Author

Byron Douglas Butt

Title

Bias in Statistics

Grade Level

Junior High – grade 7 or 8

Subject Area

Mathematics

Overview of unit/lessons/activities (assumptions of prior knowledge/learning)

Students in grade 7 and 8 work on outcomes related to data management.  The development of surveys, collection of data, display of data using circle graphs, histograms, box and whisker plots, and scatter plots, as well as the analysis of such data that is collected. 

Although in grade 7 it is a good idea to begin with hand drawn data displays, a more polished approach would be to use Microsoft Excel or Appleworks 6.0.  In fact we use these programs as enrichment in grade 7 and as a core component of the grade 8 curriculum.

Students may also use such programs as Inspiration or Writer’s Companion to plan their survey projects and a word processor such as Microsoft Word or Appleworks or Star Office to design the final product.

Students may use the Internet to do webquests, searching for survey project ideas, use Stats Can as a resource, etc…

Students may use PowerPoint to develop class presentations on how to design a proper data display.

Digital Video (IMovie / IDVD) may be used to design “math movies” that students design to demonstrate an understanding of a particular concept such as “range”, “mean average”, “median average”, or “mode average”.

Correlations to ICT and curriculum outcomes

Gr. 7 Math Outcomes: F1             communicate through example the distinction between biased and unbiassed sampling, and first- and second-hand data

                                    F3                select, defend, and use appropriate data collection methods and evaluate issues to be considered when collecting data

ICT Outcomes:          SEHI 9.3      understand, model, and assume personal responsibility for the acceptable use of copyrighted and other information resources

                                    PTS 9.5      develop multimedia presentations, based on sound principles of design, with increasing confidence,  efficiency and independence

                                    RPSD 9.1   select appropriate measuring and recording devices and/or software to collect data, discover patterns of change over time, solve problems and  make logical decisions based on their investigations; with teacher assistance

                                    RPSD 9.2   create and use electronic charts, maps, tables, graphs, spreadsheets, and databases to collect, analyse and display data independently

                                    RPSD 9.9   accurately and independently cite information sources

Projected timeline for preparation and for carrying out activities

1-2 class periods – used in the collection of information through a web based research assignment.  Students may develop good copy (either on paper or using the computer) at home or at school (if required).

Equipment Requirements: (computers, software, etc)

Computer with access to the Internet
Word processor such as Microsoft Word or Appleworks
Presentation software such as PowerPoint

Teaching materials provided (Blacklines, worksheets, templates, teacher materials)

Assignment sheet provided with rubric: (Word format) (pdf format)

Resources available for teacher/student use (websites, references, etc)

The following websites are available to students for information in order to get started. These links are given on the student assignment sheet also.

http://www.media-awareness.ca
http://mathforum.org/dr.math/
http://en.wikipedia.org/wiki/Bias_(statistics)
http://open-encyclopedia.com/Bias_(statistics)
http://skepdic.com/control.html

A document which gives links to various sites with more information about data management and the importance of statistical bias is also available. 

Bias websites: (Word format) (pdf format)

Detailed instructions for each activity or lesson (teacher notes, activity information, learning strategies, teacher role, student roles)

Instructions:  In this assignment you will learn about the term “bias” in statistical sampling and will research some issues to be considered when collecting and reporting data. You should develop your own explanations of sources of bias in statistical sampling, with examples to show your understanding. Focus on finding explanations for the terms and clear descriptions of the issues.

See student assignment sheet for more detail.   (Word format) (pdf format)

Student products expected

Choose one of the following options:

written report (1-2 pages)
PowerPoint presentation (4-5 slides)
illustrated story (cartoon-style)
brochure with illustrations

Samples (include teacher notes, assessment information, student work if available)

From Wikipedia, the free encyclopedia. (http://en.wikipedia.org)

In statistics, the term bias is used for two different concepts. A biased sample is a statistical sample in which members of the statistical population are not equally likely to be chosen. A biased estimator is one that for some reason on average over- or underestimates the quantity that is being estimated.

While the term bias sounds pejorative, it is not necessarily used in that way in statistics. A biased sample is always bad, but biased estimators may be bad or good depending on the situation.

Biased sample

A sample is biased if some members of the population are more likely to be chosen in the sample than others. A biased sample will generally give you a misestimate of the quantity being estimated. For example, if your sample contains member with a higher or lower value of the quantity being estimated, the outcome will be higher or lower than the true value.

A famous case of what can go wrong when using a biased sample is found in the 1936 US presidential election polls. The Literary Digest held a poll that forecast that Alfred M. Landon would defeat Franklin Delano Roosevelt by 57% to 43%. George Gallup, using a much smaller sample (300,000 rather than 2,000,000), predicted Roosevelt would win, and he was right. What went wrong with the Literary Digest poll? They had used lists of telephone and automobile owners to select their sample. In those days, these were luxuries, so their sample consisted mainly of middle- and upper-class citizens. These voted in majority for Landon, but the lower classes voted for Roosevelt. Because their sample was biased towards wealthier citizens, their result was incorrect.

Logistics (organization, grouping, management issues, access to technology)

Students will require access to the internet, either at home or in school.

This is an independent activity, although they could work in pairs, if necessary..

Support should be given to those students on modified learning plans – Use of “Write Out Loud” would be useful in developing the final product. Some aid in reading will be required for those students who have difficulties.

Assessment information (e.g., rubrics for products and/or process)

See Assessment Rubric: (Word format) (pdf format)

Possible extensions

Compare and contrast biasness in the media with statistical biasness.

Provide a series of situations and allow students to decide whether biasness is found in the situation.