Sequencing of Topics in an Introductory Course: Does Order Make a Difference Co-Authors: John Gabrosek | Phyllis Curtiss | Matt Race Grand Valley State University Chris Malone Winona State University

Traditional* Sequence of Topics

Descriptive Statistics Sampling Distributions Inferential Statistics Additional Topics Traditional* Sequence of Topics

Related Work - Chance, B. L., Rossman, A. J. (2001).

Traditional* Sequence of Topics Related Work - Chance, B. L., Rossman, A. J. (2001). 1. Data Analysis Data Collection 1

Traditional* Sequence of Topics Related Work - Chance, B. L., Rossman, A. J. (2001). 1. Data Analysis Data Collection 2. Bivariate Univariate Inference 2

Traditional* Sequence of Topics Related Work - Chance, B. L., Rossman, A. J. (2001). 1. Data Analysis Data Collection 2. Bivariate Univariate Inference 3. Proportions Means 3

Traditional* Sequence of Topics Related Work - Chance, B. L., Rossman, A. J. (2001). 1. Data Analysis Data Collection 2. Bivariate Univariate Inference 3. Proportions Means 4. Testing Confidence Intervals 4

Traditional* Sequence of Topics Related Work - Wardrop, Robert (1995). Statistics Learning in the Presence of Variation

Traditional* Sequence of Topics Related Work - Chance, B. and Rossman, A. (2006). Investigating Statistical Concepts, Applications, and Methods

Data: NYC Trees

Does Foliage Density tend to be larger for Native Trees compared to Non-Native trees?

Data: NYC Trees

61 vs. 56 Yes, Native trees tend to have higher Foliage Density

Data: NYC Trees 61 vs. 56 Yes, Native trees tend to have higher Foliage Density Why cannot we just reject Ho based on the fact that the average for Native Trees is 61 and the average for Non- Native is 56? Later in the semester…

Making those illusive connections A test for a single proportion is very similar to a test for a single mean

What we are thinking Test Statistic = Testing a Proportion (Native) Testing a Mean (Age)

What they see Test Statistic = But, they don’t look similar…

One Last Example Student Task: Determine whether or not more than ½ the trees in NYC are Native.

A “Good” Response Determine whether or not more than ½ the trees are in NYC are Native. A “Good” Response: There was a total of 319 trees in our sample. The percent of trees that were Native is about 55%. From the graph you can see it is above 50%. So, yes we can say that more than ½ of the trees in NYC are Native.

A “Good” Response Teacher: The 55% you’ve calculated is for your sample, correct? Student: Yes. Teacher: So, does the 55% apply to all the trees in NYC or just the trees from the sample? Student: Well, I thought it was all trees in NYC, but I guess it’s just the 319 we looked at. So, how do we make that leap to all trees? Teacher: That is a very good question. Stay tuned -- I’ll explain a little bit in Ch 5, some more in Ch 6, and we’ll finish in Ch 7! Student: What? I don’t understand this stuff! A “Good” Response: There was a total of 319 trees in our sample. The percent of trees that were Native is about 55%. From the graph you can see it is above 50%. So, yes we can say that more than ½ of the trees in NYC are Native. Getting some clarification from the student…

Descriptive Statistics Sampling Distributions Inferential Statistics Additional Topics What does a complete analysis require?

Proposed Sequence of Topics

Categorical: Singe Variable Categorical: Two or More Variables Numerical: Singe Variable Numerical: Single Variable across a Categorical Variable Numerical: Two or More Variables

Proposed Sequence of Topics Why change? 1. Students carry out a complete statistical analysis over-and-over. 2. More closely mimics what a statistician does. In particular, students identify appropriate analyses using variable types and number of levels. 3. Just-In-Time Teaching: Giving students exactly what they need, in the exact amount, at precisely the right time. 4. Starting with categorical data is easier. 5. This sequence is more intuitive.

So, does it work? Assessment Tool Description > 552 students from Grand Valley State University > 6 different instructors > 8 assessment questions -- 5 short answer, 3 multiple choice. > Exams were scored similar to AP rubric (0-4) > Fall 2005 used typical sequence, Spring 2006 used proposed sequence

So, does it work? New Traditional

Some Challenges… 1. Sampling Distributions before Means, Std Dev, Histograms, etc Required Concepts for Inference > What is the expected number of blacks? > What is the chance of seeing less than 15 blacks? > What is your cutoff for “too” few blacks?

Some Challenges… 2. Test Statistic / Unusual Outcome before Normal Distribution Concerns… > I’m not convinced that covering std. deviation for numerical data helps them understand the denominator above. > Does computing P(Z 2) really help me understand the 1/2/3 Rule better?

Conclusions > Consider what students really need to know, do they need everything we teach them? > Consider how you analyze data. Does your process of analyzing data mimic how you teach? > Students are not making as many connections between topics as we may think. > Our assessment items suggested we did not do worse, which was our first goal. > Most textbooks are not conducive to the proposed sequence.

Conclusions > Consider what students really need to know, do they need everything we teach them? > Consider how you analyze data. Does your process of analyzing data mimic how you teach? > Students are not making as many connections between topics as we may think. > Our assessment items suggested we did not do worse, which was our first goal. > Most textbooks are not conducive to the proposed sequence. Thank you!

John Gabrosek | Phyllis Curtiss | Matt Race Grand Valley State University Chris Malone Winona State University

Question #3: A computer manufacturer wants to determine if the average temperature at which a brand of laptop computer is damaged is less than 110 degrees. Thirty computers are tested to find the minimum temperature that does damage to the computer. Temperature is continuously raised until computers are no longer able to work. The damaging temperature averaged 109 degrees with a standard deviation of 4 degrees. Using significance level α =.05, conduct an appropriate hypothesis test to answer the research question. Show work and draw a conclusion. Question #2: Suppose that you want to study the question of how many Grand Valley State University students have their own credit card. You take a random sample of 1000 Grand Valley students and find that 246 of these students have their own credit card. Make an appropriate 95% confidence interval that describes credit card ownership among Grand Valley students. Interpret your interval in the context of the problem. Question #1: As part of its twenty-fifth reunion celebration, the Class of 1980 of the State University mailed a questionnaire to its members. One of the questions asked the respondent to give his or her total income last year. Of the 820 members of the class of 1980, the university alumni office had addresses for 583. Of these, 421 returned the questionnaire. The reunion committee computed the mean income given in the responses and announced, "The members of the class of 1980 have enjoyed resounding success. The average income of class members is $120,000!". Identify two distinct sources of bias or misleading information in this result, being explicit about the direction of bias you expect. Explain how you might fix each of these problems. Assessment Questions

Question #5:A teacher in a history class gives his students pre and post tests to see how much of an improvement students are making in his class. Each test is graded on a 100 point scale. A 95% confidence interval on the mean difference in test scores (pre-test minus post-test) is to Interpret this interval in the context of student achievement. Question #4: The Office of Career Services at the local state university wishes to compare the time in days that it took graduates to find a job after graduation for 2003 and 2004 graduates. Separate random samples of 75 graduates from the 2003 class and the 2004 class are selected. Tim at Career Services states, “The sample of 2003 graduates took an average of 7.3 days longer to find a job than the sample of 2004 graduates. This shows that 2004 graduates were able to find jobs quicker.” Explain the fallacy in Tim’s reasoning. Assessment Questions