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Modernizing Intro to Stats

  • 1.  Modernizing Intro to Stats

    Posted 03-10-2023 11:09

    Hello Everyone, 

    Since I've been laid off from teaching a few places, I've gone back to tutoring students in Math, Stats, Chem, Physics, etc. 

    I've had lots of students come in for help with their intro to stats classes. It's abundantly obvious to me that their profs were pure mathematicians and are merely going through the motions of teaching stats. I've also had to modify how I teach my stats classes to help my students get better grades with their online hw sets. 

    All of my students are expected to have a TI-83 or better calculator. If they don't, I have 18 I can lend out to them. I bought them with my meager salary for about $10-15 each, used. I show them how to use their calculators to the fullest extent and give them test problems were they need those skills. However, I keep having to take time away from teaching useful things to explain to my students, both in class and tutoring, that the problems they see in the online hw and on the other profs tests assume its 1923, NOT 2023. 

    For example, yesterday, I had to discuss how to calculate confidence intervals with 4 students. The problem that came up each time was, Part A) Find the point estimate, B) Find the Margin of Error, C) Find the xx% confidence interval. The online problems HAD to be done in that order. Each time, I had to discuss the use of the Z-table or the (woefully inadequate) T-table in the back of the book. We had to discuss how when n1 + n2 > 30 or 45 or 60, they should just use the Z-value instead of a t-value. Then, we worked on online HW problems where the answers were either answered using typical software or a TI-83/84 calculator and NOT what the textbook said. Other times, we had to use the Z approximation. 

    Meanwhile, their calculators allow them to answer the same questions using the various confidence interval functions. But, they'd have to answer it as: A) What is the Point Estimate? B) What is the xx% confidence interval? c) What is the margin of error? Doing the problem in this order allows students to get through problem in seconds instead of minutes. There is a lot less frustration too. 

    Along with those issues, there are also the normal approximation methods for the Binomial and Poisson distributions. These are basic functions in a TI-83. No need for them anymore. But, in order for my students to get the points on their online HW, I have to waste class time and say, "Sometimes we have to assume it's 1923 and this is how we will answer these questions." Which almost always brings up the question, "Does <programming language/package> solve problems this way?" Since the answer is "NO", I then have to explain why they will be tested on, or given hw problems based upon, the approximation methods, and the exact values from the calculator/software. Which adds to their frustration AND increases the amount of time they have to waste on exams and doing hw. 

    There are dozens more things I could complain about too. But, for now, I think this is enough. 

    Anyone have any ideas and factually based good reasons why we insist students assume it's the 1920's? 

    Thanks again! 



    ------------------------------
    Andrew Ekstrom

    Statistician, Chemist, HPC Abuser;-)
    ------------------------------


  • 2.  RE: Modernizing Intro to Stats

    Posted 03-13-2023 09:59

    I can't think of any good reason - unless we are training statisticians. But in the vast majority of cases, we are not teaching people who will be statisticians. I'm with you Andrew on this one. Here's an article I wrote up on this, wondering why we continue to insist on teaching people the mechanics and steps. If we leveraged the technology and software, we could do so much more in teaching students how to be better consumers of statistical methods, how to use them appropriately. And then we wonder why there is so much mis abuse (mostly due to ignorance) of statistical methods?

    https://medium.com/towards-data-science/redesigning-the-traditional-statistics-class-to-teach-data-consumers-8c057e55ddc4



    ------------------------------
    Willis Jensen
    HR Analytics
    W.L. Gore & Associates
    ------------------------------



  • 3.  RE: Modernizing Intro to Stats

    Posted 03-13-2023 21:50

    Over the last few years, the students in my classes have gone from being more 40% business, 40% nursing, 20% other to like 80% business, 20% other. For those business majors, I know they will take a "Business Stats 2" class. Everyone else, it's one shot. I know that 100% of my students are not, and never will even consider, stats or data science as a possible major or minor. So, I look at it through the lens of, "If I don't say anything, they will NEVER know. So, I best speak up." 

    One of the fun things I get to do with my students, because I don't waste too much time with the meaningless mechanics and pointless approximation methods, is discuss the difference between statistical significance vs practical significance and decision making with help form stats. Today, we looked at Medication A vs B. We found Med B was "Significantly different and better" and asked, " If Med A is the standard of care, should we now switch to Med B?" The textbook leads one to believe "Better is better, so switch." I threw in some other issues to think about. Like, when my G'ma had her meds switched from cheap to expensive meds. The expensive meds cost so much, she took a few per week instead of 1 per day. I asked the moral question of, "Is it better for someone to take a less effective med as prescribed or a more effective med less often than prescribed?" My argument was cheaper as prescribed is better because we know the benefit/cost. We don't know much about not taking meds as prescribed. 

    That type of dialogue doesn't occur in most intro to stats classes. But, that involves critical thinking about real world examples and how to use stats to answer it.... 

    Sadly, this approach doesn't work well with standardized tests. But, id rather have students with critical thinking skills for real world problems than "The smartest class" when it comes to a dept final. 

    I'll take a look at your article soon. Thanks for that.  



    ------------------------------
    Andrew Ekstrom

    Statistician, Chemist, HPC Abuser;-)
    ------------------------------



  • 4.  RE: Modernizing Intro to Stats

    Posted 03-14-2023 11:31

    I love this thought Andrew - I think Stats courses should be critical thinking courses on how to reason with data. How to make good decisions with data and recognizing the limitations of data. They should be taught more like law school classes than mathematics classes. I'm thinking of a law school case study approach where you argue and debate both sides of a conclusion and consider the evidence for or against that conclusion. To see how the data support the conclusion and the potential ways the data might not support that conclusion. 



    ------------------------------
    Willis Jensen
    HR Analytics
    W.L. Gore & Associates
    ------------------------------



  • 5.  RE: Modernizing Intro to Stats

    Posted 03-14-2023 11:48

    I am not in academia so certainly take this thought with a grain of salt (or less).

    I agree that teaching students (and even especially some faculty) how to think about data collection, analysis, and interpretation in a more practical manner would be great.  But are not such "statistical service courses" sanctioned by the applied departments?  (Political Science, Nursing, Biology, etc.)  If you remove the most of the technical aspects, would not all those departments decide that they could handle that better with their subject matter knowledge resulting in statistical service classes disappearing followed by statistics departments disappearing?

    Isn't that already happening in the real world with everyone with access to R thinking they're a statistician?  (I'm thinking of Rodney Dangerfield: "I don't get no respect".)

    Jim



    ------------------------------
    Jim Baldwin
    Retired
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  • 6.  RE: Modernizing Intro to Stats

    Posted 03-14-2023 14:24

    Well, there are a lot of "service" courses in stats. 

    Right now I am teaching an Intro to Stats class through a Math dept at a comm coll. I'm also teaching a service stats class through a university health dept. Most of the concepts are the same. But, the health dept course requires some extra material. At this university, the math and stats dept offers 4-5 different versions of algebra based intro to stats. Then, there are all the other departments that offer their versions of stats classes. 

    With the exception of the 2 course sequences in stats i.e. Business Stats 1 and 2, Psych Stats 1 and 2, etc, it would be really easy to cover all the different topics covered in all those different departments in one class. But, you'd need to remove pointless topics and use relevant examples. With the discussion about Med vs Med B, and which one do you actually choose, that is both a medical and business decision. For those student and departments that ask, "When are we (or my students) going to use this stuff?" They realize there is more to making a decision than "Is there a statistically significant difference?" If you can get students and departments to realize that the math dept version of a stats class is relevant to what they need in their dept, you can start to get rid of the service courses, which are usually taught by someone who uses stats a lot. Not someone that has a stats degree. So, you can start to do away with the misinterpretation of stats these service courses tend to provide. Like, when you do ANOVA, you don't need to make corrections for multiple comparisons.... (Which actually IS NOT in the basic stats textbooks I tend to use!!!) or if you have X1 to Xn, vs Y, they will do 'n' simple linear regressions or correlation analyses. instead of one multiple linear regression. 

    If you want a theory based class(es), most of the time that would be a Math Stats 1 and 2 course sequence. 

    I think it is a great service to all humanity if statisticians taught stats classes and showed how and why you do things they way we do. Unfortunately, most statisticians don't know where you would use stats. Most programs DON'T encourage students to take classes outside math and stats. If they do, it's usually a mat hand stats related course. Which means, those business case uses are a foreign idea to statisticians. (Which leads to the assumption that academic statisticians won't do well outside of academia.) True or not, doesn't really matter.  



    ------------------------------
    Andrew Ekstrom

    Statistician, Chemist, HPC Abuser;-)
    ------------------------------



  • 7.  RE: Modernizing Intro to Stats

    Posted 03-14-2023 14:04

    I agree, Willis.    At least for non-specialists, I think a Stats course should be, as much as anything, about critical thinking about evidence and of the validity of methods used, etc.  A confidence-interval procedure, for example, may provide evidence about a likely range of values for the parameter....  But the procedure getting you there requires assumptions to be made, such as about the likely true distribution of the population.  That's why I think typical textbook problem sets can be misleading:  For simplicity, they gloss over the assumptions issue; so that twenty calculation problems in a row about linear regression all neatly assume linearity assumptions apply. 

       Since now every student has a stats calculator or software at hand, why not expect them to double check, graphically or in other ways, how well the needed assumptions are satisfied... and have them reflect on the implications for their conclusions. 



    ------------------------------
    William (Bill) Goodman
    Professor (Retired) and Adjunct Professor, Faculty of Business and Information Technology
    Ontario Tech University
    ------------------------------



  • 8.  RE: Modernizing Intro to Stats

    Posted 03-14-2023 13:45

    Here is a related paper that will be appearing in the Journal of Statistics and Data Science Education soon:

    Teaching Statistical Inference through a Conceptual Lens: A Spin on Existing Methods with Examples

    Please note that the paper has not been typeset yet, and the figures are at the end of the paper.



    ------------------------------
    Mortaza Jamshidian
    California State University-Fullerton
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  • 9.  RE: Modernizing Intro to Stats

    Posted 03-14-2023 14:27

    Mortaza,

    This is one step in the right direction but there is still a huge gap in what most students need. Your suggestion removes the need to look up tables and using approximate formulas. However, you are still having students work with formulas and equations for simple hypothesis tests. In my analogy in the paper above, this is still focused on training a mechanic who is working on a car. 

    My belief is that for most students, we need to help them be good drivers rather than mechanics. A mechanic understands how all the parts work together under the hood. A driver understands how to start and stop the car and steer in the right direction. You can be an excellent driver with little understanding of what is happening underneath the hood. 

    When it comes to working with data, I believe you can be a thoughtful consumer of data analysis output without knowing any of the formulas that lead to that output. With the advances that are happening in AI, it is now possible for the computer to automatically do the correct statistical analysis of a set of data without you needing to determine the right approach. There won't be need to memorize flowcharts of which hypothesis test to use for which type of data. 

    I believe we need to de-emphasize hypothesis tests and spend more time on data visualization. Less time on statistical significance and more time on interpreting graphs. Less time of concepts of probability and probability distributions and more time on real-world variation. Less time on data analysis methods and more time on good data collection and all the ways you can be misled depending on how the data are collected. More time on determining the questions we are trying to answer, assessing whether the data we have matches that question and evaluating how the analysis output gives us the answer to the question. 



    ------------------------------
    Willis Jensen
    HR Analytics
    W.L. Gore & Associates
    ------------------------------



  • 10.  RE: Modernizing Intro to Stats

    Posted 03-13-2023 17:25

    It's especially sad that you're having to raise all these same questions and issues 15 years after I finally found a publisher to run for a while with my textbook "Modern Statistics"  (Nelson Education Limited, Canada, ISBN: 978-0 17 625179-6)   I dispensed totally with z and t tables and the rest, as well as things like the calculation formula for linear regression---which is totally non-intuitive about what it means, and makes sense only if you expect to do all the calculations manually). I got some good reviews for the book, and a few campuses besides my own used it for awhile; but the publisher told me there was resistance because it didn't include  the standard tables, and I never made it to a second edition.  Keystrokes for running calculations on specific statistical software were discussed in sidebars, rather than in the main text. As the sidebars got dated, I (and a few loyal others) just needed to provide students with updated slides or handouts about the software's changed sequences. 

    Alas, my book languishes, dormant but not out of print at TopHat, to whom Nelson's sold their post-secondary booklist.  They told me there was a way to get it declared out of print...     If it's useful for anybody, maybe I'll do that and then post the whole thing someplace for free download.  Meanwhile, I see there's a few cheap copies available from Amazon and the like.



    ------------------------------
    William (Bill) Goodman
    Professor (Retired) and Adjunct Professor, Faculty of Business and Information Technology
    Ontario Tech University
    ------------------------------



  • 11.  RE: Modernizing Intro to Stats

    Posted 03-13-2023 22:03

    Sadly, when I hear people in chatrooms on other sites, they tend to discuss how "you need to know the math behind the calculations." Which, I agree is important if you are going for higher level courses in stats or data science. But, the next question is, "What math are they doing?" 

    In my algebra level stats classes, they have the algebra level math formula. In a Calc based stats class, they use calculus. But, no one in their right mind would use ANY of those formulas to write code to do it that way. Computers use the pseudo inverse to get 'm' and 'b' from Y = mX + b. They use that same method for Y = B0 + B1X1 + B2X2 + ...... So, we have the question about, "What math do you use?" 

    Having taught Business Stats, Biostats, intro to Stats, etc, I know that they all have different topics covered too. For my students, I teach the topics from my business stats classes and modify that for my biostats students. I cover the exponential distribution and give example problems based upon dose curves, mttf, etc. Any one of my students that get into business, will know that you should look at the total cost of a part, not just the upfront cost (i.e. don't be like some of the Big 3 Automotive companies... .especially in the 80's.) 

    I'll take a look and see if I can get a copy of your book. If it hasn't been printed in a while, it'll be used. So, sorry about no royalties to you. 

    Thanks. 

      



    ------------------------------
    Andrew Ekstrom

    Statistician, Chemist, HPC Abuser;-)
    ------------------------------



  • 12.  RE: Modernizing Intro to Stats

    Posted 03-14-2023 14:34

    I would love to see a copy of that book - I think it would be totally valuable if you are able to share something. At a minimum, I would love to see the table of contents to understand the structure of the book. 



    ------------------------------
    Willis Jensen
    HR Analytics
    W.L. Gore & Associates
    ------------------------------



  • 13.  RE: Modernizing Intro to Stats

    Posted 03-14-2023 18:14

    I'll second Willis' request for a view of your book's table of contents.  Would be very interested to see the structure.



    ------------------------------
    Gregory Erkens
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  • 14.  RE: Modernizing Intro to Stats

    Posted 03-14-2023 19:46

    For anyone interested, I've tracked down my book's proof set for the contents and intro sections, etc.   Please feel free to email me at    bill.goodman@uoit.ca  and I'll be happy to send you a copy.   At the Table of Contents level, the book looks fairly conventional, but some of the other pages describe my objectives and so on. 

    Hope that helps.  



    ------------------------------
    William (Bill) Goodman
    Professor (Retired) and Adjunct Professor, Faculty of Business and Information Technology
    Ontario Tech University
    ------------------------------



  • 15.  RE: Modernizing Intro to Stats

    Posted 03-14-2023 18:11

    Great thread!  Thanks to everyone for their thoughts thus far.  Don't have a lot to add outside of what's already stated, but I'll add my $.02 with the hope that it's worth more.

    I'm a first-year teacher for the small set of students, and I take the following approach:

    1. CIs assume the Normal distribution, so I make time to discuss and reinforce the properties of that distribution. 
      1. The calculations reflect the symmetric properties of the distribution. (Which leads us to ask, "What if the data are not Normal?")
      2. The impact of the variance and sample size on the confidence intervals.
    2. CIs are also presented in the context of other topics -- such as DOE and capability analysis (my co-teacher and I use the SAS-JMP STIPS training), so students have some context for why the calculations are meaningful.

    In short, the calculations are not viewed as an end but as a means to understanding other concepts and the inevitable encounter with Murphy's Law.

    I'll also note that the STIPS class from SAS is pretty good.  Class and JMP (available via VM) are also free while using the class, and many of the topics discussed in this thread are also covered in that class.  JMP also allows for easy visualization and interacting with data without the need for coding.



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    Gregory Erkens
    ------------------------------



  • 16.  RE: Modernizing Intro to Stats

    Posted 03-17-2023 13:10

    I am a big fan of these types of software.

    When I teach at a community college, I can't assume my students have access to software other than something like Excel. So, I use Excel. Even then, I get yelled at for NOT teaching students how to use their calculator...  which I do. In my current non-comm coll classes, I expect everyone to use SPSS. For them, its the department's preferred program. So, they get how to do calcs in both Excel, SPSS and I'm writing scripts for one of my students who wants to do everything in Python. 

    I used JMP to do some foundational work for what was supposed to be part of my PhD Dissertation. But, I got kicked out of the PhD program because I took 1 class in 3 years(I signed up for a dozen. The other 11 got cancelled due to low enrollment. Apparently, when I am the only one signing up for "Advanced ...." the dept won't let that run.) , didn't have a research advisor, no plan of work either. I did notice that the newer version of JMP I am using doesn't have the same features of the edition I had used. Which makes using it for my research plans difficult. 



    ------------------------------
    Andrew Ekstrom

    Statistician, Chemist, HPC Abuser;-)
    ------------------------------



  • 17.  RE: Modernizing Intro to Stats

    Posted 03-17-2023 13:23

    Something that came up in my class on Wednesday, I was teaching ANOVA to my students. I know that ANOVA can do everything a 2-sample pooled T-test can do. But, ANOVA can compare 2+ groups. T-tests can only do 2. I would think for the betterment of humanity, we should be focusing more time on ANOVA and Regression in intro classes than we do. And try to eliminate the use of Paired and 2-Sample T-tests as much as possible. It would also save a lot of time during discussions in class where I say, "Can I be honest? The material we discuss to day gives you the same results as last time. Today's methods are better. But, because its required, we did it anyway."  

    The reason for that is, ANOVA and Multiple Regression methods allows you to change more than one thing at a time during the experiment. T-tests can only handle 1 change. Since most scientists claim, "You can't change more than one thing at a time during an experiment, because statistics doesn't allow it." Making sure everyone knows this is wrong, would mean future scientists will have better tools for doing data analysis. Had this been done sooner though, I would have an MS in Env Sci instead of MS Degrees in Applied Mathematics and Applied Statistics. 



    ------------------------------
    Andrew Ekstrom

    Statistician, Chemist, HPC Abuser;-)
    ------------------------------



  • 18.  RE: Modernizing Intro to Stats

    Posted 03-18-2023 15:04

    Even if versions of ANOVA can, in some ways, do better what can also be done with two-sample independent or paired t-tests, I can still see educational value presenting the t-test versions first.   (By all means, doing it without not bogging down in mechanical calculations.  For example, I've experimented using resampling, and found it's quite hard to find or concoct example cases where it makes any practical difference whether you treat the independent samples as having "equal variance" or not.   Instead, in a class problem, I'd simply ask students to justify the best-guess decision they make about the equal variance, based on e.g. graphical considerations.) 

    But the t-test approaches, I find, are helpful for introducing the dependent versus independent sample distinction simply, and giving class problems that require recognizing which applies.   

    Even with software, ANOVA can get tricky to implement.  For example, for repeated-measures ANOVA, some software requires you to call up Generalize Linear Methods, rather than go through ANOVA at all, on the menu sequences. So my concern with skipping directly to ANOVA, is students' facing all these complications, before they've grasped for underlying distinction. 

     The analogy isn't perfect, but I'm reminded of first being taught physics in a simpler Newtonian and Bohr's-model framework, and only getting into Valences and so on later in the course sequence

    Does this make sense?



    ------------------------------
    William (Bill) Goodman
    Professor (Retired) and Adjunct Professor, Faculty of Business and Information Technology
    Ontario Tech University
    ------------------------------



  • 19.  RE: Modernizing Intro to Stats

    Posted 03-19-2023 15:42

    Because of the limitations I have when teaching ANOVA to my Comm Coll Students, I use T-tests to determine if some of the groups they see are "Statistically Significantly Different" from each other. I have my students use a formula: P(All pairs right) = P(Any Pair Right)^(# Pairs). Because we are using calculators and not good stats software, I have to work with what I got. I tell them that the way we are going it is NOT 100% correct. But, I do it like this to reinforce that fact that we need to make changes in our cut offs for P-values based upon the number of comparisons we make. This is something that most of the Stats textbooks I've used do not discuss. I've yet to see a poster done by any scientist or social scientist that does this. So, I figure I have to discuss it while we can. 

    When we discuss ANOVA in an intro class, there is no discussion about "repeated measures".... Unless you take me. Then we talk for say 20 mins one day about "Dependent" vs "Independent" samples. Usually I discuss this in terms of a Survey Data gathering. Ex: If I ask you by yourself, in a room where only you and I know what you said, and if I tell ANYONE or give ANYONE hints about what you said, I must pay you $1,000,000 a week for the rest of your life, what would you say about whatever. That is independent. If I ask you the same question say in front of your family, friends, or someone you want ot date, will your answer change? Probably. That is a dependent answer. 

    We also discuss some other issues that come up. However, I don't give them repeated measures or dependent data to work with. 

    For the paired T-tests, we do those as is. Then, while discussing linear regression, analyze them again as Y(After) =F(Before) + error. I have some data sets that when you look at them as paired T-tests, you are lead to believe that there is no difference between the before and after.  If you look at them as say After = B0 + B1(Before) + B2(Before)^2, then you will see a pattern. 

    I even have some data sets where we can look at the data and see that, for say an exercise regimen, a person will lose an average of 10% body weight from fat but, they will increase their lean muscle mass by an average of say 10 pounds. So, when we do a paired T-test. we find no difference or a small, almost meaningless difference. Then, with regression, we find what is really happening. 



    ------------------------------
    Andrew Ekstrom

    Statistician, Chemist, HPC Abuser;-)
    ------------------------------



  • 20.  RE: Modernizing Intro to Stats

    Posted 03-17-2023 19:38

    Somewhat surprised to see no references in this thread yet to the thriving statistics education community, which has been working for many years to determine and advocate for best practices for teaching stats, many of which I suspect you would be in fairly good agreement with. :) These were codified in 2005 in the ASA "Guidelines for Assessment and Instruction in Statistics Education (GAISE) College Report" and updated in 2016.

    See https://www.amstat.org/education/guidelines-for-assessment-and-instruction-in-statistics-education-(gaise)-reports

    These have spread fairly well through many institutions, though apparently not to yours yet. For you and others who "wonder why we continue to insist on teaching people the mechanics and steps" (as Willis Jensen put it), the answer, frankly, is that anyone still doing that (or at least, who puts the focus on that) is not paying attention.

    If you're in a position to advocate for improvements, the GAISE report is a great place to start and a great resource to show people how we really can do better.

    If you want to know more, the ASA chapter on statistics education is thriving, and the annual conference on teaching statistics (USCOTS) is in-person again this June at Penn State: https://www.causeweb.org/cause/uscots/uscots23/about.



    ------------------------------
    Aaron Rendahl, Ph.D.
    Assistant Professor of Statistics and Informatics
    College of Veterinary Medicine, University of Minnesota
    300A VetSci, 612-301-2161
    ------------------------------



  • 21.  RE: Modernizing Intro to Stats

    Posted 03-18-2023 14:58

    As an adjunct, all I can control is how I teach the material I'm required to cover. I have the feeling that most of my colleagues, at least at the Comm Coll are not stats majors or minors. If all they took was a singe "Intro to Stats" class, the methods covered in the textbooks and online HW systems works out fine. So, trying to get them to change the way they teach the material would be a challenge. Getting the textbooks and online HW systems to follow suit will be even more difficult. 

    Because of that, I often find myself going forwards and backwards. I show students how to do things one way using their calculators to the fullest. Then have to backtrack in order to help my students get the most points possible with their on-line hw and their dept final exam. The online hw and dept final don't lend themselves well to nicely to showing students how to do things in a forward way using their calculator. For example, a question in the online homework going from mean to Conf Int, follows the path, mean>Margin of Error>CI and MUST be answered in that order. On the dept final exam, that would be 3 different questions using 3 different data sets. With both, there might be some question about what is the T-value or Z-value for the confidence interval. 

    The on-line hw has a lot of major issues too. Some follow the textbook guidelines, some use calculator outputs to answer the same types of questions. They expect rounding to 2-4 decimal places and will mark a student wrong if the system wants say 0.3574 and the student does the correct calculation and gets 0.3574785 and properly rounds that to 0.3575. Working as a tutor I know for a fact this happens. I tell my tutoring students to email their profs about that. I'm not sure the profs understand those sorts of things. I'd guess that most would blame the students for getting the wrong answer anyways.  



    ------------------------------
    Andrew Ekstrom

    Statistician, Chemist, HPC Abuser;-)
    ------------------------------



  • 22.  RE: Modernizing Intro to Stats

    Posted 03-20-2023 13:57

    Thank you, Aaron; I couldn't get logged into ASA over the weekend to reply with similar thoughts.  The Section on Statistics and Data Science Education is one of the longest standing sections at ASA.  We are a very welcoming bunch!  Every poster I've read so far would fit right in with us.



    ------------------------------
    Beverly Wood
    Associate Professor
    Embry-Riddle Aeronautical University
    ------------------------------



  • 23.  RE: Modernizing Intro to Stats

    Posted 04-13-2023 15:00

    I apologize for bring this conversation back up. But, I've had some time to read the GAISE report. I found myself looking at many of the report recommendations and thinking, these statements seem nice. Then thinking about all the different ways something can be interpreted.

    Recommendation 1: Teach Statistical Thinking

    There is a section here that discusses problem solving and decision making. I'll give my students a problem like: Medication A is a current standard of care. It costs $0.10/pill and has an effectiveness score of X.xx, a standard deviation of S.ss and was tested on n1 people. Medication B is a new medication. It costs $4.50/pill..... Any patient taking these medications needs to take 2 pills a day. 

    The students do their T-test and find that say Medication B is "statistically significantly" better. I'll ask them, "Which medication do you give a patient that is known to have issues affording all their current medications? Why do you think that?"

    This is problem solving and decision making that goes on every day. From traditional stats, you use the better medication. From reality, it's not clear cut. You get to have an ethical question about this too. "Is it better to take "the best" inappropriately or the standard as directed?" If I still taught my Mgt Science class, we would do a problem on this and look at "Maximizing Effectiveness" of medications taken with a constraint of cost. But, that's a topic of a different class. 

    I also give problems like, Medication C is a standard of care. It costs $2.00/pill. Medication D is a new generic medication. It costs $0.25/pill....... When they run their T-tests, they find no difference between the meds. The next question is, "Should the hospital switch medications?" and "What other information would you like to help make this decision?" 


    Again, problem solving and decision making. Not something that is in a typical stats book nor class. 


    There is also a lot about "understanding the concepts". With anything we have in stats, there is a rigid definition vs the consequence of that definition. 

    Take the confidence interval. There is a rigid definition of what it is. The consequence is that if I collect some data and make a confidence interval, say (3, 19) and you collect the same kind of data or try to repeat my experiment, your confidence interval might be (-2, 14). Your results and my results have some overlap. My mean is in your CI. Your mean is in my CI. So, our results agree with each other. But, if someone asks the question, "Does there seem to be a statistically significant result? I'll say yes, you'll say no. Thus our conclusions will differ. I got the further step and ask students to determine, "What is the probability someone else will find statistically significant results giver your data?" This fits in well with the "Be Skeptical" statement. But, any purists will be infuriated with what I have done. 


    In the section on "Suggestions for topics that might be ommitted" I agree with most of what they said. But, I'd add in MORE probability, not less. Why? Without exposure to other types of probability distributions, you get issues like what happened in Flint, Mi. The data collected on Lead concentration in tap water samples was somewhat exponentially distributed. Taking the Log of the data is really helpful. Once you do that, the Log-Normal distribution allows for a lot of things. 

    However, the scientists and engineers are generally taught that data like this is normally distributed. They are also taught to remove extreme outliers based upon an assumption of a normal distribution. If all they are taught is the normal distribution, then they assume, incorrectly, that they can and should use the normal distribution most of the time. They make bad decisions based upon their ignorance and others suffer for that. 

    I teach Poisson, Binomial, Normal, Exponential and Log-Normal distributions all with equal weight. I give real world examples of each type of problem. We usually then make fun of the textbooks for tell the students to use the wrong distribution. 




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    Andrew Ekstrom

    Statistician, Chemist, HPC Abuser;-)
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