answers obtained, but explanation lacks sufficient concrete context (including assumptions, procedures, variables, and units used)

AND/OR

only minor errors in answer

inconsistencies are at least noted as such (with fair attempt to reconcile)

 answers are error-free and/or show great insight!

AND

prose summary of answer in concrete terms in context
INTERPRETATION AND CRITICAL EVALUATION Rubric:
CRITERION In Progress Meets Exceeds
hypotheses hypotheses described are inconsistent,untestable or vague

AND/OR

confusion between null and alternative hypotheses

 no more than a couple of minor refinements short of "Exceeds" description hypotheses described in clear & precise language

AND

variables operationally defined so that it is clear what type of statistical test and data are needed to test the hypothesis

AND

distinction between null and alternative hypotheses is clear
critical thinking analysis has major errors or omissions and/or is largely superficial (i.e., at knowledge level of Bloom's taxonomy) and out-of-context analysis is basically sound and is within the comprehension, application and analysis levels of Bloom's taxonomy analysis also includes the synthesis and evaluation levels of Bloom's taxonomy, showing the ability to make defensible informed judgments with a "big picture" (i.e., executive summary) view; clear distinctions are made between "objective" facts and "evaluative judgments"
conclusions inconsistent or not adequately supported by the data analysis

AND/OR

not interpreted accurately at even a basic level

 conclusions are supported by the data and interpreted accurately at a basic level meaningfully and insightfully interpreted in context; includes reflection on any assumptions, outliers and sources of error

Sample Rubric Combinations (criteria and point values) for assignments:

LAB: punctuality(8,14,X), completeness(8,14,X), clarity(8,14,18), professional appearance(8,14,18), appropriate choices(8,14,18), reasonable answers obtained/explained(8,14,18)

MEDIA PROJECT: punctuality(5,10,X), completeness(5,10,X), clarity(8,13,15); professional appearance(8,13,15), critical thinking(26,43,50)

DATA PROJECT: punctuality(8,14,X), completeness(8,14,X), ethics(6,9,12), clarity(6,9,12), professional appearance(6,9,12), appropriate choices(6,9,12), hypotheses(6,9,12), conclusions(6,9,12); oral communication(1,2,3) is extra credit.

The Standards are supported by various forms of TECHNOLOGY, including:

1. Course webpage: A variety of information and resources is available on our course homepage (especially the Resources Page).

2. Lab Experiences with Data Analysis: The spreadsheet software package Excel will be available for you to perform computations and produce graphs and charts. This will enable you to analyze real-world data sets, not just artificially "nice" small ones that can be done by hand.

3. Writeups: In our lab room, Excel output can be readily pasted into a MSWord document, which can produce a self-contained writeup of your labs and projects.

4. Videos with On-location vignettes: The video series "Against All Odds: Inside Statistics" is broadcast on PBS at regular times as well as available for viewing in the VIDEO/FILM area (basement level) of Michener Library. Browse the descriptions of these videos and you will find one corresponding to any major topic in our textbook.