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Tips for Writing Free Response Questions on the AP Statistics Exam - PowerPoint PPT Presentation

Tips for Writing Free Response Questions on the AP Statistics Exam. Laura Trojan Cannon School. Common Topics. Exploratory Data Analysis One-variable data Descriptive statistics: Center, Shape, Spread Two-variable data Correlation, regression, residual plots, coefficient of determination

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Tips for Writing Free Response Questions on the AP Statistics Exam

Laura Trojan

Cannon School

Common Topics Statistics Exam

• Exploratory Data Analysis

• One-variable data

• Descriptive statistics: Center, Shape, Spread

• Two-variable data

• Correlation, regression, residual plots, coefficient of determination

• Hypothesis Tests

• Probability

• Experimental Design

• If asked to choose between two things (fuel additive A or fuel additive B), students should state why they would choose one AS WELL AS why they would NOT choose the other.

• If asked to compare, students should make less than/greater than statements.

• See sample question 1 from 2005 – K1 and S1.

• Compare like things. Never compare a median of one distribution to the 1st quartile of another. Instead, compare the median of distribution A to the median of distribution B.

• AP Questions often ask students to compare one-variable distributions. They’ll need to compare some measure of center, shape, and spread.

• Common Task: Test of Significance Statistics Exam

• Hypothesis Test rubrics generally look for four components:

• State the hypotheses with the correct symbols. Define any subscripts.

• Identify (by NAME or by FORMULA) a test-statistic. State and check the assumptions.

• Calculate the value of the test-statistic. Calculate the p-value and compare it to alpha. Reject or fail to reject the null hypothesis.

• State your conclusion in words in the context of the problem.

Writing Tips Statistics Exam

• Be clear, brief, and explicit. Read the question. Answer the question. No more, no less.

• Students who ramble on and on are likely to contradict themselves. Plus, when a student is succinct, it is clear that he/she knows what the question is asking and how to answer it.

• See sample question 1 from 2005 - D1 and U2.

Writing Tips Statistics Exam

• Tell students: never contradict yourself.

• If they asked to choose between items, TAKE A STAND. Make a choice. This isn’t the time to state what’s good and bad about both items.

• NEVER write calculator commands.

• Never? Never. Never ever. Not even once. Period.

Writing Tips Statistics Exam

• Be careful about strong language.

• One sample design question asked why we randomly allocate subjects to treatment groups. If students stated that random allocation ELIMINATES bias, they were given NO credit.

Writing Tips Statistics Exam

• Be careful about the converse of if/then statements.

• If the distribution is skewed right, then the mean is greater than the median.

• If the mean is greater than the median, then the distribution is skewed right.

• Can anyone give a counter-example?

Writing Tips Statistics Exam

• Do not use pronouns!

• “It is higher.” WHAT is higher?

• Don’t use no double negatives.

• I fail to reject that I don’t believe that the data are not independent.

• Common Student Errors Statistics Exam

• Failing to realize that when the directions say “Give appropriate statistical evidence to support your conclusion” or “Justify, using statistical evidence” students are being asked to conduct FORMAL hypothesis tests.

• Failing to realize that when students write the words “on average” that they’re referencing the mean.

• Using non-statistical words to convey a statistical concept.

• The graph is “even.” ??? Does the student mean uniform? Symmetric? Normal?

• The residual plot is “half above and half below.” I think the student meant randomly scattered.

• The data are “consistent.” Does the student mean less variable?

Common Student Errors Statistics Exam

• Making assumptions about how much they should write. The amount of space left for students to answer the question is NOT an indication of how much they should write.

• Not recognizing that expected value = mean.

• When stating assumptions, saying the data are normal.

• The correct assumption is that the population is distributed normally. We check that assumption by looking at the distribution of the sample data.

Common Student Errors Statistics Exam

• Confusing skewed right and skewed left.

• Confusing symmetric or bell-shaped with approximately normal.

• Confusing categorical data with quantitative data (or one-variable data with two-variable data)

• Listing everything they know and hoping that part of it is correct.

• This often leads to a “parallel solution.” The graders will grade the weakest of the solutions.

Common Student Errors Statistics Exam

• Confusing random sampling with random allocation. They need to know the difference between taking a simple random sample and randomly allocating subjects to treatment groups.

• Incorporating blocking schemes when blocking doesn’t make sense or might actually undermine the experiment.

• Editor’s note: you can’t spend too much time on experimental design!!!

Common Student Errors Statistics Exam

• Confusing interpretations of the confidence LEVEL with interpretations of the confidence INTERVAL.

• Failing to state their results and interpret their results in the context of the problem.

• Name dropping.

• Student answers, “Yes, because of the <insert theorem name here>.” NO CREDIT!!!

In the end… Statistics Exam

• It’s not what you know.

• It’s what you can PROVE that you know.