The Bottom Line: What’s Essential in an Elementary Statistics Course

1. The Bottom Line:What’s Essential in an Elementary Statistics Course Bill Navidi Colorado School of Mines Don Brown Middle Georgia State College Barry Monk Middle Georgia State College

2. Historical Perspective and Growth of Elementary Statistics

3. Statistics in the Past • 1925Statistical Methods for Research Workers R.A. Fisher • Aimed at practicing scientists • 1937Statistical Methods George Snedecor • Aimed at prospective scientists still working on degrees • 1961Probability with Statistical Applications Mosteller, Rourke, & Thomas • Aimed at the broader academic curriculum • 70’s-presentData Revolution • Analysis of data as an independent subject • Technology

4. Growth (AP Statistics Examinees)

5. Modern Elementary Statistics • 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 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.

6. Common Approaches to Teaching Elementary Statistics

7. Approach A first Statistics course generally includes the following content areas: • Sampling • Descriptive Statistics • Probability • Inferential Statistics Sampling Probability Inferential Statistics Descriptive Statistics

8. Approach 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 Sampling Probability Inferential Statistics Descriptive Statistics

9. 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

10. Light Probability Approach

11. Light Probability Approach Probability Sampling Inferential Statistics Descriptive Statistics

12. Light 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 • 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

13. Limited Probability Approach

14. Limited Probability Approach Sampling Inferential Statistics Descriptive Statistics Probability

15. 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

16. 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 • 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

17. 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

18. Correlation is not Causation 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?

19. 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.

20. Notions about Coin Tossing 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 Adapted from Red Bead Experiment – W.E. Deming

21. Probability vs. Statistics A probabilist and a statistician encounter a game of craps for the first time. Can you tell which is which? 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. Six-sided dice? Assuming that each face comes up with probability 1/6, I can figure out what my chances are of winning. Adapted from Calculated Bets: Computers, Gambling, and Mathematical Modeling to Win - Steven Skiena

22. Questions What factors should be considered when weighing the balance between probability and statistics? What trade-off’s are involved?

23. General Considerations (Or Gee-Whiz – I’m Really Behind!)

24. 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

25. Technology Considerations

26. 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

27. Critical Value vs. P-value • Critical value approach • Only tells whether a test statistic is unusual or not • Generally easier if using tables • P-value approach • Tells exactly how unusual a test statistic is • Generally easier if using technology

28. Questions 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?

29. 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 difficult to begin with the t-distribution, so what about beginning with proportions?

30. The Bottom Line:What’s Essential in an Elementary Statistics Course Bill Navidi Colorado School of Mines Barry Monk Middle Georgia State College Thank you Don Brown Middle Georgia State College