Statistics — MATH200

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• Handouts
  • Throughout the Course
  • Chapter 1: Data Collection
  • Chapter 2: Graphical Summaries
  • Chapter 3: Numeric Summaries
  • Chapter 4: Correlation & Regression
  • Chapter 5: Probability
  • Chapter 6: Discrete Probability Dist
  • Chapter 7: Normal Distribution
  • Chapter 8: Sample Variability
  • Chapter 9: Confidence Intervals
  • Chapters 9–12: Inference
  • Chapter 10: Hypothesis Tests
  • Chapter 11: Inferences on Two Samples
  • Chapter 12: Additional Inferences
  • Review for the Exam
  • General Math
• Admin
  • Raise of Grade Form
  • Can I Use a TI-89?

Statistics students in any instructor’s section will find useful material in the handouts. If you’re taking this course from Stan Brown, please select your section to find specific class materials:

• Spring 2012 section ME50, T 6:30–9:20, room 212
• completed class: Fall 2011 section ME50, T 6:30–9:20, room 283A
• completed class: Spring 2011 section ME50, T 6:30–9:20, room 121C
• completed class: Fall 2010 section ME50, T 6:30–9:20, room 283B

Assignments (for Stan Brown’s students)

Please use the links above to find the Web pages for your particular section.

Handouts

The handouts are marked with helpful symbols. A full explanation of the symbols is available, and most browsers will also show a “tool tip” if you just mouse over the symbol.

Throughout the Course

Used throughout the course

• Corrections to Sullivan’s Fundamentals of Statistics, 3rd Edition
• Statistics Symbol Sheet
• Help! — sources of assistance

Optional extras

• Recommended Statistics Books
• UCLA Statistics Case Studies — real-life applications you can work yourself
• You can’t trust Excel to do critical statistics. See these papers by David Heiser and P.J. Wells
• On-line statistics courses:
  • All Topics by Steve Simon of Children’s Mercy Hospital
  • Little Handbook of Statistical Practice by Gerald Dallal of Tufts U, with examples from nutrition and medicine
  • HyperStat Online Statistics Textbook by David Lane of Rice U (with cartoons!)
  • e-Handbook of Statistical Methods at NIST, aimed at science and engineering
  • Collaborative Statistics by Barbara Illowsky and Susan Dean, from the College Open Textbooks Community

Chapter 1: Data Collection

For class

• Guide to Chapter 1
• Viewer’s Guide to Against All Odds Part 1, “What Is Statistics?” (for some sections)
• Data Types and Variable Types
• Show Your Work!
• Practice quiz and Solutions

Optional extras

• Excel and your calculator generate pseudo-random numbers, but Random.org has lots of true random number generators, including numbers, coin flips, and dice rolls.
• In class we mentioned the 1936 fiasco of a presidential election poll. The original Literary Digest article can be found at Landon in a Landslide: The Poll that Changed Polling.
• Alternating Treatments gives lots of examples why you need to randomize your samples.
• What’s wrong with surveys where respondents select themselves? See Web Polls.

Chapter 2: Graphical Summaries

For class

• Guide to Chapter 2
• Practice quiz and Solutions

Optional extras

• The Joy of Stats video: Hans Rosling shows lots of great ways to present data. Don’t miss the segment “200 Countries, 200 Years, 4 Minutes”, also available separately
• just for fun: self-referential graphs
• The Best Stats You’ve Ever Seen video: Hans Rosing uses descriptive stats to explode the myth of First World and Third World
• MATH200A Program part 1 can be used to make histograms, and MATH200B Program part 2 graphs time series
• ticalc.org has five programs to make pie charts. Though I haven't evaluated them in depth, PIEGRAPH.ZIP looks most interesting based on the screen shots.
• STEMLEAF.ZIP (1 KB) is a TI-83/84 program that makes stemplots
• Charles Minard’s famous graph of Napoleon’s Moscow campaign
  This is one of the many examples in Edward Tufte’s The Visual Display of Quantitative Information.

Chapter 3: Numeric Summaries

For class

• Guide to Chapter 3
• Sample Statistics on TI-83/84 — mean, median, standard deviation, variance, and five-number summary
• MATH200A Program part 2 for box-whisker plots
• Empirical Rule Practice Problems with solutions
  Don’t spend too much time with this one. Earlier versions of the course emphasized the use of the Empirical Rule a lot more than we do now.
• Practice quiz and Solutions

Optional extras

• what to do about Outliers
• Standard Deviation by Steve Simon, with pictures and interpretation
• Empirical Relation Between Mean, Median And Mode
  A more technical version is Mean, Median, and Skew: Correcting a Textbook Rule
• Degrees of Freedom tells why we divide by n−1, not n, to compute standard deviation. “Variance” from David C. Ullrich (dated 12 June 2006 and archived here) explains this based on the difference between sample variance and population variance.
• Different authorities find percentiles and quartiles in different ways, though all share the same ideas. You may be interested in Dr. Math’s article in Defining Quartiles.
• Measures of Shape: Skewness and Kurtosis
• MATH200B Program part 1 computes skewness and kurtosis

Chapter 4: Correlation & Regression

For class

• Guide to Chapter 4
• Scatter Plot, Correlation, and Regression on TI-83/84
  There’s also a version for the TI-89 and TI-92.
• Finding ŷ from a Regression on TI-83/84
• Decision Points for Correlation Coefficient
• MATH200B Program part 6 for inferences about linear correlation
• Practice quiz and Solutions

Optional extras

• Cartoons about correlation and causation are here and here.
• If correlation is not Causation, how do we know that smoking causes cancer?
• What does R-squared mean?
• Least Squares — the Gory Details — Where do those formulas come from?
• Under Chapter 12 are several more inferences you can make about correlation and regression.

Chapter 5: Probability

For class

• Guide to Chapter 5
• Practice quiz and Solutions

Optional extras

• extended examples of probability: Probability of Shared Birthdays, We the Jury ..., and Medical False Positives and False Negatives
• Probability Practice Problems (for those who want to go beyond the syllabus and study the whole chapter)
• False positives and the war on terror, by Sam Savage and Howard Wainer: False Positives Calculator and explanation
• For more about the first-digit phenomenon, see Benford’s Law at Mathworld. One way it’s used to detect cheating is at Following Benford’s Law, or Looking Out for No. 1.

Chapter 6: Discrete Probability Distributions

For class

• Guide to Chapter 6
• (To find mean and standard deviation of a probability distribution, use the techniques for frequency distribution in Sample Statistics on TI-83/84.)
• MATH200A Program part 3 to compute binomial probability; or Binomial Probability Distribution on TI-83/84 if you don’t have the prrogram.
  TI-89 users: Binomial Probability Distribution on TI-89
• Swain v Alabama — racial bias in jury selection
• Practice quiz and Solutions

Optional extras

• MATH200A Program part 1 for histograms of the general discrete PD and MATH200A Program part 4 for histograms of the binomial PD

Chapter 7: Normal Distribution

For class

• Guide to Chapter 7
• Normal Calculations on TI-83/84 or TI-89 section 1
• MATH200A Program part 5 determines whether a distribution is normal
• Practice quiz and Solutions

Optional extras

• Is Human Height Bimodal? gives μ and σ for heights of US men and women from the US NHANES study
• Normal Distribution by Steve Simon — an overview

Chapter 8: Sampling Distributions and Sample Variability

For class

• Guide to Chapter 8
• Normal Calculations on TI-83/84 or TI-89 section 2
• Sampling Distributions — Summary
• Central Limit Theorem Lab II (Roulette)
• Viewer’s Guide to Against All Odds Part 18, “The Sample Mean and Control Charts”
• Practice quiz and Solutions

Optional extras

• The Behavior of the Sample Mean — pictures show how sample means are distributed and why that distribution is different from the shape of the population

Chapter 9: Confidence Intervals

For class

• Guide to Chapter 9
• MATH200A Program part 6 computes sample size
• See below for two handouts used with Chapters 9 through 12.
• Practice quiz and Solutions

Optional extras

• Why np(1−p)≥10 (or at least 5 yes and 5 no)? Despite the title, Dr. Math’s Difference of Two Proportions in Statistics answers this question for tests of one proportion as well.
• We don’t do it in this class, but if you want to know how to compute confidence intervals about σ, the population standard deviation, see Inferences about One Population Standard Deviation or MATH200B Program part 5.
• Confidence Interval with Zero Events by Steve Simon gives the “rule of three” for calculating a confidence interval when np̂ = 0.
• How Big a Sample Do I Need? explains how to find necessary sample size by formula, for those who don’t have MATH200A part 6 or would like to know how the calculations are done.
• Instead of looking up t-values in a table, you can use a program to find them: MATH200B Program part 3

Chapters 9–12: Inference

• These two handouts apply to Chapters 9 through 12, and they help you choose the right case for analyzing a given situation:
  • Inferential Statistics: Basic Cases
    
  • Triage: Which Inferential Stats Case Should I Use?
    (Use it on line for the iinteractive features.)
• Hypothesis testing a/k/a significance testing has a language and philosophy of its own, but once you get it you’ll find it’s the same for Chapters 10 through 12. These handouts replace sections 10.1 and 10.2 of your textbook:
  • Hypothesis Testing Made Simple
  • Hypothesis Tests: Six Steps (Plus One)
  • One-Tailed or Two-Tailed Hypothesis Test?
  • What Does the p-Value Mean?
  • Proper Conclusions to Your Hypothesis Tests
  • Hypothesis Test by Confidence Interval
• Look at this one after you’ve spent a week or two on hypothesis tests: Top 10 Mistakes of Hypothesis Tests

Chapter 10: Hypothesis Tests for One Pop.

For class

• Guide to Chapter 10
• The handouts under Chapters 9–12: Inference apply to all hypothesis tests. The “language and philosophy” handouts replace sections 10.1 and 10.2 of your textbook.
• Hypothesis Tests about the Mean in the Real World (σ Unknown) replaces section 10.3 of your textbook
• Hypothesis Tests of a Proportion replaces section 10.4 of your textbook
• In-class exercise (some sections): M&Ms Lab: Inferences for One Population
• Practice quiz and Solutions

Optional extras

• The logic of hypothesis testing can seem very strange at first. One way to demystify it is to read many different writeups, not just your textbook. Here are two easy and excellent ones: Is Statistics Hard? by Gerald Dallal and Logic of Hypothesis Testing, part of HyperStat
• When α is the standard 0.05, one in 20 of your significant results are actually Type I errors. How do you interpret published results, then? See Sifting the evidence—what‘s wrong with significance tests? by Sterne and Smith.
• Even professional researchers can make mistakes and publish false results through misusing hypothesis tests. “Data mining” (first gathering data, then looking for relationships) is one problem but not the only one. See Why Most Published Research Findings Are False by John Ioannidis. If you find the article heavy going, just scroll down to read the example in Box 1 and then the corollaries that follow.
• You can also do hypothesis tests about σ, the population s.d.: see MATH200B Program part 5 or Inferences about One Population Standard Deviation.

Chapter 11: Inferences on Two Samples

For class

• Guide to Chapter 11
• MATH200A Program part 6 computes sample size
• Case Study: Gardasil Vaccine
• the Worked-Out HT and CI from Chapter 11 Class in PDF format
• additional examples of Confidence Intervals for Two Populations
• The handouts under Chapters 9–12: Inference apply to all hypothesis tests.
• Practice quiz and Solutions

Optional extras

• List Operations for Paired t Test on TI-83/84
• Number Needed to Treat — statistical significance and practical significance, with examples from medical studies

Chapter 12: Additional Inferences

For class

• Guide to Chapter 12
• MATH200A Program part 7 does the calculations for section 12.1. (If you have a TI-89/92, use Testing Goodness of Fit on TI-89.)
• The handouts under Chapters 9–12: Inference apply to all hypothesis tests.
• Practice quiz and Solutions

Optional extras

• Chi-Square in Randomized Experiments: the Physicians' Health Study
  The original data can be found at Harvard’s site.
• Study of the Therapeutic Effects of Intercessory Prayer
  This abstract gives the sample sizes and incidence of complications, but does not show the incidence of mortality other than to say it was “similar across the 3 groups.” The full report in PDF is here.
• Confidence Intervals for Goodness of Fit, with Excel workbooks

Extra cases

These are not part of the course syllablus, but are included for those who would like to learn more.

• Inferential Statistics Cases contains additional cases beyond the ones required for class
• Inferences about Linear Correlation, with Excel workbook
• Inferences about Linear Regression, with Excel workbook
• Inferences about One Population Standard Deviation, with Excel workbook
• All three of the above, and more, are included in MATH200B Program — Extra Statistics Utilities for TI-83/84 with a downloadable TI-83/84 program.
• One-Way ANOVA

Review for the Exam

• Review Guide for MATH200, Statistics
• Practice Problems for Statistics and Solutions to Practice Problems for Statistics
• The handouts under Chapters 9–12: Inference apply to all hypothesis tests.

General Math

• TI-83/84 Troubleshooting
• Significant Digits and Rounding
• E notation by Steve Simon
• How to Succeed in Math includes Why is Math so Hard?  |  How to Study Math  |  How to Take a Math Test  |  How to Read a Math Book  |  How to Work a Math Problem
• Math Students’ FAQ

Administrivia (for Stan Brown’s students)

• Course Outline, grade calculators, and emails to the class: Please look at the top of this page to find the Web pages for your particular section.
• Can I Use a TI-89 for Statistics Class?
• Student Raise of Grade Form