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# Bill Navidi Colorado School of Mines THE BOTTOM LINE: WHAT’S ESSENTIAL IN AN ELEMENTARY STATISTICS COURSE Barry Monk Middle Georgia State College Don Brown.

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Bill Navidi Colorado School of Mines THE BOTTOM LINE: WHAT’S ESSENTIAL IN AN ELEMENTARY STATISTICS COURSE Barry Monk Middle Georgia State College Don Brown Middle 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 Mosteller, Rourke, & Thomas  Aimed at the broader academic curriculum  70’s-present Data Revolution  Analysis of data as an independent subject  Technology STATISTICS IN THE PAST

GROWTH (AP STATISTICS EXAMINEES) AP Statistics Examinees YearStudents 19977,667 199815,486 199925,240 200034,118 200141,034 200249,824 200358,230 200465,878 200576,786 200688,237 200798,033 2008108,284 2009116,876 2010109,609 2011120,128 2012152,750

 Taught across many disciplines and departments  Students have vastly different backgrounds and goals  Active learning  Increased use of web resources  Varied uses of technology  Emphasis on statistical literacy MODERN ELEMENTARY STATISTICS GAISE Recommendations  Emphasize 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 first Statistics course generally includes the following content areas:  Sampling  Descriptive Statistics  Probability  Inferential Statistics APPROACH Descriptive Statistics SamplingProbability Inferential Statistics

The topics covered in each of these areas and the amount of time spent on may differ depending on educational needs or curricular objectives. Two factors that shape the course approach are:  Balance between probability and statistics  Extent to which technology is included APPROACH Descriptive Statistics SamplingProbability Inferential 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  Confidence Intervals  Population Mean  Population Proportion  Hypothesis Testing  Population Mean  Population Proportion MAINSTREAM ONE-SEMESTER STATISTICS COURSE

LIGHT PROBABILITY APPROACH

Descriptive Statistics Sampling Probability Inferential 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  Confidence Intervals  Population Mean  Population Proportion  Hypothesis Testing  Population Mean  Population Proportion LIGHT PROBABILITY APPROACH

LIMITED PROBABILITY APPROACH

Descriptive StatisticsSampling Probability Inferential 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  Confidence Intervals  Population Mean  Population Proportion  Hypothesis Testing  Population Mean  Population Proportion MAINSTREAM ONE-SEMESTER STATISTICS COURSE

 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  Confidence Intervals  Population Mean  Population Proportion  Hypothesis Testing  Population Mean  Population Proportion LIMITED PROBABILITY APPROACH

 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  Normal Distribution  Inferential Statistics  Sampling Distributions and The Central Limit Theorem  Confidence Intervals  Population Mean  Population Proportion  Hypothesis Testing  Population Mean  Population Proportion Leaves time for additional topics:  Regression  Two Sample Inferences  Tests with Qualitative Data  Analysis of Variance LIMITED PROBABILITY APPROACH

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 first 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 Polygons  Ogives  Stem-and-Leaf Plots  Computation of percentiles*  Five-Number Summary  Boxplots  Chebyshev’s Inequality  Computation 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

Bill Navidi Colorado School of Mines THE BOTTOM LINE: WHAT’S ESSENTIAL IN AN ELEMENTARY STATISTICS COURSE Barry Monk Middle Georgia State College Don Brown Middle Georgia State College Thank you

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