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/