Last summer I participated as a student in an online course for the first time. The topic was how to teach an online course. The course was delivered asynchronously, but it was not self-paced because there were regular due dates on assignments. Somewhat to my embarrassment, I found that I was highly motivated by the assignments and those due dates.
As I have been teaching my own students online this term, I decided to give even more quizzes than usual to motivate my students to keep up. For each topic that we have studied, I have given a handout quiz and an application quiz. The handout quizzes have often asked the same questions that we answered as we worked through the handout, while the application quizzes have asked students to apply what they learned to a new study or situation. As long as a student attended one of my live zoom sessions or watched the videos that I prepared, and paid a modest amount of attention, they should have done very well on the handout quizzes. I even allowed two attempts on these handout quizzes, recording the average score.
My final class meeting of the term occurred on Monday of Thanksgiving week. I told my students in advance that we would not study new material on that day. Instead I provided them with practice questions about identifying which inference procedure to apply for a particular question. As this is the first course in a two-course sequence, and we spent about half of the term studying probability, we have only studied inference for a single mean or a single proportion. Here’s how I summarized things at the start of the handout for this class:
- Statistical inference draws a conclusion (i.e., infers something) about a population parameter based on a sample statistic.
- A confidence interval estimates the value of a parameter with a range of values.
- A population proportion π can be estimated with a z-interval.
- A population mean μ can be estimated with a t-interval.
- A hypothesis test assesses the plausibility of a particular claim about the parameter.
- A claim about a population proportion π can be tested with a z-test.
- A claim about a population mean μ can be tested with a t-test.
- A confidence interval estimates the value of a parameter with a range of values.
The instructions that I provided for the task were: For each of the following research questions, identify which of these four inference procedures would be appropriate. Furthermore, if the research question calls for a hypothesis test, state the appropriate null and alternative hypotheses. If the research question calls for a confidence interval, clearly identify the parameter to be estimated.
The ten questions that we analyzed were:
- a) How many hours does a full-time Cal Poly student spend studying, per week, on average?
- b) Does a full-time Cal Poly student spend an average of more than 25 hours per week studying?
- c) Does the percentage of full-time Cal Poly students who were born in California differ from 80%?
- d) What proportion of full-time Cal Poly students were born in California?
- e) What proportion of people with a driver’s license in California have indicated a willingness to be an organ donor?
- f) Have less than two-thirds of all people with a driver’s license in California indicated a willingness to be an organ donor?
- g) What is the price of an average transaction at the Subway on campus?
- h) What proportion of transactions at the Subway on campus include a soft drink?
- i) Do most transactions at the Subway on campus include a soft drink?
- j) Do weekday employees at a company take sick days disproportionately often on Mondays and Fridays?
We worked through the first four of these together. I advised students to start by identifying the observational units, variable, and type of variable for each question. I emphasized that deciding whether the parameter is a mean or a proportion boils down to determining whether the variable is numerical or categorical. I also admitted that the question itself often contains a key (giveaway) word, such as average in parts (a) and (b), percentage in (c), and proportion in (d).
Next I asked students to discuss parts (e)-(j) together in zoom breakout rooms of 4-5 students per group. Then we came back together to discuss these. I pointed out that questions (f) and (i) do not use a giveaway word, so they require more careful thought. Students need to realize that the variable in (f) is whether or not the person has indicated a willingness to be an organ donor, which is categorical, so the parameter is the proportion of all people with a California driver’s license who have indicated such a willingness. The word most carries a lot of weight in (i), revealing that the alternative hypothesis is that the proportion of all Subway transactions that include a soft drink is greater than one-half.
Question (j) is a favorite of mine. Its impetus is an old* Dilbert cartoon, available here. The joke is that the pointy-haired boss expresses outrage upon learning that two-fifths of all sick days at his company are taken on Mondays and Fridays. The observational units are sick days, and the variable is whether or not the sick day was taken on Monday or Friday. The null hypothesis asserts that two-fifths of all sick days are taken on Monday or Friday, which is what would be expected if sick days were not being mis-used to produce long weekends. The alternative hypothesis is that more than two-fifths of all sick days are taken on Monday or Friday.
* I just realized that very few, if any, of my students were alive when this particular cartoon appeared in 1996. Hmm, I wonder if my university’s special incentive to take early retirement is still available.
The title of this post promised something sneaky. You might be thinking that unless sneaky has been redefined as boring, what you’ve read so far does not even come close. Please keep reading …
I have mentioned before that my course this term is asynchronous, even though I strongly encourage students to attend my optional live zoom sessions on MWF mornings. Because of the asynchronous listing, I feel obligated to make videos to accompany the handouts for the students who cannot, or choose not to, attend the live sessions. These videos show me working through the examples in the handout. I always begin by saying something like: I strongly encourage you to pause the video, answer the handout questions on your own first, and then resume the video to watch my discussion of the questions. The videos usually show me writing answers directly in the handout file, especially when performing calculations.
But this time I purposefully did not write on the handout for the video recording. Instead I only talked about the ten questions (a) – (j). For the students who ignored my advice to answer the questions for themselves before watching the video, I wanted them at a minimum to take their own notes based on what I was saying. I hope that active listening and writing might have activated their learning to some extent.
That’s a bit of sneakiness on my part, but that does not constitute the sneaky quiz mentioned in the title of this post.
Most of my handout quiz questions throughout this term have repeated questions that were asked directly in the handout. But this time students could not answer questions on the handout quiz merely by copying answers from their notes. Here are the quiz questions:
- For how many of the ten questions in this handout are Cal Poly students the observational units?
- How many of the ten questions in this handout involve a categorical variable?
- How many of the ten questions in this handout involve inference for a population mean?
- How many of the ten questions in this handout ask for a confidence interval?
- How many of the ten questions in this handout ask for a hypothesis test with a two-sided alternative hypothesis?
I hope that this sneaky approach of mine forced students to review their notes and also reinforced some ideas about how to decide on an inference method. I hope that these quiz questions reminded students, perhaps sub-consciously, to think about the observational units (question #1), the type of variable (#2), the parameter (#3), whether the question calls for a confidence interval or hypothesis test (#4), and whether an alternative hypothesis is one- or two-sided (#5).
My writing teachers from college might be disappointed that my previous two sentences both began with “I hope …” Nevertheless, I return to that construction once more for my conclusion: I hope you agree that sneakiness is forgivable, perhaps even desirable, as a pedagogical strategy when the intent is to prompt student to think without their realizing it.