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

Common Topics Exploratory Data Analysis Exploratory Data Analysis One-variable data One-variable data Descriptive statistics: Center, Shape, Spread Descriptive statistics: Center, Shape, Spread Two-variable data Two-variable data Correlation, regression, residual plots, coefficient of determination Correlation, regression, residual plots, coefficient of determination Hypothesis Tests Hypothesis Tests Probability Probability Experimental Design Experimental Design

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. 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.” Think about “The Bachelor.”

Common Task: Compare If asked to compare, students should make less than/greater than statements. If asked to compare, students should make less than/greater than statements. See sample question 1 from 2005 – K1 and S1. 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. 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. 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 Hypothesis Test rubrics generally look for four components: Hypothesis Test rubrics generally look for four components: State the hypotheses with the correct symbols. Define any subscripts. State the hypotheses with the correct symbols. Define any subscripts. Identify (by NAME or by FORMULA) a test-statistic. State and check the assumptions. 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. 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. State your conclusion in words in the context of the problem.

Writing Tips Be clear, brief, and explicit. Read the question. Answer the question. No more, no less. 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. 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 D1 and U2. See sample question 1 from D1 and U2.

Writing Tips Tell students: never contradict yourself. 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. 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 write calculator commands. Never? Never. Never ever. Not even once. Period. Never? Never. Never ever. Not even once. Period.

Writing Tips Be careful about strong language. 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. 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 Be careful about the converse of if/then statements. 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 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. If the mean is greater than the median, then the distribution is skewed right. Can anyone give a counter-example? Can anyone give a counter-example?

Writing Tips Do not use pronouns! Do not use pronouns! “It is higher.” WHAT is higher? “It is higher.” WHAT is higher? Don’t use no double negatives. Don’t use no double negatives. I fail to reject that I don’t believe that the data are not independent. I fail to reject that I don’t believe that the data are not independent.

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 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. 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. Using non-statistical words to convey a statistical concept. The graph is “even.” ??? Does the student mean uniform? Symmetric? Normal? 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 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? The data are “consistent.” Does the student mean less variable?

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. 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. Not recognizing that expected value = mean. When stating assumptions, saying the data are normal. 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. 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 Confusing skewed right and skewed left. Confusing skewed right and skewed left. Confusing symmetric or bell-shaped with approximately normal. Confusing symmetric or bell-shaped with approximately normal. Confusing categorical data with quantitative data (or one-variable data with two-variable data) 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. 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. This often leads to a “parallel solution.” The graders will grade the weakest of the solutions.

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

Common Student Errors Confusing interpretations of the confidence LEVEL with interpretations of the confidence INTERVAL. 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. Failing to state their results and interpret their results in the context of the problem. Name dropping. Name dropping. Student answers, “Yes, because of the.” NO CREDIT!!! Student answers, “Yes, because of the.” NO CREDIT!!!

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