This unit covers survey design, observational studies, and experimental design. The standards involved are found under section II:
II. Sampling and Experimentation: Planning and conducting a study (10%–15%)
Data must be collected according to a well-developed plan if valid information on a conjecture is to be obtained. This plan includes clarifying the question and deciding upon a method of data collection and analysis.
A. Overview of methods of data collection
1. Census
2. Sample survey
3. Experiment
4. Observational study
B. Planning and conducting surveys
1. Characteristics of a well-designed and well-conducted survey
2. Populations, samples, and random selection
3. Sources of bias in sampling and surveys
4. Sampling methods, including simple random sampling, stratified random sampling, and cluster sampling
C. Planning and conducting experiments
1. Characteristics of a well-designed and well-conducted experiment
2. Treatments, control groups, experimental units, random assignments, and replication
3. Sources of bias and confounding, including placebo effect and blinding
4. Completely randomized design
5. Randomized block design, including matched pairs design
D. Generalizability of results and types of conclusions that can be drawn from observational studies, experiments, and surveys
We have looked at the mechanics used in selecting random samples using the table of random digits and simpler methods.
HW due Monday: Work as many problems from pages 371-373 as you need to be proficient with blocking and matched pairs design.
HW due Wednesday: an annotated vocabulary list from this chapter. Include explanations of why each term is good for design or a problem for design.
HW due Friday: Bring a printed copy of your electronic research proposal. We will be modifying it. You should go to the Cobb County School District website to see what the requirements are for research in our schools. Also go to the Institutional Review Board (IRB) site for the college you are most interested in and review their requirements. Be sure to answer all the questions these forms aske except for the statistical analysis questions.
Tuesday, October 27, 2009
Thursday, October 01, 2009
Chapter 4 Non-linear relationships
Standards: I D (exploring scatterplots, transformations to achieve linearity) and E (exploring categorical data, two-way tables, etc.).
Thursday 9/24 Today we revisited residuals and the LSRL. We looked at data that appeared at first to be linear, but upon inspection were clearly not linear. That's what residuals can do for you!
We also straightened our first data set. We took exponential data--ordered pairs of the form (x, ab^x)-- and transformed them into a straightened set. Once you have straightened data, you can use the LSRL function on the calculator. We found the LSRL, converted it to a curve using our knowledge of exponents and logs, and graphed the curve through our exponential data. Ooo. Ahhh.
Procedure: Enter x and y into L1 and L2
Look at the data. See that they are not straight, but exponential in shape.
Take the ln of the y values (put in L3).
Look at scatterplot of L1, L3. Straight? Then --> LSRL
Change y-hat to ln-y-hat because we used the ln y instead of y.
Solve for y.
Graph that new equation with the original L1, L2 data.
Be proud.
September 28th: We looked at several non-linear models and discovered what transformations would make the "right" side a linear function. Those realizations drive our decisions to take logs or square roots of the original variables.
HW: problems 4.11 and 4.12 from the text.
September 29th: We worked through parts of problem 4.12 and reviewed properties and purposes of logs. Do problems 4.15 and 4.16 for Wednesday.
October 1st: Worked with transformations more today. Finished up the analysis of the disappearing dice lab where we modeled exponential decay.
Took a quiz on residuals to give students an opportunity to recoup some points from the Ch 3 test. It worked for some. Why pass up an chance to improve your grade? A copy of one version of the quiz can be found on the Typepad blog. Scroll down to Documents for AP Statistics.
October 2nd: Quizzed again today on computing, graphing, and interepreting residuals. This concept is critical to continuing in Stat. Most students have now demonstrated mastery, but those of you who have not shown me that you can do it need to step up! HW due Monday: 4.26, 4.27. 4.28 from the text. Be prepared for the next quiz on finding residuals and transforming data.
October 5th and 6th: We've been spending a lot of time perfecting our understanding and skills regarding transformations, least squares regression, and interpreting residuals. We will have nearly daily quizzes to assess our progress. In addition we are looking at contingency tables (2-way tables). We computed joint, marginal, and conditional probability and took a quick look at the meaning of independence.
HW: Read section 4.2 and do problems 4.29 and 4.30. They are pretty cool.
Thursday 9/24 Today we revisited residuals and the LSRL. We looked at data that appeared at first to be linear, but upon inspection were clearly not linear. That's what residuals can do for you!
We also straightened our first data set. We took exponential data--ordered pairs of the form (x, ab^x)-- and transformed them into a straightened set. Once you have straightened data, you can use the LSRL function on the calculator. We found the LSRL, converted it to a curve using our knowledge of exponents and logs, and graphed the curve through our exponential data. Ooo. Ahhh.
Procedure: Enter x and y into L1 and L2
Look at the data. See that they are not straight, but exponential in shape.
Take the ln of the y values (put in L3).
Look at scatterplot of L1, L3. Straight? Then --> LSRL
Change y-hat to ln-y-hat because we used the ln y instead of y.
Solve for y.
Graph that new equation with the original L1, L2 data.
Be proud.
September 28th: We looked at several non-linear models and discovered what transformations would make the "right" side a linear function. Those realizations drive our decisions to take logs or square roots of the original variables.
HW: problems 4.11 and 4.12 from the text.
September 29th: We worked through parts of problem 4.12 and reviewed properties and purposes of logs. Do problems 4.15 and 4.16 for Wednesday.
October 1st: Worked with transformations more today. Finished up the analysis of the disappearing dice lab where we modeled exponential decay.
Took a quiz on residuals to give students an opportunity to recoup some points from the Ch 3 test. It worked for some. Why pass up an chance to improve your grade? A copy of one version of the quiz can be found on the Typepad blog. Scroll down to Documents for AP Statistics.
October 2nd: Quizzed again today on computing, graphing, and interepreting residuals. This concept is critical to continuing in Stat. Most students have now demonstrated mastery, but those of you who have not shown me that you can do it need to step up! HW due Monday: 4.26, 4.27. 4.28 from the text. Be prepared for the next quiz on finding residuals and transforming data.
October 5th and 6th: We've been spending a lot of time perfecting our understanding and skills regarding transformations, least squares regression, and interpreting residuals. We will have nearly daily quizzes to assess our progress. In addition we are looking at contingency tables (2-way tables). We computed joint, marginal, and conditional probability and took a quick look at the meaning of independence.
HW: Read section 4.2 and do problems 4.29 and 4.30. They are pretty cool.
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