I recently met two colleagues to solicit their advice on course creation, and the first thing they asked me was ‘are your students expected to run the models themselves?’

My first gut answer was ‘no’ – I want to focus on developing students’ statistical reasoning and literacy. What did the original course creators have in mind? The course description is:

Biostatistics for health science professionals. Concepts and methods, including confidence intervals, ANOVA, multiple and logistic regression, and non-parametric analyses. Scientific literature is used to provide a comprehensive context in which analytical evidence is employed to support practices in the health sciences.

The last sentence seems to imply a focus on literacy, but does ‘methods’ imply computation? The course objectives are that students in the course will learn to:

• Apply biostatistical concepts, including: probability, distribution, confidence intervals, inference, hypothesis testing, P-value and confidence interval.
• Apply numerical, tabular, and graphical descriptive techniques to health sciences data. 
• Conduct appropriate statistical procedures to test null hypotheses.
• Appraise statistical results in health science research articles and reports. 

Again, ‘appraise’ strikes me as a desire for literacy, but ‘conduct’ seems a clear indicator that computing is also an expectation. However, the weekly learning objectives from units focusing on ANOVA, multiple linear regression, and logistic regression paint a different story:

• Interpret estimates from a one-way and two-way analysis of variance. 
• Appraise procedures used to address the problem of multiple comparisons. 
• Explain prediction models that are grounded in the population regression line.
• Interpret regression coefficients from a multiple regression model. 
• Calculate and interpret chi-square test statistics.
• Interpret results from unadjusted logistic regression models.
• Identify the reasons for conducting a non-parametric test.
• Interpret estimates from non-parametric tests including the Wilcoxon Signed-Rank test, the Wilcoxon Rank Sum test and Kruskal-Wallis test. 

‘Interpret’, ‘Appraise’, ‘Identify’, and ‘Explain’ all seem like literacy skills to me, and the only computation that is being asked is a chi-squared test statistic, as well as (in other weeks) odds ratios, risk ratios, relative risks, and other descriptive statistics.

Perhaps this is the right place to draw the line between computation and literacy – I will ask my students to ‘compute’ descriptive statistics, but focus on literacy with regards to inference, modelling, and hypothesis testing.

I am curious though if it is possible to focus on both literacy and computation in the same course. I imagine students becoming stressed and annoyed with debugging with whichever software we might use. Whichever software I do choose ought to be able to do all the calculations I expect students to do in 2117 and 3117, and should be used in both courses.

I’ve increasingly come to think of HSCI 2117 in terms of the statistical reasoning I wish to develop in my students and the specific tools I wish to equip my students with.

I think of the reasoning goals as focusing successively on reasoning about data, reasoning about variability, reasoning about covariation, and finally reasoning about statistical inference.

I’ve think of the content of HSCI 2117 in terms of descriptive and inferential tools for different combinations of types of variables in the univariate and bivariate case. For example:

• frequency tables, bar charts, and binomial and multinomial tests for a single categorical variable
• summary tables, histograms, and T tests for a single quantitative variable
• joint and marginal frequency tables, stacked bar charts and line charts, and chi-squared tests for two categorical variables
• marginal summary tables, side-by-side boxplots, and ANOVA with multiple comparisons for one categorical variable and one quantitative variable
• summary tables, scatterplots, and T tests for correlation or ANOVA for a model for two quantitative variables

What is the best way to extend this foundation in HSCI 3117, a ‘second-course’ in statistics? Most of the research I’m familiar with in the statistics education literature focuses on the first course in statistics, and it seems we haven’t gotten around to second courses yet because the first course is still an open problem and we’re not satisfied with our solutions yet.

Using the framework of reasoning and content, I think reasoning about models and modelling and reasoning about sampling variability are the two most obvious pieces to develop in addition to a re-emphasis on reasoning about covariation and reasoning about statistical inference.

In terms of content, we would then cover combinations of categorical and quantitative variables as independent and dependent variables in the tri-variate case. This would include multiple linear regression (including multicollinearity and interaction terms), 2-way ANOVA, ANCOVA (and regression with indicator variables), logistic regression (including adjusted odds ratios), and Cochran-Mantel-Haenszel procedures.

In a previous post, I discuss common methods in public health literature. Therefore, in addition to the methods above, I feel I should include Cox Proportional Hazards Regression, non-parametric methods, and survival analysis.

There is a paucity of research on the second course in statistics. I do not know what is typical. However, this approach essentially means that HSCI 2117 will hopefully build a foundation of literacy and reasoning while HSCI 3117 will build students’ statistical skills.

References and further reading:

Garfield, J., & Ben-Zvi, D. (2008). Developing students’ statistical reasoning: Connecting research and teaching practice. Springer Science & Business Media.

Rao, V.N.V. (2019, March 31). Deciding course content [Blog post]. Retrieved from https://statisticaljourneys.home.blog/2019/03/31/deciding-course-content/

I recently attended a presentation on the Island and its use in a statistics class. The Island was developed by Dr Michael Bulmer, and is a simulated environment where students can practice data collection and study design.

We want our students to be able to use the statistical tools we teach in order to make data informed decisions, which means they will need to collect data first. Unfortunately, we typically hand students’ datasets in our classrooms. An appreciation of the data creation process can help to improve students’ reasoning when applying statistical analyses to the data (McClain & Cobb, 2001).

In order to develop this appreciation for data collection, I have begun brainstorming activities for students using the Island, such as the following activity:

• Select a sample of 10 different people. Select one person randomly from 10 different cities. You can select from any 10 cities you wish. To select your sample, choose an island, then choose a city, then randomly choose a house, and randomly choose a person in that house.
• Record which island they live on, which city they live in, their house number, their name, their age, their gender, their systolic blood pressure, and their cholesterol level.
• Summarize the distribution of the following traits of people in your sample: age, gender, systolic blood pressure, cholesterol level
• Share your dataset and your summaries with your classmates.

In having students share their results, we also create a window of opportunity to discuss sampling variability, one of the cornerstone topics of any course in statistics. I am looking forward to experimenting with this resource and evaluating its efficacy in developing students’ appreciation of a dataset.

References:

McClain, K., & Cobb, P. (2001). Supporting students’ ability to reason about data. Educational Studies in Mathematics, 45(1-3), 103-129.

With the green light to make as dramatic a proposal as I desired, I set to considering a new syllabus accompanied by general learning objectives in February 2019. My guiding principles were based on what I had recently learnt about statistics education research, my experiences teaching HSCI 2117, and my experience working as a statistician in the health sciences. I knew I wanted to make decisions supported by academic research, but before I went hunting for recommendations in the research literature, I sat down to plot out where my current visions lay.

New statistical reasoning course objectives

I wanted my students to walk out of my course with knowledge and skills that would allow them to use data to inform decisions. This meant I needed them to be comfortable asking a question, collecting relevant data, summarizing and describing data, and using data to make inferences. Specific modules could focus on:

• measurement – focusing on validity and data collection
• types of variables (categorical, ordinal, discrete quantities, continuous ratio scales) – the backbone to future instruction, as each of the tools I would introduce can be mapped to a subset of these four types in univariate and bivariate cases
• summary statistics and data visualizations
• modelling – focusing on ‘naming’ identified patterns from summaries and descriptions
• inference – focusing on sampling variability, likelihood as a measure, and interval estimation
• hypothesis testing – introducing both null hypothesis testing and also comparing two hypotheses or models in significance testing

While this helps me to decide on content, the specific reasoning skills that I could stress would be reasoning about data, reasoning about variability, and reasoning about inference. While we do touch on modelling, I feel that models and modelling require too much attention to include in addition to setting a solid foundation for inference in general.

Out with the old and in with the new

Furthermore, the manner in which I wanted to teach these materials was vastly different from the old standard curriculum. It is 2019 – I do not need my students to know how to use a normal probability table. No one does that any more. As such, I decided on the following changes in content:

• Exclude by-hand calculations – Although one could argue that working out equations is the only way to truly understand them, I wanted this course to be a statistical literacy course. What real value is there in having a student being able to calculate the standard deviation of a dataset by hand? I believe the answer is ‘none’.
• Exclude probability theory and probability distributions – I knew this was a recommendation of GAISE 2016, and it was something that students often struggled with. In the consensus curriculum, I think its introduced in order to facilitate calculations of test statistics by hand, a need now obviated.
• Exclude the critical value approach and tests statistics – although understanding sampling distributions is arguably an essential aspect of statistical literacy, I do not believe it is worth the trouble in an undergraduate introductory course. It is more important to develop students’ understanding of sampling variability, which can be done without specifically addressing sampling distributions at all. Since in practicing statisticians rely on p-values and confidence intervals, I decided to go with a combination of the p-value and the confidence interval approach, further diminishing value in introducing critical values and test statistics.
• Exclude the one-sample Z-test for a proportion and the two-sample Z-test for a difference in proportions – these tests are approximations of exact tests and were prevalent in an age before computers. If we are adopting a p-value and confidence interval approach, then the choice of the test we instruct is irrelevant. Why not just teach the exact tests?

Preparing for the hunt for a new text book

Satisfied with my proposed changes, I thought about how I would operationalize instruction for each of my major learning objectives, began to search for a new text book that would align with these values.

References and further reading:

GAISE (2016). Guidelines for assessment and instruction in statistics education. College report. Alexandria, VA: American Statistical Association

Garfield, J., & Ben-Zvi, D. (2008). Developing students’ statistical reasoning: Connecting research and teaching practice. Springer Science & Business Media.

Although I view 2117 as a statistics class, its title, Introduction to Statistics for the Health Sciences, reminds me that it is statistics situated within a specific context. 3117’s title, Principles of Biostatistics, makes this even clearer.

As such, I want the specific statistical skills students walk out of the course with to be well-aligned with the tasks they might be asked to do in their careers. How should I decide on content for the course and how do I anticipate what students will need?

I have professional experience as a statistician in the health sciences, and largely drew upon that experience in the past to decide on relevant content for this course. However, I wanted a stronger evidence-base for my decisions. Luckily, a recent study by Hayat, et. al (2017) sampled published papers in public health journals. I could use this to decide the typical basket of tools my students might need to be familiar with.

Hayat, et. al. (2017) found the following epidemiological terms common:

• Prevalance
• Relative Risk
• Odds Ratio
• Incidence
• Mortality
• Hazard Ratio

Hayat, et. al. (2017) found the following statistics tests common (including p-values and confidence intervals):

• T-test
• Chi-squared Test / Exact Test (presumably for contingency tables)
• Correlation tests
• Non-parametric tests

Hayat, et. al. (2017) found the following statistics models common:

• ANOVA
• Linear Regression
• Logistic Regression
• Poisson Regression
• Cox Proportional Hazards Regression
• Generalized Linear Mixed Models

These results gave me a frame from which I could choose content for 2117 and 3117. I will introduce prevalence, relative risk, odds ratios, and incidence in 2117, and introduce mortality and hazard ratios in 3117. I will introduce the p-values, confidence intervals, T-test, Chi-squared test, and correlation tests in 2117, and introduce non-parametric tests in 3117. I will introduce ANOVA and linear regression in 2117, and generalized linear models in 3117.

While I certainly don’t want to automatically perpetuate the status quo, if I wish my students to be statistically literate, especially in the field of the health sciences, then they must be familiar with these methods. However, I struggle between balancing this traditional base and exposing my students to more modern methods. It seems unlikely that many will take more statistics courses in their lives. Is it my responsibility to seize this opportunity to expose them now, at the risk of leaving them without common skills prevalent in their field?

Nevertheless, with these content learning objectives in place, I could now move on to the specific statistical reasoning learning objectives and content sequencing.

References and further reading:

Hayat, M. J., Powell, A., Johnson, T., & Cadwell, B. L. (2017). Statistical methods used in the public health literature and implications for training of public health professionals. PloS one, 12(6), e0179032.

In 2018, the research core curriculum director (my boss at GWU) and I decided we wanted to attempt a course re-design. She had for some time wanted to develop a course that would scaffold students through material to better guide and assess student learning and development through each module.

We conceived splitting each module (one per week) into three phases:

• 1) introduction – reinforcing previously learnt material, and ensuring students were comfortable with the base ideas that would be developed in the module.
• 2) knowledge development – guided learning through a series of lectures and activities.
• 3) reinforcement of the main ideas and review

Each of the phases would be made up of a different balance of lessons, collaborative activities, assigned readings, and assessments (mini-quizzes). This initial conception kept the status quo curriculum in place, and simply was a change to the learning environment.

However, neither of us were perfectly happy with the current curriculum. I had been making small changes to the course with increasing frequency – rewriting assignments, rerecording lessons, and rewriting test questions – as I gained experience and became more familiar with statistics education research literature. This resulted in the fall 2018 version of the course being almost unrecognizable compared to the fall 2016 version.

Fueled by the creative opportunity provided by our re-design initiative, as a thought exercise we decided imagine what we wanted to teach with as close to a carte blanche as feasible.