MATH200/ME50, Statistics

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  • Chapter 1: Data Collection
  • Chapter 2: Graphical Summaries
  • Chapter 3: Numeric Summaries
  • Chapter 4: Correlation & Regression
  • Chapter 5: Probability
  • Chapter 6: Probability Distributions
  • Chapter 7: Normal Distribution
  • Chapter 8: Sample Variability
  • Chapter 9: Confidence Intervals
  • Chapter 10: Hypothesis Tests
  • Chapter 11: Inferences for Two Pop.
  • Chapter 12: Additional Inferences
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News

(See also broadcast email to the class. The latest was dated 16 Dec.)

Grades have been posted and you may access them through myTC3/myInfo.

If you would like the details of how your grade was computed, you can request and receive that information via TC3 email.

Assignments

• Schedule and Assignments (rev. 8 Aug)
• Sleep Lab (rev. 8 Aug)
• Shoe-Size Lab (rev. 8 Aug)
• Graph paper in case you need it for the first two labs.
• ESP Lab (rev. 8 Aug)
• Field Project (rev. 8 Aug)
  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. 5 Sep)
• Advice from Your Fellow Students (rev. 29 Aug)
• Viewer’s Guide to Against All Odds Part 1, “What Is Statistics?”
• MATH200A Program — Statistics Utilities for TI-83/84 (rev. 28 Dec 2009) explains how to use the utility program that Professor Marvel puts on your calculator. You’ll use this program with Chapters 2, 3, 6, 7, 9, 11, and 12.
• Data Types and Variable Types (rev. 26 Aug 2009)
• Show Your Work! (rev. 19 Aug 2005)
• Practice quiz and Solutions (5 Jun 2009)

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 2009-12-28) and Introduction to Polling (link verified 2009-12-28). The original Literary Digest article can be found at Landon in a Landslide: The Poll that Changed Polling (link verified 2009-12-28).
• Alternating Treatments (link verified 2009-12-28) 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 2009-12-28).

Chapter 2: Graphical Summaries

For class

• Chapter 2 Lecture Notes (rev. 6 Jun)
• MATH200A Program part 1 for histograms
• Practice quiz and Solutions (7 Jun 2008)

Optional extras

• 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 (link verified 2009-12-28)
  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. 10 Jun)
• Sample Statistics on TI-83/84 (rev. 16 Feb) — mean, median, standard deviation, variance, and five-number summary
• MATH200A Program part 2 for box-whisker plots
• Empirical Rule Practice Problems with solutions (rev. 21 Sep)
• Practice quiz and Solutions (16 Feb)

Optional extras

• what to do about Outliers (link verified 2009-12-28)
• Standard Deviation (link verified 2009-12-28) by Steve Simon, with pictures and interpretation
• Empirical Relation Between Mean, Median And Mode (link verified 2009-12-28)
  A more technical version is Mean, Median, and Skew: Correcting a Textbook Rule (link verified 2009-12-28)
• Degrees of Freedom (link verified 2009-12-28) 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 Dr. Math’s article in Defining Quartiles (link verified 2009-12-28).
• Measures of Shape: Skewness and Kurtosis (rev. 23 Oct)
• MATH200B Program part 1 computes skewness and kurtosis

Chapter 4: Correlation & Regression

For class

• Chapter 4 Lecture Notes (rev. 19 Nov)
• Scatter Plot, Correlation, and Regression on TI-83/84 (rev. 21 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. 21 Sep)
• Decision Points for Correlation Coefficient (rev. 10 Jun 2009)
• Practice quiz and Solutions (24 Sep)

Optional extras

• Cartoons about correlation and causation are here (link verified 2009-12-28) and here (link verified 2009-12-28).
• If correlation is not Causation (link verified 2009-12-28), how do we know that smoking causes cancer?
• What does R-squared mean? (link verified 2009-12-28)
• Least Squares — the Gory Details (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 Jun)
• Practice quiz and Solutions (16 Jun 2009)

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 2009-12-28). One way it’s used to detect cheating is at Following Benford’s Law, or Looking Out for No. 1 (link verified 2009-12-28).

Chapter 6: Probability Distributions

For class

• Chapter 6 Lecture Notes (rev. 6 Oct)
• (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 1 for histograms of the general discrete PD, MATH200A Program part 4 for histograms of the binomial PD, and MATH200A Program part 3 for binomial probability
  also: Binomial Probability Distribution on TI-89 (rev. 7 Aug 2007)
• Swain v Alabama (link verified 2009-12-28) — racial bias in jury selection
• Practice quiz and Solutions (19 Oct)

Chapter 7: Normal Distribution

For class

• Chapter 7 Lecture Notes (rev. 27 Oct)
• Normal Calculations on TI-83/84 or TI-89 (rev. 14 Aug 2009) section 1
• MATH200A Program part 5 determines whether a distribution is normal
• Practice quiz and Solutions (21 Oct 2009)

Optional extras

• Normal Distribution by Steve Simon — an overview

Chapter 8: Sampling Distributions and Sample Variability

For class

• Chapter 8 Lecture Notes (rev. 31 Oct)
• Normal Calculations on TI-83/84 or TI-89 (rev. 14 Aug 2009) section 2
• Sampling Distributions — Summary (rev. 22 Mar 2009)
• 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 (3 Nov)

Optional extras

• The Behavior of the Sample Mean (link verified 2009-12-28) — 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. 29 Jun)
• MATH200A Program part 6 computes sample size
• Inferential Statistics: Basic Cases (rev. 4 Dec)
• Practice quiz and Solutions (24 Aug 2009)

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 2009-12-28) 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 (link verified 2009-12-28) gives the “rule of three” for calculating a confidence interval when np̂ = 0.
• How Big a Sample Do I Need? (rev. 24 Aug 2009) 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.

Chapter 10: Hypothesis Tests for One Pop.

For class

• Chapter 10 Lecture Notes (rev. 30 Dec 2009)
• See under Review for Inferential Statistics: Basic Cases and Triage: Which Inferential Stats Case Should I Use?.
• Hypothesis Testing Made Simple (rev. 17 Nov)
• Hypothesis Tests: Six Steps (Plus One) (rev. 18 Nov)
• One-Tailed or Two-Tailed Hypothesis Test? (rev. 28 Dec 2009)
• What Does the p-Value Mean? (rev. 10 Nov)
• Proper Conclusions to Your Hypothesis Tests (rev. 17 Nov)
• Top 10 Mistakes of Hypothesis Tests (rev. 13 Apr)
• M&Ms Lab: Inferences for One Population (rev. 14 Apr)
• Practice quiz and Solutions (22 Nov)

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 2009-12-28) and Logic of Hypothesis Testing, part of HyperStat (link verified 2009-12-28)
• 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 for Two Pop.

For class

• Chapter 11 Lecture Notes (rev. 21 Apr)
• MATH200A Program part 6 computes sample size
• Case Study: Gardasil Vaccine (rev. 17 Nov)
• additional examples of Confidence Intervals for Two Populations (rev. 17 Jul 2008)
• See under Review for Inferential Statistics: Basic Cases and Triage: Which Inferential Stats Case Should I Use?.
• Practice quiz and Solutions (16 Feb)

Optional extras

• List Operations for Paired t Test on TI-83/84 (rev. 26 Jul 2009)
• Number Needed to Treat — statistical significance and practical significance, with examples from medical studies (link verified 2009-12-28)

Chapter 12: Additional Inferences

For class

• Chapter 12 Lecture Notes (rev. 4 Dec)
• Testing Goodness of Fit on TI-89 (rev. 1 Jun 2008)
  For the TI-83/84, use MATH200A Program part 7.
• See under Review for Inferential Statistics: Basic Cases and Triage: Which Inferential Stats Case Should I Use?.
• Practice quiz and Solutions (24 Aug 2009)

Optional extras

• Chi-Square in Randomized Experiments: the Physicians' Health Study (link verified 2009-12-28)
  The original data can be found at Harvard’s site (link verified 2009-12-28).
• 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.”(link verified 2010-10-24) The full report in PDF is here.
• Inferential Statistics Cases (rev. 4 Dec) contains additional cases beyond the ones required for class
• Inferences about Linear Correlation (rev. 25 Dec 2009), with Excel workbook
• Inferences about Linear Regression (rev. 25 Dec 2009), with Excel workbook
• Inferences about One Population Standard Deviation (rev. 24 Dec 2009), 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 (rev. 3 Feb 2009)

Review: Prep for the exam

• Review Guide for MATH200, Statistics (rev. 16 Feb)
• Practice Problems for Statistics and Solutions to Practice Problems for Statistics (rev. 18 Nov)
• Triage: Which Inferential Stats Case Should I Use? (rev. 7 Jul 2009)
• Inferential Statistics: Basic Cases (rev. 4 Dec) — On quizzes and the exam, you may use this sheet in addition to your crib sheet.
• See under Chapter 10 for 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, and Top 10 Mistakes of Hypothesis Tests.

General Statistics:

• Your To-Do List (rev. 8 Aug)
• Corrections to Sullivan’s Fundamentals of Statistics (rev. 2 Sep)
• Statistics Symbol Sheet (rev. 10 Jun 2009)
• Help! (rev. 15 Aug 2009) — sources of assistance
• Recommended Statistics Books (rev. 27 Aug 2007)
• UCLA Statistics Case Studies — real-life applications you can work yourself (link verified 2009-12-28)
• You can’t trust Excel to do critical statistics. See these papers by David Heiser (link verified 2009-12-28) and P.J. Wells (link verified 2009-12-28)
• On-line statistics courses:
  • All Topics by Steve Simon of Children’s Mercy Hospital (link verified 2009-12-28)
  • Little Handbook of Statistical Practice by Gerald Dallal of Tufts U, with examples from nutrition and medicine (link verified 2009-12-28)
  • HyperStat Online Statistics Textbook by David Lane of Rice U (with cartoons!) (link verified 2009-12-28)
  • e-Handbook of Statistical Methods at NIST, aimed at science and engineering (link verified 2009-12-28)

General Math:

• TI-83/84 Troubleshooting (rev. 21 Jun 2009)
• Significant Digits and Rounding (rev. 14 Mar 2009)
• E notation (link verified 2009-12-28) 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 (29 Aug) — policies for this course
• Can I Use a TI-89 for Statistics Class? (rev. 19 Dec 2009)
• Two grade calculators: a downloadable 35 KB Excel spreadsheet (23 Nov) and the pencil-and-paper version (8 Aug)
• Student Raise of Grade Form (rev. 9 Sep 2009)
• Course Debriefing (8 Aug)