Stat 1600:  Statistics and Data Analysis

Spring 2016 Syllabus

Welcome to Stat 1600. This is a 3-credit general introductory course to statistics with an emphasis on data analysis and graphical presentation. Topics covered include: data collection, sampling, measurement issues, descriptive statistics, statistical graphics, normal distribution, cross-classified data, correlation and association, and formal statistical inferences.

Course Objectives

Students' skills and competence will advance beyond the level of one year elementary algebra.

Course Outcomes

Upon completion of this course, students should be able:

Prerequisites & Corequisites

MATH 1100 or MATH 1110 with a grade of “C” or better, or satisfactory score on Mathematics Department Placement Examination.

General Education Proficiency

This course satisfies General Education Proficiency 3: College-Level Mathematics or Quantitative Reasoning.

Lectures

Classes are structured in a workshop style. Lectures on course material take place during the first 50 minutes of each class, followed by hands-on work for the remaining time of the class period. Please note that daily in-class work accounts for 40% (200/500 points) of your grade. Regular attendance and participation is advised.

Workshops

There are 23 in-class workshops (none on midterm and review days). Each daily workshop is due at the end of lecture. Workshops generally consist of one multi-part problem covering course material in an application of concepts and computations. You are encouraged (but not required) to form a team of 2 to 4 members for the workshops. Each team will turn in only one copy of the work for each workshop with all members’ names listed (printed and signed). Active participation is advised, as the midterms and final exam will be similar in content to that of the workshops. Exam problems could potentially be identical to workshops except for changes in numbers. Each workshop is worth 10 points. The top twenty workshop scores will be used toward the final grade.

Materials

Evaluation/Grading

Students' grades are based on the following points distribution:
Points
Daily in-class work 200
Midterm #1 100
Midterm #2 100
Final Exam 100
Total 500

iClicker extra credit = smaller value of 20 and your total iClicker score.
These extra credit points will be added to the total you got from the workshops and exams.
The following scale will be used in determining final grades:
Final Avg. = (Total Score) / 5
Your Final Avg. is then used to determine your grade based on the following:
A BA B CB C E
≥ 85 ≥ 80 ≥ 75 ≥ 70 ≥ 60 below 60

Absence Policy

Students can make-up class work (workshops) in the case of a documented absence with instructor's approval.

Late Policy

Late workshops will not be accepted without prior instructor's approval or in the case of an approved absence.

Incomplete Policy

Department policy will be followed on incompletes.

Academic Integrity

You are responsible for making yourself aware of and understanding the University policies and procedures that pertain to Academic Honesty. These policies include cheating, fabrication, falsification and forgery, multiple submission, plagiarism, complicity and computer misuse. (The academic policies addressing Student Rights and Responsibilities can be found in the Undergraduate Catalog at http://catalog.wmich.edu/content.php?catoid=22&navoid=882 and the Graduate Catalog at http://catalog.wmich.edu/content.php?catoid=23&navoid=938.) If there is reason to believe you have been involved in academic dishonesty, you will be referred to the Office of Student Conduct. You will be given the opportunity to review the charge(s) and if you believe you are not responsible, you will have the opportunity for a hearing. You should consult with your instructor if you are uncertain about an issue of academic honesty prior to the submission of an assignment or test.

Exam Dates

There are two midterm exams and a final exam.
Take note of the following exam date information:

Exam Preparation

All exams are closed-book, closed-note exams. To avoid formula memorization, students are advised to prepare exam notes. Tables such as the cumulative probability of the standard normal (the Z table on page 44) will be attached to exams. You are allowed to bring in one 8.5″×11″ sheet (double-sided) for each midterm and three sheets for the final exam. Remember to bring a calculator with fresh batteries to your exams. Cell phones (and related electronic devices, such as iPods and mp3 players) cannot be used as calculators for exams.

Exam Accommodations

Students who need special accommodations to take any of the exams will need to contact DSS (Disability Services for Students) at least 4 school days prior to each exam to make arrangements. You will also need to inform your instructor about your arrangement.
The following statements are made by the DSS:

To assure compliance with the Americans with Disabilities Act, faculty members at Western Michigan University need to know how a disability will impact student participation and work in courses. Any student registered with Disability Services for Students who would like to discuss accommodations for this class should contact the instructor of record in a timely manner. Students with documented disabilities who are not registered with DSS should call the office at (269) 387-2116 or visit wmich.edu/disabilityservices. Students cannot request academic accommodations without scheduling an appointment and meeting with a DSS staff member. If a student does not register with DSS, their academic accommodations/modifications cannot be executed.

Make-up Exam Policy

Make-up midterms are given only with instructor's approval. There will be no make-up final exams. If you have any concerns about an exam date or time, please discuss with your instructor in advance.

Schedule

A general schedule for this course is outlined below.
Spring 2016 schedule:

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Day 1 (Jan. 12)  handout, Slides
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1 Knowledge and Data 
  1.1 Knowledge and Data  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  2
      1.1.1 Building Knowledge Step-by-step . . . . . . . . . . . . . . . . . . . . . . . . . . . .  2
      1.1.2 An example  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  3
      1.1.3 A final product . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  4
  1.2 Some fallacies in interpreting evidence .   . . . . . . . . . . . . . . . . . . . . . . . . .  5

                                 No workshop

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Day 2 (Jan. 14) handout, Slides
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2 Data Presentation                                                                                  7
  2.1 Statistics and Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  8
  2.2 Classification of variables . . . . . . . . . . . . .  . . . . . . . . . . . . . . . . . . . . 8
      2.2.1 Levels of Measurement . . . . . . . . . . .     . . . . . . . . . . . . . . . . . . . .  8
      2.2.2 Numerical versus categorical variables . .      . . . . . . . . . . . . . . . . . . . .  9
      2.2.3 Dependent versus independent variables .        . . . . . . . . . . . . . . . . . . . .  9
  2.3 Summarizing Categorical Data . . . . . . . . . .      . . . . . . . . . . . . . . . . . . . . 11
      2.3.1 Relative Frequency Table . . . . . . . . .      . . . . . . . . . . . . . . . . . . . . 13
      2.3.2 Bar Chart . . . . . . . . . . . . . . . . . .   . . . . . . . . . . . . . . . . . . . . 14
      2.3.3 Pie Chart . . . . . . . . . . . . . . . . . .   . . . . . . . . . . . . . . . . . . . . 14

                                WORKSHOP 1

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Day 3 (Jan. 19) handout, Slides
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  2.4 Summarizing numerical data . . . . . . . . . . .      . . . . . . . . . . . . . . . . . . . . 15
      2.4.1 Stem-and-Leaf Plot . . . . . . . . . . . .      . . . . . . . . . . . . . . . . . . . . 16
      2.4.2 Relative Frequency Table and Histogram          . . . . . . . . . . . . . . . . . . . . 19
      2.4.3 Dotplot . . . . . . . . . . . . . . . . . . .   . . . . . . . . . . . . . . . . . . . . 21

                                WORKSHOP 2

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Day 4 (Jan. 21) handout, Slides
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      2.4.4 Box-and-Whisker Plot . . . . . . . . . . .      . . . . . . . . . . . . . . . . . . . . 21
      2.4.5 Symmetry and Skewness . . . . . . . . . .       . . . . . . . . . . . . . . . . . . . . 24

                                WORKSHOP 3

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Day 5 (Jan. 26) handout, Slides, Mean is NOT robust, Hodges-Lehmann Estimate
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3 Location and Spread                                                                               29
  3.1 Estimates of Center . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
      3.1.1 The Sample Mean . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
    3.1.2 The Sample Median . . . . . . . . . . .       . . . . . . . . . . . . . . . . . . . . . . 30
    3.1.3 The Trimmed Mean . . . . . . . . . . .        . . . . . . . . . . . . . . . . . . . . . . 31
    3.1.4 The Median of Pairwise Averages . . . .       . . . . . . . . . . . . . . . . . . . . . . 31

                                WORKSHOP 4

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Day 6 (Jan. 28) handout, Slides, Calculate SD, Exercise 3.1
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3.2 Estimate of Spread (or Uncertainty, Variation)      . . . . . . . . . . . . . . . . . . . . . . 32
    3.2.1 The Sample Standard Deviation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
    3.2.2 Effect of Multiplication and Addition by a Constant . . . . . . . . . . . . . . . . . . . 33

                                WORKSHOP 5

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Day 7 (Feb. 2) handout, Slides, Area Under Z Curve (AUC.pdf)
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4 The Normal Distribution                                                                             37
  4.1 Using the normal curve . . . . . . . . . .      . . . . . . . . . . . . . . . . . . . . . . . . 38
      4.1.1 The Standard Normal or Z Curve            . . . . . . . . . . . . . . . . . . . . . . . . 39

                                WORKSHOP 6

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Day 8 (Feb. 4) handout, Slides, Area Under Z Curve (AUC.pdf)
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  4.2 Calculating percentiles . . . . . . . . . . .   . . . . . . . . . . . . . . . . . . . . . . . . 41
  4.3 Calculating symmetric tail areas . . . . .      . . . . . . . . . . . . . . . . . . . . . . . . 42
      4.3.1 The Empirical Rule . . . . . . . .        . . . . . . . . . . . . . . . . . . . . . . . . 43
  4.5 Z-table . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

                                WORKSHOP 7

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Day 9 (Feb. 9)
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  Review session for Exam 1.  
  Handout sample exam with problems like workshops: 
      --mean, median, quartiles, trimmed mean, median of pairwise averages, SD,
        normal curve, percentiles.
  Spring 2013 Midterm Exam #1, Form A

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Day 10 (Feb. 11)
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  EXAM 1:  Problems similar to workshops

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Day 11 (Feb. 16) handout, Slides
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5 The Binomial Distribution                                                                           45
  5.1 Binomial Probabilities . . . . . . . . . . . . . . . . . . . . .    . . . . . . . . . . . . . . 46
  5.2 Computing Binomial Probabilities . . . . . . . . . . . . . .        . . . . . . . . . . . . . . 46

                                WORKSHOP 8

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Day 12 (Feb. 18) handout, Slides, Area Under Z Curve (AUC.pdf)
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  5.3 Expected Value and SD of a Binomial Random Variable . . . . . . . . . . . . . . . . . . . . . . 47
  5.4 Computing Binomial Probabilities Using the Normal Curve . . . . . . . . . . . . . . . . . . . . 48
  5.5 Some Approximations Are Better Than Others  . . . . . . . . . . . . . . . . . . . . . . . . . . 50

                                WORKSHOP 9

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Day 13 (Feb. 23) handout, Slides, Area Under Z Curve (AUC.pdf)
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6 Sampling Distribution of the Proportion                                                             53
  6.1 The Sample Proportion . . . . . . . . . . . . . . . . . .       . . . . . . . . . . . . . . . . 54
      6.1.1 The Sampling Distribution of p is Approximately Normal    . . . . . . . . . . . . . . . . 55

                                WORKSHOP 10

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Day 14 (Feb. 25) handout, Slides
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  6.2 Estimating the Population Proportion p . . . . . . . . .        . . . . . . . . . . . . . . . . 57
  6.3 Estimating the Population Proportion Using Intervals .          . . . . . . . . . . . . . . . . 58
  6.4 Sample Size for Estimating the Population Proportion .          . . . . . . . . . . . . . . . . 58

                                WORKSHOP 11

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Day 15 (Mar. 1) handout, Slides
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7 Comparing Two Proportions   . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
  7.1 Estimating the difference between independent proportions . . . . . . . . . . . . . . . . . . . 62
      7.1.1 Using a confidence interval . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

                                WORKSHOP 12

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Day 16 (Mar. 3) handout, Slides
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  7.2 Statistical significance  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
      7.2.1 The P-value . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
  7.3 Risk ratio and odds ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
      7.3.1 Risk ratio  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
        7.3.2 A 95% confidence interval for risk ratio        . . . . . . . . . . . . . . . . . . . . 67

                                WORKSHOP 13

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Day 17 (Mar. 15) handout, Slides
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        7.3.3 Odds ratio  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
        7.3.4 A 95% confidence interval for odds ratio  . . . . . . . . . . . . . . . . . . . . . . . 69

                                WORKSHOP 14

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Day 18 (Mar. 17) handout, Slides
handout, Slides ------------------------------------------------------------------------------------------------------- 8 Threats to Valid Comparisons 73 8.1 Hidden Confounder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 8.1.1 Apples and oranges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 8.1.2 In the news . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 WORKSHOP 15 9 Study Designs 79 9.1 Randomized trials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 9.1.1 Double-blind randomized controlled trials (RCT) . . . . . . . . . . . . . . . . . . . . 82 9.2 Observational studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 9.2.1 Case-control studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 9.2.2 Case-crossover studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 WORKSHOP 16 ------------------------------------------------------------------------------------------------------- Day 19 (Mar. 22) ------------------------------------------------------------------------------------------------------- Review session for Exam 2. Handout sample exam with problems like workshops: --binomial, proportions, difference, risk ratio, odds ratio Spring 2013 Midterm Exam #2, Form A ------------------------------------------------------------------------------------------------------- Day 20 (Mar. 24) ------------------------------------------------------------------------------------------------------- EXAM 2: Problems similar to workshops ------------------------------------------------------------------------------------------------------- Day 21 (Mar. 29) handout, Slides, Area Under Z Curve (AUC.pdf) ------------------------------------------------------------------------------------------------------- 10 Sampling Distribution of the Mean 85 10.1 Behavioral Properties of the Sample Average . . . . . . . . . . . . . . . . . . . . . . . . . 86 10.2 Estimating the Population Mean . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 10.3 Estimating the Population Mean Using Intervals . . . . . . . . . . . . . . . . . . . . . . . 90 WORKSHOP 17 ------------------------------------------------------------------------------------------------------- Day 22 (Mar. 31) handout, Slides ------------------------------------------------------------------------------------------------------- 11 Comparing Two Means 93 11.1 Estimating the Difference between Independent Means . . . . . . . . . . . . . . . . . . . . . 94 11.1.1 Using a confidence interval . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 11.1.2 Statistical significance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 11.1.3 The P-value . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 WORKSHOP 18 ------------------------------------------------------------------------------------------------------- Day 23 (Apr. 5) handout, Slides ------------------------------------------------------------------------------------------------------- 11.2 Paired data (before-and-after) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 11.2.1 Paired data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 WORKSHOP 19 ------------------------------------------------------------------------------------------------------- Day 24 (Apr. 7) handout, Slides ------------------------------------------------------------------------------------------------------- 12 Categorical Variables: Association or Independence 101 12.1 Association versus independence in an r x c table . . . . . . . . . . . . . . . . . . . . . .102 12.1.1 Testing for statistical association . . . . . . . . . . . . . . . . . . . . . . . . .103 WORKSHOP 20 ------------------------------------------------------------------------------------------------------- Day 25 (Apr. 12) handout, Slides, Calculate Correlation ------------------------------------------------------------------------------------------------------- 13 Correlation 107 13.1 Correlation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .108 13.2 Computing the Pearson Correlation Coefficient . . . . . . . . . . . . . . . . . . . . . . . .109 14 Linear Regression (starting Linear Regression) 113 14.1 Simple Linear Regression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .114 WORKSHOP 21 ------------------------------------------------------------------------------------------------------- Day 26 (Apr. 14) handout, Slides, LS Solution is Sensitive to Outliers ------------------------------------------------------------------------------------------------------- 14 Linear Regression 14.2 Calculating the Least Squares . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .115 WORKSHOP 22 ------------------------------------------------------------------------------------------------------- Day 27 (Apr. 19) handout, Slides ------------------------------------------------------------------------------------------------------- 14.3 More on Simple Regression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .117 WORKSHOP 23 ------------------------------------------------------------------------------------------------------- Day 28 (Apr. 21) ------------------------------------------------------------------------------------------------------- Review for Final Exam. Practice Final Exam: Spring 2013 Final Exam, Form A ------------------------------------------------------------------------------------------------------- ------------------------------------------------------------------------------------------------------- Final Exam:  Section 10929 (TR 9:30am class) — Tuesday, April 26, 8:00-10:00  Section 12249 (TR 11am class) — Wednesday, April 27, 8:00am-10:00am  Section 14047 (TR 12:30pm class) — Wednesday, April 27, 2:45pm-4:45pm  Section 10934 (TRMW 2:00pm class) — Thursday, April 28, 2:45pm-4:45pm 12:30pm-2:30pm