Statistics can be defined as the science of reasoning or drawing conclusions from data. Its purpose is to aid people in making decisions on the basis of numerical information. Most people encounter statistical reasoning in everyday life. At the end of the course, the student should be a more critical consumer of numerical information, graphs, and descriptions of sample surveys and experiments that they see in the media.

The course can be divided into three parts. The data analysis section covers basic graphical summarization tools for analyzing one batch of measurements, comparing two batches, and studying the relationships in bivarate data. We briefly discuss collecting data by use of sample surveys. This topic introduces the basic inferential setup (populations and samples) and how to take a simple random sample. The last section of the course introduces statistical inference -- the science of drawing conclusions about models from samples.

All of the MATH 115 sections have the same general goal of introducing the student to the use of statistics in drawing conclusions from data. Most of the MATH 115 sections are currently taught using the traditional format using the text Basic Practice of Statistics by Moore. In this format, the students learn about data analysis, the collection of data by sample surveys and designed experiments, and the fundamentals of inference by lectures and assigned homework. Statistical inference is taught using the classical approach. The key idea to understand is the notion of a sampling distribution -- this idea is key to correctly interpreting a confidence interval or a statistical test.

The activity MATH 115 sections are different from the traditional sections in two fundamental ways. First, and most important, the sections are taught by means of collaborative learning. Most of the class time is spent on group work on directed activities from the Rossman and Albert text An Introduction to Statistics: Data, Probability, and Learning from Data. The instructor's primary responsibility is to facilitate this learning by interacting with the groups and answering questions on an individual student basis.

The second difference in the MATH 115 activity class is the Bayesian approach to introducing statistical inference. Students get introduced to inference by means of Bayes' rule. This approach to inference is introduced in the basic setting where the population (model) is categorical, and then the methods are extended to inference problems with one and two proportions.

The Bayesian approach is being used since it can be very difficult to get student to understand the basic ideas behind classical statistical inference, and the students may learn more about the concepts of inference from a Bayesian perspective. The Bayesian prior probability distribution provides a convenient way for students to think about the population parameter, there is only recipe to learn (Bayes' rule) to perform statistical inference, and Bayesian statistical conclusions can be more intuitive and understandable by students.

MATH 115 satisfies a math elective requirement for students majoring in Arts and Sciences. In addition, students in other colleges, such as Health, are required to take this class to fulfill a statistics requirements. Your students will have a broad selection of majors.

The mathematics level of the course is that of high school algebra. The students should have taken MATH 095 or have the equivalent math skills before taking MATH 115. It may be desirable in the future to give an arithmetic competency test to these students to ensure that they have the necessary skills.

1. You should pass out a syllabus, which contains the following:

a. You name, office location, office hours, and how to reach you (phone number and email).

b. The name of text and where to buy it (University Bookstore).

c. A brief overview of what will be covered in the class. (You can copy from above.)

d. Grading policy (see below).

e. Prerequisite - MATH 095. Tell them what this means.

f. Give Rossman's "Top Ten" suggestions for success in this class.

10. Come to class. 9. Ask questions. 8. Use office hours. 7. Don't get behind. 6. Don't get overconfident 5. Work together. 4. Read carefully. 3. Write well. 2. Have fun! 1. Think!

2. Talk about what's on the syllabus, especially the importance of coming to class.

3. Talk about the workshop approach and what a typical class will be like.

4. Pass out cards to learn about the students. You can ask them their names, major, class year. Also, this is a good opportunity to collect data that will be used in Topic 1.

5. Start doing a couple of activities from Topic 1.

An important aspect of this class is collaborative learning, so more credit is given to classwork which includes turned-in classroom and homework activities and quizzes. It is also important to test understanding, so there are three exams scheduled, the last exam given during the final exam time.

Turn-in activities and quizzes 150 pts

3 test, each worth 100 points 300 pts

Class project 50 pts

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TOTAL 500 pts

It is important to establish a routine is this class. Students may not like this format since it is too free and it appears that the instructor is not doing anything. You have to set a structure for their learning. For each class, the students should know (1) what activities will be covered (2) what the important ideas are and (3) what is coming up in the near future (turn-ins, tests, etc.)

This is my currently thinking about a good typical class. You may have to change this depending on your teaching schedule (MWF or TR) and the students in your class.

1. I open the class by asking if there are any questions form the previous class. This includes the activities done in the previous class and any homework assigned.

2. I give a mini-lecture (length 10 minutes) on the topic to be studied that day. My lecturing style is pretty informal. I do a simple example that will be similar to the ones in the directed activities. For each new idea in the ext., there is an example presented before the activities. This mini-lecture could consist of a brief discussion of the example in the book.

3. The class now breaks into small groups of sizes 2-4, working on one or two classroom activities that you assign. After they get going, you walk around the room to see how they are doing. You answer any questions on an individual basis. If no questions are asked, then you can drop into a group and ask them a question from an activity. These questions can be as simple as "How are you doing?" Your basic job is to keep the students on task.

4. With 5 minutes to go, you stop the group work and talk to the whole class. Hopefully, most of the students have finished the classroom activities assigned. In these final few minutes, you can (1) talk about what should have been learned (2) answer any questions and (3) assign activities for homework.

Important. The class works when there is a good learning atmosphere. You want to students to talk among themselves, and you want a relaxed atmosphere where students feel free to ask questions from the instructor. It is okay for the students to socialized, but they should spend most of the time working on the activities. Unfortunately, classes will vary, and students may be more or less supportive of this format. You may have to use different teaching styles with different classes. Some students will want to work alone. This is okay for a few students, but it should not be the norm.

In this sample, there is a sample survey project. The idea of this project is to give the students some experience in doing their statistical inference. Groups of 2-4 students think of two questions which they would like to ask the BGSU undergraduate student body, devise how to take a random sample, and take a phone survey. They perform a complete Bayesian inference. For each question, they formulate a prior for the proportion of interest, and compute the posterior using the Minitab macro p_disc. From this posterior, they construct a probability interval for the proportion.

A big part of this project is a written report which describes in detail all of the steps of their statistical investigation. In my experience, students generally were weak in preparing these reports. TO get better reports, it might be better to have students turn in a draft report a few weeks ahead of time. You can give students some feedback about their projects which would help in the preparation of their final report.

The computer plays an important role in MATH 115. By using the computer, the students will see that statistical packages such as Minitab are an important tool of the modern statistician. In addition, the computer will allow the students to easily perform calculations such as a standard deviation and a least-squares line. Since these quantities are easily computed using Minitab, the class can focus on the correct interpretation of these quantities instead of their computation.

Most of the computer work should be done during class time. Make a reservation for your class with Computer Services -- it is best if you make it at least a few days ahead.

Many of the activities, especially those in Topics 6-8 (bivarate data), rely on the computer. I have outlined below a list of Minitab labs that I have used in previous classes. After the students have become familiar with the basics of using a Macintosh computer and Minitab, they can be brought to the lab to perform classroom or homework activities that need an available computer.

How does the lab work?

What I typically do is prepare a short handout that outlines what will be done during that particular lab. I don't recommend writing down detailed instructions. I think it is best to tell them what to do and then walk around and assist those with trouble. If students work in pairs, then they can learn from each other.

(Can be done during Topics 1-4) Illustrate launching Minitab, entering data directly into the worksheet, graphing stemplots, dotplots, and histograms, and getting summaries. (Learn Minitab commands stem, dotplot, hist, describe.)

I had them do Activity 5.1, which compares ages of pennies, nickels, dimes and quarter. I had the data stored as a Minitab worksheet popchang.mtw in the class folder of the Sci Computing Lab folder. They get summaries by group (using the describe command) and graph parallel boxplots (using boxplot command).

Have the students get experience graphing scatterplots on the computer (using Minitab plot command) using activities in Topic 6. Data can be stored on Minitab worksheets or entered by hand.

The students work on relating patterns in scatterplots with the correlation values. I did the "guess the correlation" activity using random data stored in the worksheet rscatter.mtw. Also correlations between all possible pairs of variables can be computed for the climate conditions activity with data stored in climate.mtw. We also did the Letterman "Topic 10 Rankings" activity.

Worked on fitting line on class height and foot data. We fit lines to entire dataset and then separately to men data and women data. Used Minitab macro %fitline which produces scatterplot, gives least-squares equation, and displays line on top.

Students looked at ratings of various movies over the internet. They also played a java roulette game -- they continually played a certain bet and kept track of their winnings.

Did the yahtzee activity in computer lab. The students first played the java yahtzee game and then did the activity.

Students were given a public release from a recent Gallup Poll which surveyed family values of people sampled from 15 different countries. After answering several questions about the article, the students constructed a probability interval for the proportion of interest using a uniform prior on the values 0, .01, ..., .99, 1 and the data presented the article. The Minitab macro 'p_dsic' was used to find the posterior probabilities.

If you get to this topic, you might want to illustrate use of the Minitab macro 'pp_disc' that is used to compute the posterior probabilities in this topic.