CAUSE WebinarTuesday, Dec. 11th, 2007

"Content Barriers to Effective Pedagogy in the Introductory

Statistics Course"

Mark L. BerensonMontclair State University

Webinar Abstract

• As we consider how we might improve our introductory statistics course we are constrained by a variety of environmental/logistical and pedagogical issues that must be addressed if we want our students to complete the course saying it was useful, relevant and practical.

• If not properly addressed, such issues may result in the course being considered unsatisfying and/or unnecessarily obtuse.

Webinar Goals

• This Webinar will focus on key course content concerns that must be addressed and will engage participants in discussing resolutions. Participants will also have the opportunity to describe and discuss other content barriers to effective statistical pedagogy.

Motivation

Before the semester, as we prepare to teach the introductory course again, we can “rethink”:

• What did we do last time?

• How did we do it?

• How can we do it better this time?

Issues to Contemplate

• Class size• Class homogeneity

– Students’ mathematical preparation– Students’ technological preparation

• Classroom capability– Computers– Doc Camera– Overhead projector– Clickers– Shape of room and seating

Other Considerations

• Course topics to be selected-Multi-section course with uniform syllabus?-Service course for other departments?

• Textbook to be selected-Classroom notation concordant with text notation?

• Computer software selected-Software is a tool?

Having a Goal and Keeping Your Eye on the Prize

• Regardless of how we decide to address the aforementioned issues, we will still be faced with various pedagogical dilemmas concerning course content (i.e., “Peck’s Gorillas”) that need to be thoroughly considered if we want our students to leave the course saying:

• It was useful, relevant and practical• It increased critical thinking and analytic skills• It increased communication skills

Content Barriers (“Peck’s Gorillas”)

1. Addressing Statistics Language Barrier

2. Choosing Software

3. Observing Bad vs Good Graphics

4. Presenting Tables of Z, t, F and

5. Teaching a Z-Test with Numerical Data

2

Addressing Statistics Language Barrier

• Bootstrapping • Collectively Exhaustive • Hinges• Multicollinearity• Point Biserial Correlation• Robust• Standard Normal Deviate

Bootstrapping

Collectively Exhaustive

Hinges

Multicollinearity

Point-biserial correlation

Robust

Standard Normal Deviates

Choosing Software

• Professional Package (JMP, Minitab or SPSS)

• Textbook Add-ons (PHStat)

• Microsoft Excel

• Hand-held Calculator

• “God-given” Calculator

Observing Bad & Good Graphics

Multiple Choice:Why does there seem to be a plethora of bad graphics shown in newspapers, magazines and reports?

A. There are no daVincis left. Artists are typically mathematically illiterate.

B. Artists and statisticians don’t seem to communicate.

C. A graph must attract attention to sell.

Bad Graph

Resource: The NEW YORK TIMES, Firday, April 20, 2007

Bad Graph

Bad Graph

• To enhance the learning process, students need to make connections quickly. The current textbooks fail to facilitate the learning process when presenting and demonstrating the use of statistical tables.

Presenting Tables of Z, t, F and

2

Z Table

Z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.090.0 0.5000 0.5040 0.508 0.5120 0.5160 0.5199 0.5239 0.5279 0.5319 0.53590.1 0.5398 0.5438 0.5478 0.5517 0.5557 0.5596 0.5636 0.5675 0.5714 0.57530.2 0.5793 0.5832 0.5871 0.5910 0.5948 0.5987 0.6026 0.6064 0.6103 0.61410.3 0.6179 0.6217 0.6255 0.6293 0.6331 0.6368 0.6406 0.6443 0.6480 0.65170.4 0.6554 0.6591 0.6628 0.6664 0.6700 0.6736 0.6772 0.6808 0.6844 0.6879

Cumulative probabilities

Z Table--Better

Z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.090.0 0.5000 0.5040 0.508 0.5120 0.5160 0.5199 0.5239 0.5279 0.5319 0.53590.1 0.5398 0.5438 0.5478 0.5517 0.5557 0.5596 0.5636 0.5675 0.5714 0.57530.2 0.5793 0.5832 0.5871 0.5910 0.5948 0.5987 0.6026 0.6064 0.6103 0.61410.3 0.6179 0.6217 0.6255 0.6293 0.6331 0.6368 0.6406 0.6443 0.6480 0.65170.4 0.6554 0.6591 0.6628 0.6664 0.6700 0.6736 0.6772 0.6808 0.6844 0.6879

Cumulative probabilities

T Table

df 0.25 0.1 0.05 0.025 0.01 0.0051 1 3.0777 6.3138 12.7062 31.8207 63.65742 0.8165 1.8856 2.9200 4.3027 6.9646 9.92483 0.7649 1.6377 2.3534 3.1824 4.5407 5.84094 0.7407 1.5332 2.1318 2.7764 3.7469 4.60415 0.7267 1.4759 2.0150 2.5706 3.3649 4.0322

Upper-Tail Areas

T Table--Better

0.75 0.9 0.95 0.975 0.99 0.995

df 0.25 0.1 0.05 0.025 0.01 0.0051 1 3.0777 6.3138 12.7062 31.8207 63.65742 0.8165 1.8856 2.9200 4.3027 6.9646 9.92483 0.7649 1.6377 2.3534 3.1824 4.5407 5.84094 0.7407 1.5332 2.1318 2.7764 3.7469 4.60415 0.7267 1.4759 2.0150 2.5706 3.3649 4.0322

Upper-Tail Areas

Cumulative Probabilities

Table

df

2

df 0.995 0.99 0.975 0.95 … 0.05 0.025 0.01 0.0051 0.001 0.004 … 3.841 5.024 6.635 7.8792 0.010 0.020 0.051 0.103 … 5.991 7.378 9.210 10.5973 0.072 0.115 0.216 0.352 … 7.815 9.348 11.345 12.8384 0.207 0.297 0.484 0.711 … 9.488 11.143 13.277 14.8605 0.412 0.554 0.831 1.145 … 11.071 12.833 15.086 16.750

Upper-Tail Areas

2 Table--Better

0.005 0.01 0.025 0.05 … 0.95 0.975 0.99 0.995

df 0.995 0.99 0.975 0.95 … 0.05 0.025 0.01 0.0051 0.001 0.004 … 3.841 5.024 6.635 7.8792 0.010 0.020 0.051 0.103 … 5.991 7.378 9.210 10.5973 0.072 0.115 0.216 0.352 … 7.815 9.348 11.345 12.8384 0.207 0.297 0.484 0.711 … 9.488 11.143 13.277 14.8605 0.412 0.554 0.831 1.145 … 11.071 12.833 15.086 16.750

Upper-Tail Areas

Cumulative Probabilities

F Table

Denominator, df2 1 2 3 4 … 120 INF 1 161.448 199.500 215.707 224.583 … 253.253 254.3142 18.513 19.000 19.164 19.247 … 19.487 19.4963 10.128 9.552 9.277 9.117 … 8.549 8.5264 7.709 6.944 6.591 6.388 … 5.658 5.628

NUMERATOR, df1Upper-Tail Areas = 0.05

F Table--Better

Denominator, df2 1 2 3 4 … 120 INF 1 161.448 199.500 215.707 224.583 … 253.253 254.3142 18.513 19.000 19.164 19.247 … 19.487 19.4963 10.128 9.552 9.277 9.117 … 8.549 8.5264 7.709 6.944 6.591 6.388 … 5.658 5.628

Cumulative Probabilities = 0.95Upper-Tail Areas = 0.05

NUMERATOR, df1

Teaching a Z-Test with Numerical Data

The Three Questions:

• 1-Why do we do it?

• 2-How do we do it?

• 3-How can we cover the topic better?

“Making the Teaching of Statistical Inference

More Effective in Business Schools”

Mark L. Berenson and Kimberly Killmer Hollister

(Presented at DSI, November 2007)

Change the Way Inference is Covered in the Texts

• Introductory statistics books must be made more practical. – Responsibility:

• Publishers/editors

• Authors

• Instructors

– Encourage authors to remove all end-of-section and all end-of-chapter exercises using "sigma known." 

• Such exercises cause problems by making the subject of statistical inference unrealistic.

• Such exercises cause problems by making the subject of statistical inference confusing. (How can we know “sigma” but not “mu”? ) 

The Root Causes of the Problem

• Background of faculty teaching statistics • Faculty with sufficient formal and practical training.• Faculty with insufficient formal and/or practical training.• Graduate students.

• Texts and software with inappropriate materials• Texts provide significance tests and confidence interval

estimates with “sigma known.” • Widely used software such as Microsoft Excel 2007 and

Minitab Version 14 provide significance tests and confidence interval estimates with “sigma known.”

Content Barrier to Teaching Inference

• Traditional textbook topic sequencing and follow-up classroom instruction lead to a confounding of “concepts and theory” with “practice” by weaker students, resulting in the mixing of applications requiring Z and t.

Moves to Change the Teaching of Introductory Statistical Inference

• Conover and Iman – for over 20 years have said teach it through a nonparametric/distribution- free approach instead of traditional normal theory approach.

• MSMESB – for the past 20 years have said “limit it if not eliminate it.”

• USCOTS/ASA Statistical Education – in recent years have said teach it through resampling techniques instead of traditional normal theory approach.

• Berenson and Killmer-Hollister – have been saying teach the traditional normal theory approach to business students from a more practical and realistic perspective by altering topic sequence and demonstrating actual inferential applications.