Bill Navidi Colorado School of Mines THE BOTTOM LINE: WHAT’S ESSENTIAL IN AN ELEMENTARY STATISTICS...

Bill NavidiColorado School of Mines

THE BOTTOM LINE:

WHAT’S ESSENTIAL IN AN ELEMENTARY STATISTICS COURSE

Barry MonkMiddle Georgia State College

Don BrownMiddle Georgia State College

HISTORICAL PERSPECTIVE AND GROWTH OF ELEMENTARY

STATISTICS

1925 Statistical Methods for Research Workers R.A. Fisher

Aimed at practicing scientists 1937 Statistical Methods

George Snedecor

Aimed at prospective scientists still working on degrees

1961 Probability with Statistical Applications Moste l ler , Rourke, & Thomas

Aimed at the broader academic curriculum

70’s-present Data RevolutionAnalysis of data as an independent subjectTechnology

STATISTICS IN THE PAST

GROWTH (AP STATISTICS EXAMINEES)

AP Statistics ExamineesYear Students1997 7,6671998 15,4861999 25,2402000 34,1182001 41,0342002 49,8242003 58,2302004 65,8782005 76,7862006 88,2372007 98,0332008 108,2842009 116,8762010 109,6092011 120,1282012 152,750

1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 20120

20000

40000

60000

80000

100000

120000

140000

160000

180000

Students

Taught across many disciplines and departments

Students have vastly diff erent backgrounds and goals

Active learning Increased use of web resourcesVaried uses of technologyEmphasis on statistical literacy

MODERN ELEMENTARY STATISTICS

GAISE RecommendationsEmphasize statistical literacy and

develop statistical thinking.Use real data.Stress conceptual understanding,

rather than mere knowledge of procedures.

Foster active learning in the classroom.Use technology for developing

concepts and analyzing data.Use assessments to improve and

evaluate student learning.

COMMON APPROACHES TO TEACHING ELEMENTARY

STATISTICS

A fi rst Statistics course generally includes the following content areas:

SamplingDescriptive StatisticsProbability Inferential Statistics

APPROACH

Descriptive Statistics

Sampling ProbabilityInferential Statistics

The topics covered in each of these areas and the amount of time spent on may diff er depending on educational needs or curricular objectives. Two factors that shape the course approach are:

Balance between probability and statisticsExtent to which technology is included

APPROACH


Sampling ProbabilityInferential Statistics

Sampling Types of Samples Types of Data Design of Experiments Bias in Studies

Descriptive Statistics Graphical Displays of Data Measures of Center Measures of Spread Measures of Position

Probability Basic Ideas & Terminology Addition Rule Conditional Probability &

Multiplication Rule

Counting techniques Random Variables

Binomial Distribution Poisson Distribution Normal Distribution

Inferential Statistics Sampling Distributions and The

Central Limit Theorem Confi dence Intervals

Population Mean Population Proportion

Hypothesis Testing Population Mean Population Proportion

MAINSTREAM ONE-SEMESTER STATISTICS COURSE

LIGHT PROBABILITY APPROACH



Sampling Probability Inferential Statistics



Probability Basic Ideas & Terminology Addition Rule* Conditional Probability &

Multiplication Rule

Counting techniques* Random Variables







LIMITED PROBABILITY APPROACH



Sampling

Pro

babili

ty

Inferential Statistics




Multiplication Rule







MAINSTREAM ONE-SEMESTER STATISTICS COURSE




Multiplication Rule










Probability Basic Ideas & Terminology

Normal Distribution Inferential Statistics

Sampling Distributions and The




Leaves time for additional topics: Regression Two Sample Inferences Tests with Qualitative Data Analysis of Variance


A vocabulary test was given to elementary school children in grades 1 through 6.

There was a positive correlation between the childrens’ test scores and their shoe sizes.

Does learning new words make your feet grow?

CORRELATION IS NOT CAUSATION

In a study of weightlifters, the least-squares regression line was computed for predicting the amount the weightlifter could lift (y) from his weight (x).

The line was y = 50 + 0.6x.

Joe is a weightlifter. He figures that if he gains 10 pounds, he will be able to lift 6 pounds more.

CORRELATION IS NOT CAUSATION

Each student tosses a coin 50 times and records the number of heads.

Students who toss the most heads are praised

Students who toss few heads are criticized for not being good at tossing heads

Message: Much variation in workplace performance is due to chance

NOTIONS ABOUT COIN TOSSING

Adapted from Red Bead Experiment – W.E. Deming

A probabilist and a statistician encounter a game of craps for the fi rst time. Can you tell which is which?

PROBABILITY VS. STATISTICS

Six-sided dice? Assuming that each face

comes up with probability 1/6, I can figure out what my

chances are of winning.

Those dice may look OK, but how do I know

they’re not loaded? I’ll watch for a while and

keep track of how often each number comes up.

Adapted from Calculated Bets: Computers, Gambling, and Mathematical Modeling to Win - Steven Skiena

What factors should be considered when weighing the balance between probability and statistics?

What trade-off’s are involved?

QUESTIONS

GENERAL CONSIDERATIONS (OR GEE-WHIZ – I’M REALLY

BEHIND!)

Light treatment or potential omission of:Frequency PolygonsOgivesStem-and-Leaf PlotsComputation of percentiles*Five-Number SummaryBoxplotsChebyshev’s InequalityComputation of standard deviation of discrete probability distribution

*Computation given light treatment, but the concept should be covered

GEE-WHIZ, I’M REALLY BEHIND!

TECHNOLOGY CONSIDERATIONS

To what degree should technology be used to: Construct graphical displays of data

Should the focus be on the construction of the display or the interpretation? Compute descriptive statistics

How much computation should students do to build intuition Determine the area under a curve

Table vs. Technology What are the advantages/disadvantages of each?

Construct confidence intervals and perform hypothesis tests Technology implies P-value approach

TECHNOLOGY CONSIDERATIONS

Critical value approach Only tells whether a test statistic is

unusual or not Generally easier if using tables

CRITICAL VALUE VS. P-VALUE

P-value approach Tells exactly how unusual a test

statistic is Generally easier if using technology

Where should the line be drawn between “by hand” calculations and technology?

What kind of technology should be used and why? Is there a particular advantage to one type of technology over another?

QUESTIONS

Historically, inference begins with sample means. With technology, the case where is known is less important and rarely used.

Is it necessary to cover the known case for conceptual reasons?

It may be diffi cult to begin with the t-distribution, so what about beginning with proportions?

QUESTIONS

Bill NavidiColorado School of Mines

THE BOTTOM LINE:

WHAT’S ESSENTIAL IN AN ELEMENTARY STATISTICS COURSE

Barry MonkMidd le Georg ia State Co l lege

Don BrownMidd le Georg ia State Co l lege

Thank you

Bill Navidi Colorado School of Mines THE BOTTOM LINE: WHAT’S ESSENTIAL IN AN ELEMENTARY STATISTICS...

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