MATH200/ME50, Statistics

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  • Chapter 9
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  • Chapter 1
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  • Chapter 3
  • Chapter 4
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  • Chapter 7
  • Chapter 8
  • Chapter 9
  • Chapter 10
  • Chapter 11
  • Chapter 12
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  • Course Debriefing

Welcome! Please bookmark this page and check back here at least once a week, whenever you miss a class, or when new material is announced in class.

News

(See also broadcast email to the class. The latest was dated 18 Nov.)

3 Nov: Solutions to the Chapter 9 quiz are now on line.

Older news is still available for viewing.

Assignments

• Schedule and Assignments (rev. 13 Oct)
• Sleep Lab (rev. 16 May)
• Shoe-Size Lab (rev. 13 Oct)
• ESP Lab (rev. 12 Apr)
• Field project information:
  • First read this Field Project protocol (rev. 17 May) with grading rubric.
  • Then make out your Field Project Plan on this form (rev. 2 Jan 2007).
  • Projects about TC3 students may use this database from TC3 Institutional Research.

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.

Chapter 1: Data Collection

For class

• Chapter 1 Lecture Notes (rev. 6 Sep)
• Advice from Your Fellow Students (rev. 1 Aug)
• Viewer’s Guide to Against All Odds Part 1, “What Is Statistics?”
• Data Types and Variable Types (rev. 26 Aug)
• Show Your Work! (rev. 19 Aug 2005)
• Practice quiz and Solutions (5 Jun)

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.
• Read about the Literary Digest polling fiasco for the 1936 presidential election (mentioned in class) at Classic Polling Surprises (link verified 2008-08-31) and Introduction to Polling (link verified 2008-08-31). The original Literary Digest article can be found at Landon in a Landslide: The Poll that Changed Polling (link verified 2008-08-31).
• Alternating Treatments (link verified 2008-08-31) gives lots of examples why you need to randomize your samples.
• What’s wrong with surveys where respondents select themselves? See Web Polls (link verified 2008-08-31).
• What Is a Survey? (link verified 2008-08-31), edited by Fritz Scheuren for the American Statistical Association

Chapter 2: Graphical Summaries

For class

• Chapter 2 Lecture Notes (rev. 16 Sep)
• Descriptive Statistics Utilities for TI-83/84 (rev. 14 Nov), includes downloadable program: section 1 makes histograms and section 3 (optional) graphs time series
• Practice quiz and Solutions (7 Jun 2008)

Optional extras

• 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 (link verified 2008-08-31)
  This is one of the many examples in Edward Tufte’s The Visual Display of Quantitative Information.

Chapter 3: Numeric Summaries

For class

• Chapter 3 Lecture Notes (rev. 25 Oct)
• Sample Statistics on TI-83/84 (rev. 8 Dec 2008) — mean, median, standard deviation, variance, and five-number summary
• Descriptive Statistics Utilities part 2 for box-whisker plots
• Empirical Rule Practice Problems with solutions (rev. 16 Feb 2008)
• Practice quiz and Solutions (16 Feb 2008)

Optional extras

• what to do about Outliers (link verified 2008-08-31)
• Standard Deviation (link verified 2008-08-31) by Steve Simon, with pictures and interpretation
• Empirical Relation Between Mean, Median And Mode (link verified 2008-08-31)
  A more technical version is Mean, Median, and Skew: Correcting a Textbook Rule (link verified 2008-08-31)
• Degrees of Freedom (link verified 2008-08-31) 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.
• The way we find percentiles and quartiles in class is just one of the commonly accepted methods. You may be interested in Max Petzold’s A Comparison of Some Commonly Used Percentile Definitions (PDF, 102 KB) (link verified 2008-08-31). A simpler treatment is offered by Dr. Math in Defining Quartiles (link verified 2008-08-31).
• Measures of Shape: Skewness and Kurtosis (rev. 11 Feb)
• Descriptive Statistics Utilities part 4 computes skewness and kurtosis

Chapter 4: Correlation & Regression

For class

• Chapter 4 Lecture Notes (rev. 22 Sep)
• Scatter Plot, Correlation, and Regression on TI-83/84 (rev. 22 Sep)
  There’s also a version for the TI-89 and TI-92.
• Getting ŷ from Any x in a Regression on TI-83/84/89 (rev. 16 Aug)
• Decision Points for Correlation Coefficient (rev. 10 Jun)
• Practice quiz and Solutions (20 Jul)

Optional extras

• Cartoons about correlation and causation are here (link verified 2009-07-15) and here (link verified 2009-07-15).
• If correlation is not Causation (link verified 2008-08-31), how do we know that smoking causes cancer?
• What does R-squared mean? (link verified 2008-08-31)
• Least Squares, Down and Dirty (rev. 9 Aug 2007) — 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

• Chapter 5 Lecture Notes (rev. 23 Aug)
• Practice quiz and Solutions (16 Jun)

Optional extras

• extended examples of probability: Probability of Shared Birthdays (rev. 25 May 2003), We the Jury ... (rev. 24 Aug 2003), and Medical False Positives and False Negatives (rev. 12 Jan 2004)
• Probability Practice Problems (rev. 20 Apr 2008)
• For more about the first-digit phenomenon, see Benford’s Law at Mathworld (link verified 2008-08-31). One way it’s used to detect cheating is at Following Benford’s Law, or Looking Out for No. 1 (link verified 2008-08-31).

Chapter 6: Probability Distributions

For class

• Chapter 6 Lecture Notes (rev. 27 Oct)
• (To find mean and standard deviation of a probability distribution, use the techniques for frequency distribution in Sample Statistics on TI-83/84.)
• Descriptive Statistics Utilities part 1 for histograms of the general discrete PD, Descriptive Statistics Utilities part 6 for histograms of the binomial PD, and Descriptive Statistics Utilities part 5 for binomial probability
  also: Binomial Probability Distribution on TI-89 (rev. 7 Aug 2007)
• Swain v Alabama (link verified 2008-08-31) — racial bias in jury selection
• Practice quiz and Solutions (13 Oct)

Chapter 7: Normal Distribution

For class

• Chapter 7 Lecture Notes (rev. 13 Oct)
• Normal Calculations on TI-83/84 or TI-89 (rev. 14 Aug) section 1
• Descriptive Statistics Utilities part 7 determines whether a distribution is normal
• Practice quiz and Solutions (21 Oct)

Optional extras

• Normal Distribution by Steve Simon — an overview

Chapter 8: Sampling Distributions and Sample Variability

For class

• Chapter 8 Lecture Notes (rev. 25 Oct)
• Normal Calculations on TI-83/84 or TI-89 (rev. 14 Aug) section 2
• Sampling Distributions — Summary (rev. 22 Mar)
• Central Limit Theorem Lab II (Roulette) (rev. 23 Oct 2007)
• Viewer’s Guide to Against All Odds Part 18, “The Sample Mean and Control Charts”
• Practice quiz and Solutions (30 Jun)

Optional extras

• Simulations (link verified 2009-06-29) lets you control the simulation by selecting various types of parent distribution and various sample sizes
• The Behavior of the Sample Mean (link verified 2009-06-29) — 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

• Chapter 9 Lecture Notes (rev. 28 Oct)
• Inferential Statistics Utilities part 1 computes sample size
• Inferential Statistics Cases (rev. 25 Oct)
• Practice quiz and Solutions (24 Aug)

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 (link verified 2008-08-31) 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 Inferential Statistics Utilities part 2.
• Rule of Three as explained by Steve Simon (link verified 2008-08-31) gives a technique to calculate a confidence interval when np = 0.
• How Big a Sample Do I Need? (rev. 24 Aug) explains how to find necessary sample size by formula, for those who don’t have the MATH200I program or would like to know how the calculations are done.

Chapter 10: Hypothesis Tests for One Pop.

For class

• Chapter 10 Lecture Notes (rev. 4 Nov)
• See under Review for Inferential Statistics Cases and Triage: Which Inferential Stats Case Should I Use?.
• One-Tailed or Two-Tailed Hypothesis Test? (rev. 9 Apr 2008)
• Proper Conclusions to Your Hypothesis Tests (rev. 3 Nov)
• What Does the p-Value Mean? (rev. 17 Nov 2008)
• Top 10 Mistakes of Hypothesis Tests (rev. 30 Aug)
• M&Ms Lab: Inferences for One Population (rev. 17 Nov)
• Practice quiz and Solutions (7 May)

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 (link verified 2008-08-31) and Logic of Hypothesis Testing, part of HyperStat (link verified 2008-08-31)
• You can also do hypothesis tests about σ, the population s.d.: see Inferential Statistics Utilities part 2 or Inferences about One Population Standard Deviation.

Chapter 11: Inferences for Two Pop.

For class

• Chapter 11 Lecture Notes (rev. 18 Nov)
• Inferential Statistics Utilities part 1 computes sample size
• Case Study: Gardasil Vaccine (rev. 28 Oct 2007)
• additional examples of Confidence Intervals for Two Populations (rev. 17 Jul 2008)
• See under Review for Inferential Statistics Cases and Triage: Which Inferential Stats Case Should I Use?.
• Practice quiz and Solutions (24 Aug)

Optional extras

• List Operations for Paired t Test on TI-83/84 (rev. 26 Jul)
• Number Needed to Treat — statistical significance and practical significance, with examples from medical studies (link verified 2008-08-31)

Chapter 12: Additional Inferences

For class

• Chapter 12 Lecture Notes (rev. 24 Aug)
• Testing Goodness of Fit on TI-89 (rev. 1 Jun 2008)
  For the TI-83/84, use Inferential Statistics Utilities part 3.
• See under Review for Inferential Statistics Cases and Triage: Which Inferential Stats Case Should I Use?.
• Practice quiz and Solutions (24 Aug)

Optional extras

• Chi-Square in Randomized Experiments: the Physicians' Health Study (link verified 2008-08-31)
  The original data can be found at Harvard’s site.
• Inferences about Linear Correlation (rev. 4 Apr 2008), with Excel workbook
• Inferences about Linear Regression (rev. 4 Apr 2008), with Excel workbook
• Inferences about One Population Standard Deviation (rev. 24 Nov 2008), with Excel workbook
• All three of the above, and more, are included in Inferential Statistics Utilities for TI-83/84 with a downloadable TI-83/84 program.
• One-Way ANOVA (rev. 3 Feb)

Review: Prep for the exam

• Review Guide for MATH200, Statistics (rev. 28 Jul 2008)
• Practice Problems for Statistics and Solutions to Practice Problems for Statistics (rev. 26 Aug)
• Triage: Which Inferential Stats Case Should I Use? (rev. 7 Jul)
• Inferential Statistics Cases (rev. 25 Oct) — On quizzes and the exam, you may use this sheet in addition to your crib sheet.
• See under Chapter 10 for One-Tailed or Two-Tailed Hypothesis Test?, What Does the p-Value Mean?, Proper Conclusions to Your Hypothesis Tests, and Top 10 Mistakes of Hypothesis Tests.

General Statistics:

• Your To-Do List (rev. 13 Aug)
• Corrections to Sullivan’s Fundamentals of Statistics (rev. 15 Sep)
• Symbol Sheet (rev. 10 Jun)
• Help! (15 Aug) — sources of assistance
• Recommended Books (rev. 27 Aug 2007)
• UCLA Statistics Case Studies — real-life applications you can work yourself (link verified 2008-08-31)
• You can’t trust Excel to do critical statistics. See these papers by David Heiser (link verified 2009-07-24) and P.J. Wells (link verified 2009-07-24)
• On-line statistics courses:
  • Steve’s Attempt to Teach Statistics by Steve Simon of Children’s Mercy Hospital (link verified 2008-08-31)
  • Little Handbook of Statistical Practice by Gerald Dallal of Tufts U, with examples from nutrition and medicine (link verified 2008-08-31)
  • HyperStat Online Textbook by David Lane of Rice U (with cartoons!) (link verified 2008-08-31)
  • e-Handbook of Statistical Methods at NIST, aimed at science and engineering (link verified 2008-08-31)

General Math:

• TI-83/84 Troubleshooting (rev. 21 Jun)
• Significant Digits and Rounding (rev. 14 Mar)
• E notation (link verified 2008-08-31) by Steve Simon
• How to Succeed in Math (25 Sep 2008) 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 (5 Mar 2003)

Administrivia

• Course Outline (6 Oct) — policies for this course
• Can I Use a TI-89 for Statistics Class? (23 Sep)
• Two grade calculators: a downloadable 42 KB Excel spreadsheet (9 Aug) and the pencil-and-paper version (9 Aug)
• Student Raise of Grade Form (rev. 9 Sep)
• Course Debriefing (30 Oct)

Quiz Solutions

Solutions to quizzes are posted here within 24 hours; here’s a list of the ones given in class so far. (Practice quizzes, with solutions, are listed under each Chapter above.)

• 3 Nov Quiz on Chapter 9: Solutions (revised 8 Nov)
• 27 Oct Quiz on Chapter 8: Solutions (revised 1 Nov)
• 20 Oct Quiz on Chapter 7: Solutions (revised 21 Oct)
• 13 Oct Quiz on Chapter 6: Solutions (revised 13 Oct)
• 6 Oct Quiz on Chapter 5: Solutions (revised 12 Oct)
• 29 Sep Quiz on Chapter 4: Solutions (revised 5 Oct)
• 22 Sep Quiz on Chapter 3: Solutions (revised 29 Sep)
• 15 Sep Quiz on Chapter 2: Solutions (revised 15 Sep)
• 8 Sep Quiz on Chapter 1: Solutions (revised 15 Sep)
• Take-home Quiz on Course Outline: Solutions (revised 15 Sep)