Tips for Writing Free Response Questions on the AP Statistics Exam

1. Tips for Writing Free Response Questions on the AP Statistics Exam Laura Trojan Cannon School

2. Common Topics • 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

3. Common Task: Choose • 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. • Think about “The Bachelor.”

4. Common Task: Compare • 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.

5. Common Task: Test of Significance • 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.

6. Writing Tips • 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.

7. Writing Tips • 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.

8. Writing Tips • 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.

9. Writing Tips • 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?

10. Writing Tips • 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.

11. Common Student Errors • 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?

12. Common Student Errors • 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.

13. Common Student Errors • 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.

14. Common Student Errors • 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!!!

15. Common Student Errors • 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!!!

16. In the end… • It’s not what you know. • It’s what you can PROVE that you know.