Mr. Rogers - AP Statistics Objectives

Syllabus 1st Quarter 2nd Quarter 3rd Quarter 4th Quarter 1 Distributions 2 N-Distribution 3 Regression 4 NL Regression 5 Data

Unit Plan Practice Test

AP Statistics Standards I. Exploring Data: Observing patterns and departures from patterns (continued) D. Exploring bivariate data Transformations to achieve linearity: logarithmic and power transformations
Objectives Essential Question: Is everything we'd like to study and model linear? Chapter 4 : 2 Variable Data Continued Modeling Non-Linear Data Explain how both power and exponential functions can be transformed into linear forms. Give examples where an exponential regression model would be appropriate. Growth or decay situations (response variable multiplied by a fixed amount in each time interval) such as: bacteria population growth the doubling of computer power radioactive decay (decay of a population of atoms) Give examples where a power regression model would be appropriate. Scaling problems: Volume & mass scale with the cube of the scaling factor Area scales with the square of the scaling factor Explain how to determine if an non-linear model is appropriate. theoretical basis such as 2 & 3 above random residuals Explain why a model should not be selected on the basis of optimizing r-square. Perform linear regression on transformed data and convert the results to the appropriate power or exponential equations. Homefun: Read section 4.1; prob. 4.1, 4.4, 4.13, 4.17	Activities Lesson 1 Key Concept: Transforms Purpose: Create a linear plot from nonlinear data Interactive Discussion: Objectives. Explain the terms concaved upward and downward. Review logarithms and explain why the common transforms use them. Demo: Use Fathom software to show that any nonlinear data set can be transformed if the equation is known. Seat Work: work example problems
Essential Question: What is the most common form of extrapolation? Interpreting Correlation and Regression Decry the evils of extrapolation. Identify possible lurking variable. (An important variable which is not included in the study.) Name the most common lurking variable. (time) State the pitfall of using averaged data. (The results look artificially good.)	Lesson 2 Key Concept: Extrapolation and lurking variables   Purpose: Understand how conclusions drawn from data can be disastrously wrong Interactive Discussion: Objectives. Explain real growth curves--usually sigmoidal.
Essential Question: Can we ever be completely sure that causation exists? Causation In other words, is the association between the x and y variables due to  the x-variable actually causing a response in the y-variable. State 4 possible explanations for getting a strong association based on regression/correlation analysis. Causation --Sometimes it's true Common response variables (affect both x & y variables), example: rum and Methodist Ministers are both affected by the common response variable of time. Confounding variables (affect the y variables but not the x), example: The shaman chants an incantation and five days later the patient gets well. Random chance Explain 4 ways that causation can be established. multiple independent studies of different types Account for control or eliminate lurking variables Turn the causative variable on and off Develop a plausible theory Homefun: Read section 4.2; prob. 4.25, 4.27, 4.29	Lesson 2 Key Concept: Extrapolation and lurking variables   Purpose: Understand how conclusions drawn from data can be disastrously wrong Interactive Discussion: Objectives. Video: use video on smoking
AP Statistics Standards I. Exploring Data: Observing patterns and departures from patterns (continued) E. Exploring categorical data 1. Frequency tables and bar charts 2. Marginal and joint frequencies for two-way tables 3. Conditional relative frequencies and association 4. Comparing distributions using bar charts
Essential Question: Can data sets be added together to obtain a larger sample size and hence more meaningful conclusion? Categorical Data & Simpson's Paradox Create frequency tables for categorical data. Convert the above tables into bar charts. Use conditional distributions based on relative frequencies to establish associations. Compare distributions using bar charts. Interpret 2-way tables. 2 variables Convert to % Interpret marginal distributions. 2 for each table, horizontal & vertical Histogram like Single variable only Calculate and interpret conditional distributions Analyze data for Simpson's paradox. Conclusions based on parts can be reversed when considering the whole Conclusions based on parts is more likely to be valid. State two conditions which must exist for Simpson's Paradox to occur. One or more lurking variables Data from unequal sized groups being combined into a single group. State how Simpson's paradox can be prevented. Avoid combining data from unequal groups into a single study Identify and include lurking variables in the study Homefun: Read Simpsons's Paradox - When Big Data Sets Go Bad prob. 4.37, 4.39, 4.45	Lesson 2 Key Concept: Simpson's Paradox   Purpose: Understand how conclusions drawn from data can be disastrously wrong Interactive Discussion: Objectives. Work through hospital example of Simpson's paradox. Individual work: Work through Simpson's paradox worksheet provided by teacher. Use Titanic data to determine if the class of one's ticket had an association with the chances of survival. Materials: Simpson's Paradox Worksheet and Titanic data.