It is the International Year of Statistics so all statisticians are obligated to tell you why statistics are so rocking awesome. Here is my two cents worth – I’m not a morning person. No, you have NO idea. I feel bad about it sometimes when I am having my lunch break at 10:30 pm, but that’s just the way I am. As soon as I could work it out – which was about two years into my career – I never worked an 8-5 job again. I’ve been up before 8 a.m. exactly once in the past six months – to go to a workshop on using games to teach statistics. I normally roll out of bed somewhere around the crack of noon and then work for the next 14 hours straight because that is how I like my life.
So, today, since Hart Fisher, host of American Horrors, invited me to their Christmas party in North Hollywood, it was perfect timing. I knocked off work a little early, knocked off a couple of beers around midnight and then armbarred a zombie while the devil took my picture.
See, you thought I was kidding about the devil but I got his business card as proof.
There you have it then, young people, yet another reason to become a statistician – you can arrange your hours to accommodate your biological clock, which, in my case, seems to be set on Vampire Time.
You can listen to the band, St. Madness, here. I thought they were quite good.
Very often, researchers (including me) use multiple-choice tests to collect data to determine whether or not an intervention has worked. Does the Dance Your Way to Math curriculum really result in higher test scores? Does Lollipop Spelling reduce the number of spelling errors? and on and on.
I remember being told that statistics to be generalized to the population, like internal consistency reliability or test-retest reliability should be computed either only using the pre-test scores (in the case of internal consistency) or only the control group in the case of both test-retest correlations and post-test internal consistency reliability. The reason, we are told, is that “something has been done” to the intervention group, which means that they are no longer representative of the population. While I agree with that reasoning in the case of test-retest correlation, I am not so convinced in the case of internal consistency.
Let’s talk about floor and ceiling effects for a minute.
A floor effect is when most of your subjects score near the bottom. There is very little variance because the floor of your test is too high. In layperson terms, your questions are too hard for the group you are testing. This is even more of a problem with multiple choice tests. With other types, if the subject doesn’t know, they aren’t likely to guess that the answer is, say (a+b)(a-b) and so they get it wrong. With a multiple-choice test with four choices, they will randomly get it correct 25% of the time. If there are a bunch of questions that are too hard, you have a bunch of people randomly getting each one right just by chance. Combine low variance with a lot of random error and your internal consistency reliability is going to be in the toilet. So, let’s say you have exactly that on your pre-test. Then, you test again after some time and your control group, having had no training in the meantime, is equally low, the problems are still too hard, you still have random guessing and low variance.
A ceiling effect is the opposite, all of your subjects score near the top. There is very little variance because the ceiling of your test is too low. In layperson terms, your questions are too easy for the group you are testing. Here you don’t have the problem of random guessing, but you do have low variance. Think back to Statistics 101 – restriction of range attenuates correlations. Again, in layperson terms, if you correlate height and weight of NBA players, for example, you find almost no relationship between height and weight because they are ALL very tall and ALL very heavy. If you make the questions on your pretest easier, that may give you better internal consistency reliability at pre-test, but since a good percentage of your subjects knew the questions at the beginning, by the end of your training maybe nearly all of them will, and then you run into a ceiling effect.
My suggestion is to compute internal consistency reliability at the beginning of your study for the whole group and at post-test for the control and intervention groups separately. You may find that, having successfully avoided both floor and ceiling effects for the post-test intervention group that you get good internal consistency reliability for them.
“I went to a strip club once. I looked around and thought, ‘All of these guys are complete losers.’ Then I asked myself what was I doing here. I must be a loser, too. I got up and left and I’ve never been in one since.”
This is a little more interesting take on the “You are the average of your five closest friends” meme that has been going around these days. (I am still puzzled by whatever motivated my extremely conservative friend to ever go to a strip club in the first place.) While Buford Taylor’s post was on software engineering, the same applies to life in general. Here are a few examples I have observed how my life has gotten SO much better since I quit associating with people that I frankly did not think were good people.
Honesty. I have heard too many times, “It’s just business.” If you work with people who bend the truth, cut corners and look the other way, eventually, you start to feel that is normal. When you find yourself in that situation, get out as soon as you can. Trust me on this one. Of my five closest friends, four are scrupulously honest, as in, wouldn’t tell a lie if they were under torture. The fifth – well, he might tell you he scored the winning run in the high school state championships when he was actually on the bench, but as far as anything that ever mattered, he is batting 1,000.
Courage. All of my friends have courage in spades. I have friends who were in the Marines, fire department and law enforcement. I also have a couple who have never faced anything more life-threatening than a computer virus. Courage is not just running into a burning building or standing in the line of fire. It is also standing up in a meeting when everyone else has agreed to a plan of action that you think is wrong and saying, “No.” It’s being able to withstand a storm of public criticism, ridicule and possible lawsuits to stand up for what you believe is right.
Intelligence. I don’t have any dumb friends. Everyone I know is smarter than me about some things and I ask their advice often. When I’m with my friends, I’m never the smartest person in the room. That’s a good thing. Both The Rocket Scientist and I are convinced we married someone smarter than ourselves and got a good deal.
Reliability. If you met my closest friends, you might think they are quite different. Some people, like me, work all of the time. Others might have a lot of days when they completely screw off but then pull all-nighters. Some get up at 5 a.m. and some, like me, only see 5 a.m. on their way to bed. A couple of my friends don’t do a minute more work than they absolutely must and the others live for their work. None of them have ever missed a deadline.
One of the nicest things anyone ever said about me (it’s been a few years so excuse me if it isn’t exact) was when a friend of mine was defending me to someone who had criticized some position I’d taken,
“Look, the difference between you and AnnMaria is that if she agrees to meet you April 23rd, 2015 in front of the Eiffel Tower, when that day comes around, she’ll be there and you won’t!”
I’ve learned over the years that most people, when they say they will do something, mean that they will do it if the roads aren’t too bad, or they don’t get a better offer or they just don’t feel like it that day. Then there are people who when they say they will do something, will simply do it.
This is a super-important lesson and it took me a long time to learn it. You ARE the people you associate with. Don’t buy that line that you need to associate with unethical or incompetent people because you need a job, it’s only business, they coach your kids, you want to win – whatever excuse you have, it’s not worth it. As Carly Fiorina said,
“Once you sell your soul, no one can buy it back for you.”
If you are unhappy with your job, your friends, your love life, think about this – what are the non-negotiable qualities for the people around you? If your friends are people who are athletic, attractive, successful and funny, is that what you want? Before you say, “Yes, who wouldn’t want that?” take a look at the qualities I just listed and think again.
A couple of years ago, I made the comment to someone that I have better friends than I deserve. He responded
“I don’t think that’s possible. I think it’s an oxymoron. I believe people get exactly the friends they deserve.”
I sure hope he is right and I advise you to act as if he is.
Today, someone asked me,
“Is it really true that guy you see on the Internet with all of the question marks on him, that it’s possible to get a government grant for anything?”
In a word, no. People come to me all of the time with ideas that not even your own mother would fund. They want to pay for a preschool program for upper-middle-class families or to start an ice cream shop in Santa Monica or start a ferret preserve. Okay, well no one asked me to help them write a grant for a ferret preserve, but the other two really did happen.
Here are what you really need for a successful grant proposal:
- Need. Whatever there is has to be lacking and it’s lack must affect the public good in some way. Whether or not children from privileged families benefit from preschool is open to debate (although the advantages for low-income children are well-established). While ice cream is very yummy, I’m not sure the city would fall into the sea without it.
- Program. Say you do document a need – unemployment is bad, therefore you should give me money for an ice cream shop so I can hire people. Even with half the equation, you have to convince grant reviewers that your program is a better way to meet that need than funding a training center so that people can learn computer skills and qualify for a better job than scooping ice cream. There will be lots of proposals to reduce unemployment and you need to provide numbers and studies to back up that yours will probably have a better outcome than the rest.
Here is a secret that novice grant-writers often miss : Start early. Start months before the request for proposals is published.
How does that make sense? How can you respond to a request before it is published? First of all, government agencies tend to have the same schedule year after year. If they released an RFP for small business innovation research grants in December of last year and for vocational rehabilitation for American Indian reservations in March, they will probably release very similar RFPs at about the same time this year. So, around January, you get last year’s RFP and you start preparing for the one to be announced in March. If it says you need letters of commitment from school districts, you go around and start talking to the superintendents of schools in your area. If you need resumes from all the staff members who will be involved, email them and tell them to all update their resumes. You’re going to need a literature review. Start reading those books and articles now.
I used to be proud of myself as on top of things because I would watch the Federal Register and know as soon as a request for proposals was released. I would pride myself on the fact that no one could possibly have been working on this one minute longer than me. (I was very young.) I’d also be confused as to how anyone could get all of this done in the four weeks or so allowed from when the RFP was released to the due date.
This all came back to me today when I was surprised to get an RFP. I was surprised because we have been working on this proposal for two months. Of the five sections, two are almost final. I sent both out for review, got the review back from one person and made the changes. A second section has been revised twice and I should be finished with it next week. The other three sections – literature review, program plan and budget – I have drafts written. So, when I got the email in my inbox today, I briefly wondered, “What’s this?” and then realized, oh, yes, it was officially released today – and I’m more than half done.
The second secret to grant-writing is so obvious but it is unbelievable how many people miss this: Follow the instructions. All of them.
When I received the RFP today, I read it. All 52 pages of instructions. By the time I submit the proposal, I’ll know those instructions better than God knows the Bible. That wasn’t too bad because the last one I wrote had 83 pages of instructions. The instructions were very similar to last year, but not identical, so I needed to make some changes in my proposal. Some years, for some proposals, they are quite different. For example, the page length went from 25 to 15 pages. In that case, since I already had a draft done, I had to cut everything by more than half. If it says the grant should be 12-point font, 1 inch margins, then it has to be or they will reject it. If they say you need a bibliography, cite scientific literature, review how this relates to your own prior research – whatever it is, do it! You’d truly be amazed the number of grants I’ve reviewed that were obviously written for a different competition.
Follow these two suggestions and it really will help you win more grant money.
Today, I’d like to add #4 to 6 to my list of things I have learned in my 55 years. (You can find the first three here.) These are:
- You were hired to DO shit.
- No, you are NOT smarter than God.
#4 You were hired to DO shit
Newly-minted PhDs are only marginally the worst, plenty of non-PhDs give them a run for their money. Maybe it is because in school you aren’t required to do much, not actually start a business, or design and build a new product, but simply answer questions on how it should be done or how the company in the case study did it wrong, and cite some sources. I will always remember the day, fed-up with a new employee coming into meetings and lecturing us on what we needed to do differently, one of our senior partners growled,
“Listen, we didn’t hire you to tell us what to do. We hired you to DO shit!”
In other words, if you think we should write a survey, read an article and cite it in a proposal, create a macro, hold a focus group, meet with schools to recruit subjects, don’t come into my office and tell ME to do it. Do it. If you need my permission, ask me if it is okay. If you want my advice, bring me a draft of your work and have me review it. Two examples, that just made my jaw drop:
A person with a degree in medieval English literature or modern languages or one of those things that no one actually pays you to do, was hired to do some editing. She sent me back the document with all kinds of instructions on grammar – delete this comma, read the Microsoft style guide on how to do headers, change this to a semi-colon. It would have taken her much less time to make the changes than to send it back to me and no, she didn’t make the changes and track them for me to approve – she had a comment on each one telling me what I should do there.
I gave someone a figure that needed to be reduced to fit within the page size for publication. They sent it back with instructions on what I could do to reduce the size and suggestions on elements to take out.
When I was getting my MBA, a very useful piece of advice came from one of my professors who said,
“No boss ever hired anyone for the express purpose of pointing out problems. Never go to your boss with a problem without at least a suggestion for a solution that YOU can do to fix it.”
This is the reason many people fail as consultants. Although the word means “one who is consulted”, that is asked, what most clients want isn’t for you to advise them. They want you to fix their problem. No matter how brilliant you sound, if you don’t fix it, next time they’ll call someone else.
#5 No, you are not smarter than God
I’m sure you went to a top school and you learned a lot of stuff, some of which I don’t know, because there is a huge amount of knowledge in the world and I only have a teeny-tiny fraction of it. So do you. Don’t speak contemptuously of your boss, co-workers, fellow students or professors because they don’t know PHP or how to code a CONTRAST statement or the author of whatever it is that you last read. It will get back to them and they will probably be annoyed. They may be so annoyed that when you should know something, they won’t tell you because, after all, you know everything.
These days, I try to do at least a little programming every week, but I have two grant proposals do, a report to a client and a book coming out (on groundwork for judo and mixed martial arts). There have been periods in my career when I was lucky if I could write a program a month. That’s when I realized that my old professors or the out-of-date person I worked for way back when was probably not the tiniest bit duller than me. They had other things to do than know the latest technology or every current article on bean-counting, because they were bringing in the grant money, contracts or students that kept the doors open and paid my salary.
Related to this, don’t go charging in anywhere and insist derisively that things need to change here and here and here and here. Wait a while and you may see that the reason we have several very old computers is so that we can test applications on hardware our clients might use, or try to replicate a problem a client had. You may find out that the reason we don’t randomly assign students to experimental and control groups is that we need to work with the school and they can’t really see explaining to parents why their children didn’t get to be in the group using the shiny new toy.
Another good bit of advice from the commencement speaker, also when I got my MBA (in 1980, if you must know)
“Ladies and gentlemen, when you get your diploma, read every word of it. Turn it over and look on the back. Notice that nowhere on there does it say, ‘I now know everything.’ Act accordingly.”
Don’t be one of those people who just is waiting for their turn to speak. Ask people what they think, not as a device you learned for networking or sales or some crap like that. Ask because you really want to learn from them. (See #4 above.)
When young people do all of the above, do I think they are annoying and stupid. (Okay, honestly, sometimes.) More often, I think this is God’s punishment because the above were my three absolute greatest faults as a young person and I work on them to this day. On the other hand, it may depress you to know that sometimes when the boss says,
“You remind me of myself at your age.”
That it’s not always a good thing.
“Ebrary? Oh, yeah, I think the university where I teach has that, but I wasn’t interested so I never looked into it.”
So said a young professor today when I mentioned ebrary. I actually had looked into it years ago when I worked at a different university. It was all right but I could only access on my computer and I spend so much time in front of my computer working that reading books on it didn’t particularly appeal to me except as a last resort. There is a lesson here about taking a second look at software applications and companies you dismissed five or more years ago. If they are still around, they are probably dramatically better – or they wouldn’t be still around.
What is ebrary? It’s a sort of electronic library. According to their website they have over 590,000 titles. They also now have an iPad app. It’s much, much simpler than when I used it in those pre-iPad days. You can register an account and then access it on your computer or download the app and read books on your iPad. You can also download many of the books so that if you happen to be traveling and you don’t have wi-fi, you can read the book on your device, then just click to return it when you are done. I’m not sure how many you can have out at a time. I currently have four. So, basically, imagine if you could get most of the books on Amazon, but free.
Another resource to look into is if your university has a digital subscription to Safari O’Reilly books on-line, which also lets you download and print chapters. It also has apps for reading on mobile devices.
Some universities have a subscription to Lynda.com that offers online courses for learning about technology and design. I hate to say that I have never signed up for one despite all of the times that I looked at the website and thought, “That sounds interesting.”
There is also Film on Demand , which has around 7,000 educational films. You could show these in your class or just watch yourself to further your own education. I happened to watch a really interesting one on Rett Syndrome today.
I can’t imagine there is a university out there that does not have some type of full-text retrieval for journal articles. Personally, I’ve found those often to be so bent on preventing any unauthorized access that they can be a real pain. You might want to try the Directory of Open Access Journals instead, which is open to everyone.
All of the above have the benefit of not having to move. Since you are already sitting at your computer reading this, you might want to take ten minutes and see what your university offers that you might be missing.
I forgot how old I was for a while. Someone asked me how old The Rocket Scientist is and I said 57, then I had to think how that could be when he is three years older than me. So, yes, I will be 55 this year. I guess turning 54 happened when I was busy and it kind of came and went. This is the age when one could theoretically retire under a lot of the old gold-plated retirement plans, though people usually don’t. The Rocket Scientist actually retired at 56. Young people starting work now, I think have to work until they turn 82 or drop dead in their tracks, whichever comes first. It’s also the age at which one is supposed to have some sort of wisdom to impart.
Inspired by this really good post from the Chicago Tribune on 50 things I’ve learned in 50 years, I decided to add my own, but since unlike that author, writing is NOT my full-time job, I thought I would try to get 55 out by the end of the year. Maybe even by my 55th birthday. Here are my first three. These aren’t necessarily the most important, but these are three things I learned that were worth learning.
1. Learn tact.
Last week, I was interviewed for an HBO special they are doing on my daughter’s upcoming UFC fight. The interviewer was incredulous when I said there were some things I would not say, since even someone who has known me for only 20 minutes can see that I am pretty outspoken. Here is when you should not say something:
- When it would gratuitously hurt someone’s feelings. There is no point in telling your neighbor her baby is ugly as a little monkey. Young people often excuse this kind of talk by protesting, “Well, it’s true! I’ve seen spider monkeys that look just like that!” Just because it’s true doesn’t excuse you from causing someone else pain, even a little bit.
- When it offends the people who pay you and there is no ethical reason you have to say it. This is known as not biting the hand that feeds you. What I am NOT saying is that if your employer is biased against certain religious, political or ethnic groups that you can’t post pictures on your Facebook page with people from those groups talking about how awesome your black, communist, Buddhist, gay friend Bob is. What I am saying is that if your employer thinks everyone on earth should use Gantt charts and has published several white papers on that topic, you don’t go writing a blog post on how the Gantt chart is the stupidest idea anyone ever had and spend 1,700 words mocking them. Again, I hear young people object, “They can’t tell me what to do!” After kindergarten, you shouldn’t be using that excuse to justify your behavior any more.
Just because you have the right to say something doesn’t mean you should. You can’t go through life not offending anyone. That’s impossible. You should try not to hurt people and not to do damage to your professional relationships. In short, don’t be an ass.
2. Find some perspective
For 14 years of my life, I competed in judo. I won a world championship, the first American to ever do so. Even though I earned two degrees, married and had a job, for most of that time, my life centered around judo training and competition. If I lost, I felt as if I had lost my best friend. Then, I went on to have four children, get divorced, get a Ph.D., bury my second husband and start a couple of companies (not in that order). The first time the national championships had passed months ago without me even remembering to check who won, it made me realize how much my priorities had changed.
These days, I can be working 80-hour weeks trying to get a proposal out and it seems like getting funding for our game is the most important thing in the world. Actually, it turns out that the world is a really big place and that billions of people have never heard of our game. To some of them, this year’s harvest is the biggest thing in the world. To others, it’s that their a capella group wins the nationals (I presume they have nationals) and to others it is finishing that needlepoint that they have been working of for months, or getting tenure as an Associate Professor of Italian in the Modern Languages Department and if they don’t, they’re a FAILURE.
How can I possibly equate a life-changing event like failing to get tenure, failing to complete a needlepoint and crop failure? Two reasons. One is that while it may be of great importance to you personally, to the vast, vast, overwhelming majority of humanity, it doesn’t matter a rat’s ass. It is NOT even close to the end of the world because …
3. Failure is not permanent and neither is success.
Now that I am old, and I have my own office, it often happens to me that I will be looking for something in a file drawer and I will come across a reminder from years ago – a medal, or a grant proposal. At the time, whatever it was meant a lot to me – several hundred thousand dollars that we used to pay staff for a couple of years and provide training to people in reservations across the Great Plains. But now it’s over. Maybe it was an article that got published or a grant that got rejected. Either way, it made me happy or upset at the time but now it is just stuck in a drawer. Even my trophy from the world championships is in a box in a closet somewhere. I’d really, really like to get the proposals I’m working on now funded. But, if I don’t, I’ll just turn around and write another one.
Wednesday, I went to a workshop, Mixed Models for Professors. It was a combination of discussion of the mathematics of mixed models, using SAS Enterprise Guide and examples for teaching. Since I was too lazy to actually take notes, I just tweeted it. Three useful pieces of advice, even if you don’t like my notes:
- SAS offers classes for professors for free several times a year. I don’t know who you need to suck up to for an invitation. I was not on their mailing list and now I am.
- The class notes book they give you is a great deal. It’s also free.
- If you live in southern California, there is a GLIMMIX class in June at National University.
Interaction in a mixed model – if at least one of the effects is random, the interaction is random
Randomized complete block design – blocks are random, treatments are fixed.
In randomized block design don’t take blocking variable out of the model even if it’s non-significant
Analyzing a randomized block design? Need to have 1 observation per level of fixed effect per block. (Repeated records per block)
“Repeat after me – I will never use PROC GLM again”
Why would you find an interaction between block & treatment if assignment was truly random?
Kolmogorov-Smirnov is a test for significance of difference in vodka quality (ok, I lied it really tests normality)
For random effects in
#SAS EG click random effects, then ADD, then click … to select effect (as in, click on three dots)
Half the benefit of the
#SAS classes is the book of notes they give you. Like how the mixed one explains every bit of output. (It would be nice if it explained every option in the screens, too) #SAS will also be offering a GLIMMIX workshop in San Diego in June, I hear. Really nice to have close to home #SAS workshops for professors are free, just FYI
Mixed models are robust to departures from normality “If it aint too bad”
The larger your n, the harder to get normality because a larger n makes it easier to reject a slight departure from normality
Two problems in regression – non-normality and non-constant variance
In mixed models, non-constant variance can be accommodated, unlike in regression where we assume constant variance
To inspect normality of residuals, look at quantile plots <– sentence which made sense to me
In mixed models errors are assumed to be neither independent nor homogeneous
PROC MIXED allows for different covariance structures
Fixed effects specified in MODEL statement. Random effects specified in RANDOM statement
2 methods to obtain mixed estimates, maximum likelihood and restricted maximum likelihood (REML)
In general REML estimators of the variance components are unbiased in PROC MIXED while ML estimates are biased low
V = ZGZ’ + R used in generalized least squares method
“Kenward-Rogers degrees of freedom is Satterthwaite on steroids” – recommend as PROC MIXED df method. May give fractional df
Generalized Linear and Nonlinear Models for Correlated Data: Theory and Applications Using SAS by Vonesh. Recommended text.
Nested effect – hierarchical data structure in which smaller experimental unit is nested within larger one, e.g., students within classes
PROC GLM contrast statement uses ‘/’ where PROC MIXED uses ‘|’
CONTRAST ’3 levels’ varname 1 -1 0 ; = How to write contrast statement in PROC MIXED to test diff between means of variable with 3 levels
ESTIMATE ‘level 3 mean’ int 1 varname 0 0 1 = estimates mean at lvl 3 for varname variable – how to code PROC MIXED ESTIMATE statement
M1* is the average mean over all levels of M. (Sum of M11 – M1K)/(number levels)
#SAS EG PROC MIXED does not include Type IV hypothesis test (never noticed that before)
Should not use Type III SS when treatment combination is missing. What then?
The answer to that last question is that there is no easy answer
R(a|μ b) testing for main effect a, adjusting for the intercept and main effect b, but is that really what you are doing?
Reminder: Type I is model-order dependent while Type II, III are model order independent
Recommends starting with the general model testing for unequal slopes and unequal intercepts
#SAS EG on line plot go to INTERPOLATIONS under APPEARANCE and select REGRESSION to get a regression line
PROC MIXED like ANOVA, GLM, interaction tests whether the slopes are equal. Main effect tests whether intercepts are equal
random coefficient model includes term for variation around mean for level of the random effect
PROC GLM ANCOVA assumes intercepts are fixed. Random coefficients model assumes they are random
An effect can be considered both fixed and random (I did not know that)
“I’m XX years old and I’ve never used (insert any statistical technique here). Why do I need to know this?”
I’ve heard some version of the above on every topic from linear regression to structural equation models, and at every age from teenagers to executives in their sixties. I’ve even made comments like that myself. All of those people, especially me, were wrong. Not in the “I’ve never used this”. I believe that. It is the implication that you wouldn’t use it if you knew it. I’ve never used my non-existent knowledge of Chinese and I got by when I was in Hongkong and Beijing and with the various Chinese people I have met, but if I had known Chinese I am sure I would have used it and probably learned a lot more interesting things about the places I went and people I met.
Now that I’m going to San Diego, I’m seeing mixed models everywhere. For example, I am planning a study where we present students with instructional choices for a topic, say frequency distributions. The choices could be a web page, video, applet that lets you create distributions. Choices would vary in difficulty and quality (as rated in advance by me & some other people). My dependent variable in this case would be how much time the student spends reading, watching or playing with this resource. Student is going to be a repeated random effect here. Difficulty is a fixed effect, as is quality.
So … that is a mixed model.
I’m also looking at improvement in students who play our math game we’ve developed. There is a pretest and posttest, so that is the repeated factor. There is the group – intervention or comparison – so that’s a fixed factor. Other variables I could include are grade (fixed) or teacher (random). What if I included, though, how involved their teacher was with the students using the game, either (high- providing hints, made up a cheat sheet, taught the same material in class if she noticed students were having difficulty) , low (sat and read the newspaper) or moderate? Anyway you look at it, this could be a mixed model.
Then I got to thinking of something else where I could have the type of instructional resource a student chose as a dependent variable, say a video, web page or some active option like a game or applet. Then I would do a multinomial logistic regression and have things like difficulty and quality as variables. However, the same student would be making lots of choices. Instead of 6,000 independent records, I might have 100 students each making an average of 60 choices during the game. In this case, I could use the generalized estimating equations (GEE) method to control for correlated observations. I definitely would not use PROC MIXED.
My point is that once I started thinking about mixed models, I started seeing where I could and couldn’t use them. Not only did this get me thinking about mixed models it also started me looking at other ways to work with repeated and random effects. I think the same would be true of almost any statistical technique.
Speaking of going to class … I try to do that whenever I can. I’ve been so swamped writing two grant proposals that it’s been impossible to get away for very long. So much so, that when the Joint Mathematical Meetings were in San Diego last week, I skipped the conference and just took a class.
A couple of years ago, I was at the Western Users of SAS Software conference and went to a class on survival analysis given by Gerry Hobbs. It was very good. A much younger colleague saw me and asked why I would be going to a class. He said,
“I’ve heard you give talks on survival analysis. Why would you go to a class by someone else?”
I thought the answer was obvious,
“Because I’m sure he knows some things I don’t, either details about the technique, about programming or about how to present it . And I want to learn.”
It reminded me years ago of when I was an assistant professor at Minot State University. I happened to be taking a class in microbiology because my friend, Nina Parker, was teaching it and I heard she was a great professor (she was). Another professor, in the chemistry department, was taking a French course at the same time. We both got the same startled reactions from other students. He said to me,
“One of them actually asked me, ‘You have a PhD, why are you taking an introductory French class?’ and I told her, To learn French!”
Learn new stuff. It’s not a strange concept. Really.
As anyone who reads this blog often knows,
a. I like Chardonnay
b. You need to get a life
c. The purpose is for me to write down stuff I want to remember later. Serendipitously, this often turns out to be stuff other people would like to know as well.
If you teach statistics …
Teacher’s Domain data analysis and probability section – this is for younger students, most of the videos and lesson plans here are for grades 4-8, with a few that are lower or higher. On the other hand, I was very impressed with the quality. The Spoiled One watched the video on interpreting line graphs and commented,
“Yeah, this is less boring than that stuff you usually have me watch.”
which is as good an endorsement as a parent usually gets on anything from a teenager. (Can I get an “Amen”?)
Rice Virtual Lab in Statistics - is another one that has been around for over a decade and when I found it I thought, “Oh my, God, where have you been all of my life?”. It has examples from actual studies with research design, code in SAS and JMP, output, interpretation and you can even have it read to you by the author. I’d put this solidly at the undergraduate level.
Stats2Lab at Grinnell College – is a nice example of what Vygotsky would call scaffolding for students in their second course in statistics. It provides research designs using games, with detailed procedures for data collection, hypotheses and even suggestions on literature review.
Socialresearchmethods.net – as the name implies, it is not only statistics, but it does include a free online statistics textbook that is good, a book in simulations, an application to help you choose the correct statistic and many full-text articles for download.
Three that I mentioned last month but I am mentioning them again so that I don’t forget ….
Consortium for the Advancement of Undergraduate Statistics Education, a.k.a. causeweb.org - where have you been all of my life? Don’t let the name fool you, there are workshops, webinars and resources for you whether you teach high school or graduate level statistics as well.
Against all odds – statistics videos done in 1989, but still timely. Seriously, a normal distribution hasn’t changed much.
SAS Curriculum Pathways – I mention this again, even though I mentioned it in a previous post, simply because I knew about it for years and never looked at it. It’s really cool. I’ve recommended it to several teachers I know who have never looked at it, either. I know why, too. We are all busy. I knocked off work at 1:30 to write this blog, so I can relate. Seriously, though, this site has explanations, examples, problems. Like a textbook, but better, and free. My favorite was their part on box and whisker plots. I’m going through a graphs with bars period in my life. Everything I’ve seen here is high school level or below. May-be at the introductory undergraduate level.
If I ever have time (how many things in life do I preface with that?) …. some day I would like to create a statistics course with no textbook, just access to online resources and activities. I’d also cut the lecture time in half and just have them read some of the great resources on the web, then we’d discuss those in class.