Advanced Placement Statistics Syllabus
AP Statistics Syllabus
Course design
Statistics is a tool to make predictions and manage uncertainty. It tells us what is possible and probable. We use it in mathematics, behavior and social sciences, biology, economics, the applied science and business. This course introduces the major concepts and tools for collecting, analyzing and drawing conclusions from data.
AP Statistics is the high school equivalent of a one semester, introductory college statistics course. In this course, students develop strategies for collecting, organizing, analyzing, and drawing conclusions from data. Students design, administer, and tabulate results from surveys and experiments. Probability and simulations aid students in constructing models for chance phenomena. Sampling distributions provide the logical structure for confidence intervals and hypothesis tests. Students use a TI-83/84 graphing calculator, Fathom and Minitab statistical software, and Web-based java applets to investigate statistical concepts. To develop effective statistical communication skills, students are required to prepare frequent written and oral analyses of real data.
Students in AP statistics have already mastered most of the basic concepts covered in the course. The main focus is to develop a truly deep understanding of the concepts, and prerequisites for the different areas of analysis. Class time is filled with discussion on the how and why of the independent work students have done outside of class.
“There are three types of lies -- lies, damn lies, and statistics.”
― Benjamin Disraeli
COURSE GOALS: In AP Statistics, we will:
Skills
? Produce convincing oral and written statistical arguments, using appropriate terminology, in a variety of applied settings.
? When and how to use technology to aid them in solving statistical problems
Knowledge
· Essential techniques for producing data
o Surveys
o Experiments
o observational studies
o simulations
o analyzing data
§ graphical
§ numerical summaries
· modeling data
o probability
o random variables
o sampling distributions
· and drawing conclusions from data
o inference procedures
§ confidence intervals
§ significance tests
Habits of mind
· To become critical consumers of published statistical results by heightening their awareness of ways in which statistics can be improperly used to mislead, confuse, or distort the truth.
“A single death is a tragedy; a million deaths is a statistic.”
― Joseph Stalin
Texts: TBD
Technology:
Every student is required to have a TI-83 or 84. The textbook is designed to be used with the graphing calculator and we take every opportunity to explore the capabilities of those programs
Teacher Information:
Instructor: Mr. James Bretney
Contact information: [email protected]
Homework, Attendance, and Effort:
? The purpose of homework and other assignments is to allow you to practice what we have learned and discussed in class, to prepare you for the next time we meet, and to prepare you for tests.
? Expect daily assignments.
? Doing homework should improve your skill and understanding. Homework will be checked for completion at the end of every chapter.
? Sometimes in class homework assessments will be given to ensure that students understand the week’s material. Do not expect to do well on these or quizzes or test if you have not completed the assignments.
? You will frequently have access to answers for assignments. Answers aren't the same thing as solutions-- answers are usually an end result, whereas a solution usually has all the intermediate steps included. Having access to the answers means that you are responsible for the solution.
? Use class time to your full benefit and be actively engaged in the lesson. It is the student’s responsibility to keep track of missed notes and work and when it is due.
? Notes and/or handouts will be given most days and these should be completed and filed in your binder.
Absent Work Policy: You are expected to make arrangements to make up absent work as soon as you return to school. The week’s assignments and handouts are kept in the crate at the front of the room and daily assignments will be posted on the course website.
“Facts are stubborn things, but statistics are pliable.”
― Mark Twain
Late Work: Late work is not accepted for credit except in situations previously specified
Emergency Procedures:
? Evacuation (Fire): Exit room, turn left, go down stairway and exit building going toward the football field. Group together as a class and wait for further instructions
? Shelter in Place (Tornado): Exit room, turn left, go down stairway and turn right down the social studies hallway. Follow teacher instructions.
Academic Honesty: Collaborate responsibly and submit your own work. I value collaboration and encourage you to form study groups because it can facilitate learning, but it is essential that everyone learns the material. Collaboration has little value if each group member works only a few problems and just copies the rest. It is better to make an honest attempt at every problem and then compare and discuss your results. Academic honesty should be maintained at all times. Academic dishonesty issues will be handled in accordance with the school policy.
Academic dishonesty includes, but is not limited to:
? communicating verbally or nonverbally in order to exchange information during a test, quiz, or other assessment
? giving or receiving information during a test, quiz, or other assessment without permission
? using unauthorized materials during a test, quiz, or other assessment
? copying the work of another and presenting it as your own
? helping someone else to cheat
Course Outline
Overview: What is Statistics?
Exploring data
· Basic graphical displays: Graphs, stemplots, pie charts, dotplots, histograms, boxplots, bar graphs
· Numerical summaries: mean, variance, standard deviation, range, interquartile range, effects of transformations
· constructing and interpreting; histograms vs. bar graphs
· Features: shape, center, spread, outliers
· Numerical measures of center and spread/variability
· Mean, median, mode; Range, IQR; boxplots and the 1.5xIQR criterion for outliers
Academic Vocabulary
Data
Mean
shape
Graphs
variance
center
quantitative variables
Stemplots
standard deviation univariate data
bar graphs
Dotplots
Range
Outliers
pie charts
Histograms
interquartile
spread
Boxplots
range
Table
“Reports that say that something hasn't happened are always interesting to me, because as we know, there are known knowns; there are things we know we know. We also know there are known unknowns; that is to say we know there are some things we do not know. But there are also unknown unknowns- the ones we don't know we don't know.”
― Donald Rumsfeld
the normal distribution
? Standard normal distribution, z-scores
? Table and calculator Computations
Numerical measures of center and spread/variability
standard deviation; determining which summary statistics to use when; changing units of measurement
Comparing distributions: Side-by-side or segmented bar graphs; back-to-back stemplots;
parallel boxplots
Describing location in a distribution
Measures of relative standing: percentiles and z-scores; Chebyshev’s inequality
Density curves; Normal distributions and the 68-95-99.7 rule
Standard Normal curve and table; Nonstandard Normal curves and calculations
critical statistical analysis
Assessing normality: Normal probability plots; other graphical and numerical methods
Academic Vocabulary
Standard normal distribution
inference procedures
confidence intervals
significance tests
probability
variability
segmented bar graphs
percentiles
z-scores
Chebyshev’s inequality
Density curves
Surveys
data analysis
simulations
modeling data
z-scores
spread
back-to-back stemplots
Normal distributions
the 68-95-99.7 rule
Standard Normal curve
Standard Normal table
Experiments
observational studies
graphical summary
numerical summaries
random variables
sampling distributions
parallel boxplots
Nonstandard Normal curves calculations
critical statistical analysis
Normal probability plots
“If your experiment needs a statistician, you need a better experiment.”
― Ernest Rutherford
Examining Relationships Exploring bivariate Data
? Scatterplots
? Correlation
? Least-squares linear regression
More on two variable data
? Transformations for regression
? Categorical data
Scatterplots: Direction, shape, strength (and outliers)
Correlation: calculations & properties defining correlation; what affects correlation?
Introduction to linear regression: interpreting the slope and y-intercept in context; prediction vs. extrapolation
More linear regression: the least-squares principle and properties; on LSRL
More on Relationships between Two Variables
Transforming to achieve linearity powers and logs
Exponential models Exponential growth; log y transformation
Power models log x, log y transformation
Choosing the best model with technology
Relationships between categorical variables: marginal and conditional distributions
Establishing causation: Lurking variables; causation, common response, and confounding
Academic Vocabulary
Relationships
Bivariate Data
Scatterplots: Direction
Scatterplots: shape
Scatterplots: strength
Scatterplots: outliers
Correlation
Exponential models
Exponential growth
log y transformation
log y transformation
common response
computer aided Regression
Scatterplots
Correlation
linear regression
y-intercept
prediction
extrapolation
marginal distributions
conditional distributions
causation
Lurking variables
confounding
linear regression
Transformations
regression
the least-squares principle
Regression
residuals
residual plots
influential points
logs
log x
slope
linearity
powers
Analyzing model quality
Residuals
Unusual points in regression
Outliers
Analyzing model quality
Residual plots
Unusual points in regression
influential points
Analyzing model quality
Constructing
Analyzing model quality
Interpreting
Analyzing model quality
Calculation
Cautions
Correlation
Analyzing model quality
Interpretation
Cautions
regression
“All statistics have outliers.” - Nenia Campbell
Producing data
Planning a study
? Observational study, census, survey
? Simple, systematic, stratified, and probability random samples
? Experimental design
? Simulation
Producing Data – Surveys, Experiments, Observational Studies, and Simulations
Sampling: good and bad methods
Voluntary response; convenience samples
Simple random sample (SRS); stratified sampling; cluster sampling, systematic sampling, multi-stage sampling
Designing polls and surveys
Undercoverage, nonresponse, question wording, potential bias;
Basics of experimental design Subjects, factors, treatments, explanatory & response variables; completely randomized design
Principles of experimental design: control, random assignment, replication; placebo effect; blinding and double-blinding; multi-factor experiments
More advanced experimental designs Block designs (RCB); why block?; blocking vs. stratifying
Matched pairs designs A special form of blocking!; cross-over designs
“By the time your perfect information has been gathered, the world has moved on.”
― Phil Dourado
Academic Vocabulary
Samples
Observation
Designing polls
Undercoverage
nonresponse
Observational Studies
Simulations
Voluntary response
explanatory variables
response variables
completely randomized design
Experiment
Random
surveys
question wording
potential bias
Surveys
Experiments
Subjects
factors
treatments
bad methods of Sampling
good methods of Sampling
Simulation
Probability
convenience samples
Simple random sample (SRS)
stratified sampling
cluster sampling
systematic sampling
multi-stage sampling
Basics of experimental design
Block designs (RCB)
blocking
stratifying
Matched pairs designs
A special form of blocking!
cross-over designs
Principles of experimental design
Control
Principles of experimental design
random assignment
Principles of experimental design
Replication
Principles of experimental design
placebo effect
Principles of experimental design
Blinding
Principles of experimental design
double-blinding
Principles of experimental design
multi-factor experiments
“I can prove anything by statistics except the truth.”
― George Canning
Probability
anticipating patterns
? Sample spaces, events, outcomes
? Sum and product formulas
? Disjoint and independent events
Simulations: Basic process and examples—one where labels represent individuals; one where labels represent outcomes of chance phenomenon
Basic probability concepts Probability as long-run relative frequency; randomness; legitimate probability models; sample spaces, outcomes, events
What is Random Behavior?
Basic probability rules Addition rule for disjoint events; complement rule; Venn diagrams – union and intersection; equally likely outcomes
Independence & the multiplication rule; general addition rule Definition of independent; multiplication rule for independent events
Conditional probability General multiplication rule & tree diagrams
Independence & Bayes' theorem Proving independence; disjoint vs. independent
Academic Vocabulary
Disjointed Events
Probability
Simulations
one where labels represent individuals
one where labels represent outcomes of chance phenomenon
Basic probability concepts
Probability as long-run relative
legitimate probability models
multiplication rule for independent events
Conditional probability
General multiplication rule
Independent Events
sample spaces
outcomes
events
frequency
randomness
Independence
independent
tree diagrams
Bayes' theorem
complement rule
Venn diagram
Venn diagram union
Venn diagram intersection
Random Behavior
Basic probability rules
Addition rule for disjoint events
equally likely outcomes
the multiplication rule
general addition rule
Proving independence
disjoint vs. independent
Random variables
? Discrete random variables
? Continuous random variables
? Mean and variance
? Mean and variance for trans-
Introduction to random variables; Discrete vs. continuous; probability distributions; notation
Mean and variance of a random variable; law of large
Rules for means & variances; linear transformations; linear combinations of random variables; independence
Combining Normal random variables
Academic Vocabulary
Mean of a random variable
variance of a random variable
Rules for means & variances
linear combinations of random variables
Combining Normal random variables
notation
independence
random variables
law of large numbers
linear transformations
Discrete random variables
continuous random variables
probability distributions
Discrete
“Love doesn't read statistics!”
― Suzette Vearnon
Formations, sums, and differences
The binomial and Geometric Distribution
? Geometric distribution
? Binomial distribution
? Means and variances
? Normal approximations
Binomial & Geometric Random Variables
Binomial settings & the binomial random variable BINS; X = # of successes; introduction to calculating binomial probability
Binomial coefficient and mathematical expression
Binomial distributions: mean and variance Using the calculator; Binomial pdf vs. binomial cdf
Normal approximation to the binomial distribution; binomial simulations Estimating binomial probabilities with Normal calculations
Geometric distributions BITS; Y = # of trials up to and including 1st success; calculating geometric probabilities
Academic Vocabulary
Formations Binomial Random Variables
Geometric Random Variables
Binomial settings
the binomial random variable
X = # of successes
calculating geometric probabilities
Binomial pdf vs. binomial cdf
Geometric distribution
Binomial coefficient
mathematical expression
Binomial distributions
mean
variance
binomial probability
Binomial distribution Normal
binomial simulations
binomial probabilities
Geometric distributions
BITS
BINS
Y = # of trials up to and including 1st success
approximation to the binomial distribution
“Lack of statistics is to hide inconvenient facts.”
― Albert Bertilsson
Binomial distributions
Sampling distribution
? Sampling distributions for means
? Sampling dist. For proportions
? Central Limit Theorem
Estimating an unknown parameter
Idea of a confidence interval; connect with sampling distributions
What Is a Confidence Interval Anyway?
Confidence interval for when known Inference toolbox introduced
Confidence interval considerations Changing confidence level; interpreting CI vs. interpreting confidence level; determining sample size
Confidence interval for when is unknown: t-distributions and the one sample t interval
Paired t procedures & Robustness of t procedures
Estimating an unknown population proportion Confidence interval's for p with the inference toolbox
Determining sample size for proportion intervals
Sampling distributions
What is a sampling distribution? Moving towards inference; bias and variability
Sampling distributions of Mean and standard deviation of sampling distribution; Central Limit Theorem (CLT)
Academic Vocabulary
Central Limit Theorem
unknown parameter
confidence interval
sampling distributions
Inference toolbox
determining sample size
Sampling distributions of Mean
t-distributions
one sample t interval
Paired t procedures
Robustness of t procedures Sampling distributions
inference
bias
unknown population
proportion
Confidence Interval
inference toolbox
sample size
proportion intervals
Central Limit Theorem (CLT)
standard deviation of sampling distribution
variability
Blackadder: Baldrick, what are you doing out there?
Baldrick: I'm carving something on this bullet, sir.
Blackadder: What are you carving?
Baldrick: I'm carving "Baldrick", sir!
Blackadder: Why?
Baldrick: It's part of a cunning plan, actually!
Blackadder: Of course it is.
Baldrick: You know how they say that somewhere there's a bullet with your name on it?
Blackadder: [haltingly] Yyyyyyyyes...?
Baldrick: Well, I thought that if I owned the bullet with my name on it, I'll never get hit by it! Cause I'll never shoot myself...
Introduction to inference
Statistical inference
? Confidence intervals
? Hypothesis tests
? Power
Testing a Claim
Introduction to significance testing; Stating hypotheses
Components of a significance test: Conditions, calculations, interpretation; one-sided vs. two-sided tests; statistical significance and P-value
Inference Toolbox & Tests from Confidence Interval’s duality
Uses and abuses of tests; Statistical significance vs. practical importance
Type I & II errors, Power Type I and II error in context; connection between power and Type II error
Academic Vocabulary
Inference
Statistical inference Testing a Claim
significance testing
hypothesis
Components of a significance test: Conditions
Components of a significance test: calculations
Components of a significance test: interpretation
Components of a significance test: P-value
Confidence intervals
Hypothesis tests
Inference Toolbox
Uses and abuses of tests
Power
Type I errors
Type II errors
Components of a significance test: statistical significance
Components of a significance test: one-sided vs. two-sided tests
Statistical significance vs. practical importance
Tests from Confidence Interval’s duality
Inference for Distribution
? Confidence interval-one sample
? Confidence interval-two sample
? Hypothesis test for one mean
Significance Tests in Practice
Testing a claim about : the one-sample t test
Paired t tests
Testing a claim about p Significance tests with the inference toolbox
What if the conditions aren’t met? A brief look at some nonparametric testing options
Academic Vocabulary
Inference for Distribution
Paired t tests
Significance tests
Confidence interval-one sample
inference toolbox
conditions
Confidence interval-two sample
Hypothesis test for one mean
nonparametric testing
“Statistics, likelihoods, and probabilities mean everything to men, nothing to God.”
― Richelle E. Goodrich
Matched pairs samples
? Hypothesis test for two means
Inference for Proportions
? Confidence interval-one proportion
? Confidence interval-two proportions
? Hypothesis test-one proportion
? Hypothesis test-two proportions
Comparing Two Population Parameters
Comparing two population parameters: paired data vs. independent samples; estimating two-sample t tests and assorted df possibilities
Estimating: the two-proportion z interval
Significance test for comparing two population proportions
Academic Vocabulary
Matched pairs samples
Hypothesis test for two means
Inference for Proportions Population Parameters
paired data
independent samples
Confidence interval-one proportion
Confidence interval-two proportions
estimating
Two-sample t tests
assorted df possibilities
Hypothesis test-one proportion
Hypothesis test-two proportions
the two-proportion z interval
Significance test
Inference for tables: Chi-Square
? Chi-square distribution
? Goodness of fit
? Test for independence
? Test for homogeneity
Inference about Distributions of Population Proportions
Chi-square goodness of fit test
The chi-square family of distributions
Chi-square test of homogeneity
Independent SRS's or randomized experiments
Chi-square test of association/independence
Distinguishing between homogeneity and association/independence questions
Academic Vocabulary
Chi-square distribution
Goodness of fit
Chi-square goodness of fit test
Chi-square family of distributions
Test for independence
Chi-square test of association
Chi-square test of independence
Test for homogeneity
Chi-square test of homogeneity
Independent SRS's
randomized experiments
“I have studied many languages-French, Spanish and a little Italian, but no one told me that Statistics was a foreign language.”
― Charmaine J. Forde
Inference for regression
? Confidence interval for slope
? Hypothesis test for slope and
Review of Linear Regression – conditions for inference for regression
Standard error about the regression line, Confidence Interval for slope
Significance tests about Nasty formulas; computer output; inference toolbox
Academic Vocabulary
conditions for inference for regression
Standard error about the regression line
Confidence Interval for slope
Test for independence
Significance tests about Nasty formulas
Correlation
Test for homogeneity
Significance tests about computer output
Significance tests about inference toolbox
Review
? Review past open response
? Two day final exam
AP Statistics Practice Exams will be used throughout the year and AP exam review days are built into the schedule. Although there will be time allotted in class to review, you will be required to take practice tests and review on your own time as well. We will use the 5 Steps (which will be provided to all AP Statistics students) book for review purposes.
You may use your calculator and the standard AP Statistics formulas and tables handout when taking these exams. We will review answers to these practice exams in class and then you will need to review the detailed explanations of answers for those questions that you do not answer correctly.
“Statistics are no substitute for judgment.”
― Henry Clay
AP EXAM REVIEW (6-10 days)
- Practice Exam
- TPS Part Review Exercises
- Practice AP Free Response Questions
- Mock Grading Sessions
- Practice Multiple Choice Questions
AP STATISTICS EXAM (1 DAY) – Thursday, May 12th, Noon – mark your calendars now and make sure you take off work, the exam is slotted for 12:00 noon to 4:00 pm.
AFTER THE AP EXAM:
- Students complete a final project, alone or in pairs, on a topic of their choice. The purpose of the project is for students to demonstrate an understanding of the major conceptual themes of statistics.
- Students will be graded based on the following tasks:
- Topic/Study Design Proposal – detailed research question, rationale, proposed study design, and method of data analysis
- Progress Report – summary of project progress after one week
- Participation – use of class time, daily effort on completing project
- Written Report – final report including written descriptions of the research question, rationale, study design, raw data summary, exploratory data analysis, inferential procedure, interpretation, conclusion, obstacles encountered and suggestions for further analysis
- Oral Presentation – 10-15 minute class presentation of the project utilizing visual aids
Expectations of students: Responsibilities and Respect
- Use core values of hope, respect, responsibility, courage, justice, compassion, integrity and wisdom.
- Follow school policies according to the handbook.
- No gum chewing will be allowed in class.
- Follow class rules:
- Follow Directions
- Raise Your Hand
- Stay in Your Seat
- Be Respectful
- Try Your Best
- Be on time for class. You will be marked tardy if you enter the class after the door is closed.
- Arrive to class in compliance with the Dress Code as stated in the handbook.
- Be prepared for class with all required materials. Do NOT leave materials in the classroom.
- A lot of sharpened pencils! Do NOT ask teacher for a pencil – YOU are responsible
- Your personal Agenda book
- A notebook
- Your personal assigned math textbook –- Replacement fee TBD.
- Enter the class respectfully and begin working on the do now as soon as possible.
- Ask questions if you are unsure. Teacher available during lunch by appointment only.
- Use your integrity when doing your work because it should show what YOU know – not what your classmate knows or what you can read out of the back of the book.
- Academic dishonesty and/or cheating will not be tolerated and will be dealt with accordingly.
“Many people that have been through the unemployment system realize that the corporate government unemployment statistics only report the short term unemployed and the long term unemployed and disabled are ignored.”
― Steven Magee
Expectations of students: Behavior
All students should follow the Code of Conduct at all times. A violation of the code, disturbance in the learning environment, or inappropriate behavior for school will result in an appropriate consequence as directed by the student handbook.
Expectations of students: Attendance
- Students are responsible for all missed learning and making up missed work or assignments, since all assignments are included in this syllabus, you are responsible for completing assigned work when you are absent.
- Students are expected to discuss with the teacher any missed work and assignments.
- Emailing teacher is best method of communication – [email protected]
- Missed work must be completed in the same number of days as the length of the absence, up to a maximum of one week.
- After the allowed amount of make up days, the assignments will be marked as a ZERO. Tests and quizzes must be taken either that day the student returns or the next day.
- It is suggested that each student have classmates that they can contact in case of an absence to contact and get information about what was missed.
“I guess I think of lotteries as a tax on the mathematically challenged.”
― Roger Jones
Evaluation (Grading):
Your grade in this course will be determined by your performance on tests, quizzes, homework, graded assignments, projects, and exams. Late work (other than the daily homework) is penalized 10% per day and will not be accepted after a Unit test.
- Formal Assessments – 75% of grade
- Tests Tests will be given about once every other week. Corrections with reflections may be made on any test for up to half-credit. I will provide more information following our 1st test.
- Quizzes There will be occasional announced or unannounced quizzes on course content. Corrections are generally not available for quizzes.
- Projects I will distribute a grading rubric with each project (Special Problem). If you have a group project - remember that each member of your group will earn the same grade, and that I expect you to do an equal amount of work.
- Practice – 25% of grade
- Homework Homework will be inspected and/or collected regularly, 10 points maximum. For each assignment, a t (7-8 points) will be awarded for a satisfactory effort to complete all assigned questions according to directions provided in class. A t+ (10 points) may be awarded for exceptional work, and a t- (1-5 points) may be awarded for incomplete work or for failure to follow prescribed format. You will receive one HOMEWORK PASS per trimester that you may submit in lieu of an assignment. You may also "redeem" an unused pass at the end of a quarter for 10 points. Incomplete homework will not be tolerated. Late homework will be awarded at most 5 points.
- Graded assignments Computer assignments, activities/labs, CSA’s, and cumulative reviews will be scored on their statistical accuracy, organization, appearance, and communication quality. The purpose of these assignments is to draw connections between all aspects of the statistical process including design, analysis, and conclusions.
- Exams There will be exams modeled off of the AP exam scheduled at the end of the 1st on November 13th and 2nd trimester on March 4th. Due to the AP exam in May and the nature of an AP course, there is no Final Exam for this course.
“99 percent of all statistics only tell 49 percent of the story.”
― Ron DeLegge II
Grading Scale: The school grading scale will be used, (A: 90 - 100, B: 80 - 89, C: 70 - 79, D: 60 - 69, F: 0 - 59). Semester grades are comprised of two quarter grades (at 40% each), and an objective final exam (20%).
High expectations are required for a successful mathematical experience. To meet these expectations, appropriate conduct and effort is required of you.
I am taking responsibility for textbook numbered _______. This textbook must either be returned to school in the same condition it was given or paid for in full at a price of $107.
I, , have read and understand this syllabus. By signing, I accept all terms and agree to do my personal best to ensure a positive school year.
Student’s Signature Guardian’s Signature Date
“Regression analysis is the hydrogen bomb of the statistics arsenal.”
― Charles Wheelan