By the time we reach voting age, almost all Americans have at least a high school education. That means we have been exposed to numerous math courses, and hopefully passed them. But that does not mean we have a good sense of numbers. Innumeracy in the modern sense means that one does not have a good grasp of statistics and probability and how they impact one’s worldview. This article by FiveThirtyEight discusses a recent study of how little the blue and red teams know about each other, a prime example of how innumeracy is causing real problems in America.
Back in the dark ages of my undergraduate degree at the Air Force Academy, terms were the still traditional 15 weeks, more or less. And after a period of adjustment to the rigors of that school, I soon found my stride and ended up near the top of my class. Much later in my doctoral program, terms were still 15 weeks and were usually long enough for most of us to get a fair understanding of the material. Now I teach online for a really very good school, but they felt the pressure from students, I think, who seem to want to believe they can learn enough by taking that same 15-week’s of content in an eight-week term. Perhaps for some courses and for some students, eight weeks might be enough. But for many of my students who are taking statistics for the first time, the eight-week terms are not working out. You see, and I hate the term, my students are “non-traditional.” All are significantly older than the kids coming out of high-school, and almost all are working full-time in demanding jobs. As suggested by Knowles, all want to see their studies producing skills they can use immediately. They do not much like spending time learning things they will not, in their minds, use. Hence, their preference for eight-week terms: the better to get done with “useless’ courses required for their degree as fast as possible.
Unfortunately, the courses I teach – statistics and quantitative methods – require mastery of fundamental concepts that lay the foundation for subsequent concepts. And, in my view for many students, forcing them to rush through critical material to keep up with the eight-week clock is not giving them that mastery. As Sal Khan explains in the following video, that approach is akin to building a house on a foundation that is only 80% complete; technically passing the assessment, but setting up students for struggles later on. So I am leaning toward mastery pacing instead of the clock; just not sure how to get that done. And I am moving from andragogy to heutagogy – adult, lifelong learners as my target students.
I found these two short videos while looking for an introductory video for my upcoming BUS 233 course. The first one is great and includes Roger Peng, “my” instructor in the Data Science Specialization I’m working on: Why You Need to Study Statistics.
The second, What is Statistics, is also good and funny, something that never hurts. It is by Scot Crawford and is set to the music of “Where are you Christmas.” But then I heard Crawford’s “500 Trials” and knew I had to share it too. Enjoy!
StatCrunch is a great statistical analysis app that resides on the web and thus works equally well for both PC and MAC users. If you are taking a stats course and do not have good Excel skills, I suggest you consider learning to use StatCrunch. My sense is that students find StatCrunch’s learning curve, the time and effort needed to get up to a reasonable skill level, is much shorter and not as steep as learning both basic Excel skills and how to use Excel’s statistical formulas to crunch the numbers. This is especially true for short time frame, i.e. 8-week term, introductory statistics classes.
StatCrunch homepage If you bought access to MyStatLab, which has StatCrunch embedded, you should be able to use your Pearson MySTatLab to log in here. If you no longer have access to MyStatLab, you can purchase a 6 or 12 month access key for $13.75/$24.20.
The Null and Alternative
The most common problem I noticed on this assignment was caused by failing to properly identify the appropriate null and alternative hypotheses. In part, this is due to the Evans text’s somewhat confusing explanation of how to do this – the “burden of proof” approach. There is a much simpler approach that always works.
First, make sure you closely read the problem statement looking for key words and phrases. This table may help:
The null hypothesis always [Read more…] about Setting up Hypothesis Tests