Statistics Critical Thinking in Intro Stats Roger Woodard

Statistics How many of you teach intro stats?

Statistics What do you want them to learn?

Statistics ST311 General introduction to statistics Mix of Majors Hybrid course –Part online Learn basic facts using online videos –Part face-to-face Tackle the difficult problems Supported by other students and instructor

Statistics GAISE* recommendation Stress conceptual understanding rather than mere knowledge of procedures –Calculation is not the important part –why do we do the calculation –what does the calculation tell us *(GAISE college report)

Statistics Conceptual understanding Apply statistics to answer questions –Making decisions –Be able to make logical arguments using statistics We should ask more complex questions –Require students to do more complex things that are not about the calculations –Move up Bloom’s taxonomy

Statistics An example Megacorp International is a large manufacturing company, which has tens of thousands of employees. The company knows that 30% of its employees are members of a labor union. A junior executive for the company was assigned to take a simple random sample of 300 of the company’s employees. He reported that 40% of the sampled employees were members of a labor union. His department head was skeptical and stated “We know that 30% of all employees are in labor unions, so I don’t see how you could take a random sample of 300 employees and find that 40% of them are in the unions. I think you either made an error in taking your sample or you simply faked your data. Either way I think I should put a letter of reprimand in your file.” The junior executive replied that this is just an example of random sampling variability. Is the junior executive correct that this result is reasonable based on random sampling variability? Explain your logic.

Statistics Types of questions Comparative –Method 1 vs 2 –Which is correct Is this statement correct? –By the way it is always wrong Does the model fit? –Is the normal distribution appropriate?

Statistics Why would this be painful to grade?

Statistics Why would this be painful to grade? Two answers to the question Poor organization Complete download of everything they know We need to train students to build logical arguments

Statistics Structure for good answers Sentence 1 answer the question –Give one and only one answer Sentence 2, what are the appropriate facts? –More than one sentence can be used if needed –Irrelevant facts will be penalized Avoid complete download

Statistics Structure for good answers Sentence 3, what does that imply? –Combine your knowledge with the facts to produce a logical connection –Student must show their understanding Sentence 4, how does this implication lead to the answer?

Statistics A rubric 1.Student answers the question 2.Student supplied relevant facts from the problem. 3.Student provides implications of those facts based on their statistical knowledge 4.Student links implications to the answer 5.Student does not include irrelevant facts

Statistics How do we teach it? Spend face-to-face class time doing it. –Critical thinking is the important part! –Expect students to learn the facts and calculations in the online part of the class. Have students make arguments in groups Give them examples of bad answers

Statistics How does it work? Grading is now not constrained to specific points for specific things –Holistic –Is the student communicating clearly Students are able to answer questions

Statistics Comparison of question on final exam Which of the two methods would you select for estimating the average yearly income? Included on the final –Spring of 2014 (before introduction of method) –Spring of 2016 (after introduction of method)

Statistics Comparison of question on final exam Is it correct? General discussion of value of sampling method –2014: 72% correct answers –2016: 87% correct answers Better answers –2014: 7.1% gave an indeterminate answer –2016: 2.8% gave an indeterminate answer

Statistics Conclusions We can get students to answer different kinds of questions Rubric works well Our graduate instructors are thinking –Asking what we really want the students to know We need to continue to expand the types of questions –What type of question should we ask abou

Statistics Emphasizing Critical Thinking in Introductory Statistics Roger Woodard: North Carolina State University Recent polls have shown that critical thinking skills are a top priority among employers. Many universities including N.C. State are starting programs to help students develop these skills. ST311 is an introductory statistics course at N.C. State. The majority of the sections of ST311 are taught in a hybrid format in which two hours per week of content are online and the students meet face-to-face with an instructor for one hour per week. We have used the hybrid format to emphasize the critical thinking skills. Students learn basic facts and concepts during the online component of the course. During the face-to-face session of the class we spend time on how to answer critical thinking questions. During this presentation we will discuss the structure of the course and present example questions and a rubric we use to help student emphasize critical thinking. Good answers in 4 sentences Sentence 1 answer the question. Sentence 2, what are the appropriate facts? Sentence 3, what do the facts imply? Sentence 4, how does this implication lead to the answer? Grading Rubric Student answers the question. Student supplied relevant facts from the problem. Student provides implications of those facts based on their statistical knowledge. Student links implications to the answer. Student does not include irrelevant facts.

Statistics An example: Megacorp International is a large manufacturing company, which has tens of thousands of employees. The company knows that 30% of its employees are members of a labor union. A junior executive for the company was assigned to take a simple random sample of 300 of the company’s employees. He reported that 40% of the sampled employees were members of a labor union. His department head was skeptical and stated “We know that 30% of all employees are in labor unions, so I don’t see how you could take a random sample of 300 employees and find that 40% of them are in the unions. I think you either made an error in taking your sample or you simply faked your data. Either way I think I should put a letter of reprimand in your file.” The junior executive replied that this is just an example of random sampling variability. Is the junior executive correct that this result is reasonable based on random sampling variability? Or is the department head correct and it is unreasonable to think that we would get such a random sample. Explain your logic.

Statistics Additional Examples Comparative Question As part of its twenty-fifth reunion celebration, the class of 1989 at a state university held a reunion on campus. In an informal survey, the director of alumni development asked 50 of the attendees about their incomes. The director felt the members who attended the reunion may be different from the class as a whole. A more detailed survey of the class was planned to find a better estimate of the income as well as other facts about the alumni. The staff developed two methods based on the available funds to carry out the survey. Method 1: Send out an to all 6,826 members of the class asking them to complete an online form. The staff estimates that at least 600 members will respond. Method 2: Select a simple random sample of members of the class. The selected members will be contacted directly by phone. The staff will use follow-up methods to ensure that all responses are obtained. Because method 2 will require more time than method 1; the staff estimates that they could only contact 100 members of the class using method 2. Which of the two methods would you select for estimating the average yearly income of all 6,826 members of the class of 1989? Explain your reasoning by comparing the two methods and the effect of each method on the estimate.

Statistics Additional Examples Does the model fit? A large county in a western state collects information on all single family homes in the county. The county auditor knows that there are over 100,000 single family homes in the county. She also knows, for all single family homes in the county, the size of the homes in square feet has an average of 2172 and has a standard deviation of 976. The auditor has not created a histogram of the size of the home but would like to use the normal distribution as a model for them. Would it be appropriate to use the normal as a model for these home sizes? Explain. Is the statement correct? A group of researchers was interested in the number of hours students at Mid-South State University (MSSU) spend exercising in a week. The group believes that the average number of hours per week of exercise is 6 hours with standard deviation of 4.5. One of the researchers, Dr. Jones said “There are over 40,000 students at MSSU which is clearly a large population. Therefore the Central Limit Theorem allows us to say the distribution of the amount of exercise will be normally distributed.” Is Dr. Jones correct? Explain.