On the front page of the Los Angeles Times today was a story about three of the middle schools in Los Angeles serving the highest proportion of students in poverty. My daughter, “The Perfect Jennifer”, did her student teaching at one of the three and teaches at a second.
She said to me today,
Mom, the beginning of your story is very common among the students I teach. The families don’t have a lot of money, they have problems at home, the dad isn’t always around, they end up in foster care, have problems with the police, go to juvenile hall. Usually, these stories don’t end with – And she got a Ph.D., became a statistical consultant, runs her own company and lives by the beach in Santa Monica. You do know that’s not the way these stories usually play out, don’t you?”
The reverb10 prompt for yesterday was what you wondered in 2010. I know that was yesterday but I tend to live by my own rules and time lines as much as the law and the necessity to make a living will allow. It’s also Computer Science Education Week where we are treated to videos of real live computer scientists telling us how great it is to be in computer science. After watching one, the house’s resident rocket scientist commented,
“The first mistake they made in producing this video was allowing those people to dress themselves.”
What I wonder about is what would have happened to me if I had sucked at math. I think back to when I was young and, in most ways, less promising than the students my daughter has today. My family didn’t have money or connections in this country. I was female, short, chubby, near-sighted, Latina – in a time when it was still legal to advertise jobs for men only and people thought it was okay to say things like,
“You shouldn’t be offended by comments about Hispanics. No one thinks of you as Hispanic because you are so intelligent.”
I was somewhat less sweetness and light back then than I am now and my most likely reaction to comments like that was either to say, “What the fuck?” or punch the speaker in the face (hence the acquaintance between myself, the foster care system and the juvenile authorities).
So, what happened?
Well, I had a sixth grade math teacher named Sister Marion who thought I should make A’s, and I knew better than to argue with a nun. In middle school, I had an Algebra teacher named Mr. Cartwright who just assumed I should excel in Algebra and demanded to know what my problem was any time I got less than an A on a test. I went to an alternative school, Logos High School, back when it was in the inner city, before they decided to move the school to the rich suburbs and do well instead of doing good. There, I had a math teacher named Chris, who was a conscientious objector to the Vietnam War and another math teacher named Phyllis who taught matrix algebra. We were just getting the chance to program computers when I was in high school, through an arrangement with St. Louis University, down the street.
I took the SATs, did well, got admitted to Washington University in St. Louis and took some classes on programming – BASIC and FORTRAN – just because. I took Calculus and Statistics because I thought these might be useful some day, but, if not, they were kind of interesting courses. I took regional economics and urban economics and learned about actual applications of matrices where you had the sales from region A to other people in region A, then their sales to region B in the next cell, their sales to region C — and it all started to make sense. I did not ace all of my courses in college. In fact, I pretty much majored in parties (don’t tell my mom) and I worked full-time.
BUT … and I think it goes back to Sister Marion … I always assumed there wasn’t any subject I couldn’t learn if I put my mind to it. When I was at General Dynamics and nine months pregnant, the managers were really freaked out about having a very, very pregnant woman engineer climbing around on the machines. One manager said to me that it was a liability because I could fall down. I told him that I had been walking since I was a year old and that I hadn’t fallen down since. I know the reason they sent me to that SAS programming class was to get me out of the factory.
I didn’t start out with looks, money, connections or even good behavior. By the time I was an engineer, I still didn’t have the sense not to be a smart ass to upper management. What I did have going for me was that I was good at math and learned to program a computer very well. There were not enough people that could say that, so I was tolerated and helped until I learned to dress myself and shut the hell up on occasion.
One of the few poems I remember ever learning was from Robert Frost and it ended
A path forked in the woods and I
I took the one less traveled by
And that has made all of the difference.
If I had studied poetry instead of math and computer programming, I don’t know where I’d be but I don’t think it would be here.
I wonder, if I had sucked at math, would I still be able to take trips to Tunisia, Costa Rica, Beijing and Athens just because I felt like it.
I wonder if I would have been able to go to the Bahamas and seen the marching flamingos at the Bahama Zoo. I really wonder who the hell sits around a zoo and suddenly says,
“You know what we should do, today? We should try to teach the flamingos to march.”
Seriously, how does that ever enter your brain? I REALLY wonder about that.
Trivial pursuit answer of the day: The flamingo is the national bird of the Bahamas.
For the first time in two years, an application came in my email for a technical position from a person under 30 who was an American citizen. This isn’t because I don’t look for people. I have talked to lots of young people I know who are pretty good with computers and asked if they would be interested in learning about statistical software. We would train them. Nope. They want to go to law school (lots of them), get an MBA (lots of them) with the odd few who want to be teachers, journalists or artists.
Last night, I was reading a data mining book that had NO equations and I had one of those mental stumbling blocks, you know, like when you can’t remember the name of your youngest child? Well, that happens to ME all the time, anyway. I doubt it is due to all the drugs in college because I’ve always had that problem. [Not that I ever personally did any drugs, of course. I am referring to second-hand smoke.]
Just out of the blue for no reason I was not 100% sure of the definition of an inverse of a matrix. So I asked my husband,
“Hey, the inverse of a matrix is the matrix you multiply it by to get the identity matrix, right?”
“Yes, but sometimes there is no matrix you can multiply by to get the identity matrix. Then the inverse is undefined. That usually doesn’t happen unless your variables are correlated.”
I guess he added the part after “Yes”, just in case a whole section of my memory had been wiped out. Of course the whole problem with multicollinearity in regression is obvious if you know this because you cannot invert a matrix so you cannot solve the normal equations to get your coefficients.
I sat in a graduate course today taught by a very knowledgeable professor, surrounded by graduate students at a selective university in a course they paid a lot of money to take. Several times, he said something like this:
“What is regression? You have some X’s and there is a black box and then you get a predicted Y.”
I am looking at his drawing on the board and thinking to myself, no, it is not a black box. When I looked at his black box, this is what I saw:
And I thought
A. You take the X matrix and transpose it. You know you need to transpose it because you can only multiply a matrix if the number of rows in one matrix equals the number of columns in the other. You multiply that (the transposed matrix) by X (the original matrix).
B. You then take the inverse of the result from step A.
C. Then you multiply the inverse of the product of the transposed X matrix and the original X matrix by the transpose of X.
D. You multiply that by the Y vector
and that gives you the vector of regression coefficients.
Here is a really good explanation of least squares estimates in matrix notation, by the way. Thanks to Pennsylvania State University.
I do not blame the professor at all for not saying any of that because he has two problems with this course, neither of which have ANYTHING to do with his competence as a professor or of the ability of the students. I know because I have experienced this problem growing and growing over the past 25 years.
1. We are cramming a ludicrous amount into courses with names like “research methods” or “data mining” or “statistics”. The poor soul teaching this course must cover data mining, data warehousing and business analytics in one course. That is impossible. Because students are often working full-time while going to graduate school and because schools have gotten more and more expensive, there is a lot of pressure to cut the number of courses. So, what used to be three courses is now one. When I learned multiple regression, it was a course all by itself. The normal equations, above, are not basic but not incredibly difficult, either. Certainly the vast majority of graduate students could learn to transpose a matrix and multiply the result. When I was in graduate school we had the luxury of spending an entire three-hour class just going over these equations and even some of the next week’s class for students who had questions. When we put too much into a course it is impossible to cover ANY of it in-depth. I have seen the same problem in my children’s math textbooks from fifth-grade on up. We wised up with the youngest one and now spend time at home making sure she understands not just the definitions and rules of, say plane geometry, but also how she can apply those. We fool ourselves by saying we are rigorous by cramming 42 topics into one textbook but all that happens is that people learn a little bit about a lot of things and a lot about nothing. I’m not joking here, I think this is why so many people want to go into management and “See the big picture” and will tell you, “I’m not a detail person”. Writing code that runs – that takes details, something as simple as ending a statement with a semi-colon, with knowing the difference in SPSS between rules for batch processing versus interactive. Details matter.
2. Again, because people want to “get out and get it over with” we are requiring fewer and fewer in terms of prerequisites. Many colleges no longer require any mathematics beyond algebra – if that! As I said before, I think College Algebra is an oxymoron. You should have learned algebra in high school. Certainly, many students never learned matrix algebra. When I was in graduate school, the professor could write equations in matrix notation because we were supposed to have learned it as undergraduates and the majority of us did. There was an entire course in descriptive statistics and if you didn’t have it as an undergraduate, guess what, you had to take it. And if it meant that you didn’t finish your graduate degree as soon as you would have liked, oh well. If you hadn’t learned it somehow, there was a teaching assistant and you went to him or her to help you understand the class.
So …. we don’t give our students the prerequisites at the lower level, at the upper level we cram three times as much in a course as they could really hope to comprehend in that short of a time. In the end, they don’t know very much about math and they are convinced that they aren’t any good at it because they don’t have the talent and math is hard. The truth is that math isn’t all that hard, it just takes time, like anything else, and we have no idea if they could be good at if we gave them the time and really tried to teach it to them, starting with,
“The identity matrix has all ones in the diagonal and zeroes in the off-diagonal elements.”
Here is my modest proposal to fix all of this:
1. Have LESS material taught in each math class, that is, fewer topics.
2. Require MORE classes of students
3. Do NOT let students waive or skip prerequisites unless they test out of them. (Do let students test out of classes, by the way. I always encourage that.)
4. Don’t write the mathematics out of courses. Leave it in. If you do #1 -3, students WILL understand it.
This is why:
A. I support affirmative action
B. I think some kids succeed in math and science while most don’t.
For the past several days, this call has been heard in our house at least once every five minutes,
“Mom! Dad! I need help!”
It is science project time for the sixth grade at St. Anne’s School. This year, the world’s most spoiled twelve-year-old has gotten on sciencebuddies.org and decided to do her project on how the density of a solution can be determined by the index of refraction. Plus, it involves lasers, so it is hard to beat that. So, every five minutes we hear,
“Mom! Dad! I need help!”
“Yes, what is it?”
“I found on the internet that Snell’s Law is sine(theta1) divided by sine(theta2). What’s a sine function?”
So, I sat down with the white board in the living room floor. (WHY do we have a white board on our floor? Who put it there? I don’t know.) and wrote:
y = f(x)
“So you multiply f and x, right?”
We realized then that she had only gotten so far in school and to her the notation f(x) meant you multiply f by whatever is inside the parentheses. So, I explained the idea of a function, drew out a linear function, a curvilinear function and a sine function.
A few minutes later,
“Mom! Dad! I need help!”
“What is theta1 and theta2?”
So, we find an article on wikipedia that explains Snell’s law and has a diagram showing theta1 and theta2. We explain that theta is a Greek letter, that in math people use Greek letters a lot to stand for things. We point out which one is theta1 and which is theta2 on the diagram in the article. Satisfied, she writes up the first part of her science project – her question and hypothesis.
While she’s at work, Dennis gets on line and orders prisms and lasers from MiniScience.com . In an amazing burst of restraint he only orders two prisms and four lasers and nothing else. Realizing we need something to measure density, I walk down to Sur La Table and pick up a measuring cup that has a digital readout in the handle that tells the weight in grams of what you put into the cup.
She spends a good bit of Sunday afternoon setting up her apparatus and taking measurements, the first part of that is messing with the cup, putting in sugar, checking the weight in grams, dumping in water, calculating the percentage. It involves making a mess and not getting yelled at, a combination hard to beat. Calculating ratios and density is secondary. Being only slightly higher on the maturity scale, Dad helps.
Eventually, he holds the laser while she marks the spot it hits on the ubiquitous white board. They repeat this with solutions varying in density.
“Mom! Dad! I need help!”
“What is it?”
“On this paper it says I am supposed to write down which are my dependent and independent variables and which are my controls. Which is it?”
“Well, the thing that you changed would be your independent variable -”
“The density, how much sugar was in the solution. So the independent variable is the thing that changed and the dependent variable is the thing that stayed the same?”
“No, variables change. That’s what vary means, to change…”
A discussion of variables versus constants ensues.
Over the days that Julia works on her science project she learns about math, including trigonometry, measurement in grams and centimeters, refraction and more. She uses the Internet and finds some sites that interest her. She spends a lot of time on sciencebuddies.com , looking at other projects she doesn’t choose. She reads about Snell’s Law and refraction on wikipedia. Does she understand it all, even with explanation? Nope, but she understands a lot more than she did last month. In making her project board, she uses OpenOffice, decides she doesn’t like that and switches to Microsoft Office. She tries the chart feature within PowerPoint, decides that sucks and does her chart in Excel. She learns how to edit a chart in Excel….
“Mom! Dad! I need help!”
“How do I fix this chart?”
“Right-click on it. Pick select data. Click where it says X axis category labels.”
We have another discussion about X axis and Y axis, categorical data versus numeric data. And so it goes until the project is done. Every year, Julia is required to do a science project because every child at her school is required to do a science project. Similarly, every child in her school takes Algebra in the eighth grade because that is the only math class that is offered. A teacher at a public school district bragged to me recently that her district did the same, every child took Algebra in the eighth grade. I found that fascinating because a few years ago I had done an evaluation for a program at the high school that was addressing the problem that 65% of the NINTH-GRADERS were failing Algebra. So, the solution, apparently, was to teach Algebra in the eighth grade.
This is like back in the 1970s when the solution to children from lower-income families entering kindergarten behind those from middle-class families was to have mobiles over the crib and other accoutrements of the typical suburban nursery.
What Julia has that those children don’t have is both a school that requires more of her and a home environment that provides the support to meet those requirements. There are three computers within reach of where I am sitting, with Unix, Macintosh and Windows operating systems all with either Open Office or Microsoft Office. There is a wireless network in the house. While the stuff makes it easier to do her project, it is not just the stuff and it is not just the requirement to do a science project.
She also has two parents sitting around who are willing (albeit grudgingly at times) to drop what they are doing and explain anything from the concept of f(x) to how to label the X categories on a graph in Excel. While I am writing this, because a documentary on the financial market is on TV, Julia and her father are arguing about economic theories based on rational behavior versus Schiller’s theory of irrational economic behavior. It involves some rather immature discussions of what he might do to the stuffed monkey he is offering to buy from her and tossing of the monkey back and forth.
In the past couple of weeks alone, Julia has probably received 20 hours of tutoring in math and science. Vygotsky would be pleased. Two years from now, she’ll be taking exams to get into high school and I am > 99% sure that she will get into the high school that we have already picked out. Is that arrogant? Nope. With nine years of the advantage of a good private school and day after day of patient (usually!) explanation of functions, sine(theta), X axis, angles of refraction and more I expect she will do well. Currently, she also has an older sister in the house who was a history teacher and is living at home while she finishes her masters. She makes sure to check Julia’s social studies homework and quiz her on that.
Why am I in favor of affirmative action? Because I am not stupid. The world’s most spoiled twelve-year-old has had years of individual tutoring, just about every resource money can buy and excellent, caring teachers every single day. I realize that any child that comes from a low-income home with parents who have never graduated from college and does just as well as Julia on the high school or college entrance exams is probably more motivated, smarter or in some way exceptional.
That’s the way the world is, right? I’ve never been too happy with that answer. So, I am sending an email to the urban schools program at the university offering to teach their teachers how to use SAS On-demand for Academics (hey, it will be free beginning in August). Yes, it is a small thing. I am pretty sure, though, that big changes come from a combination of small things added together.
Maybe you could do something to help. Probably you have your own spoiled twelve (or ten or eight) year old that hollers every five minutes that she needs help, but maybe there’s some little bit you could do to help someone else’s, too.
Of course I am most grateful for my family. As daughter number two, a.k. a. , “The Perfect Jennifer”, commented yesterday,
“This is the only family I know where everyone in the family actually talks to one another.”
It’s true we don’t have any made-for-TV movie problems. No one is in rehab, no divorces, incarcerations, homelessness, domestic violence. The depth in our household is the occasional excess whining.
On the other hand, after reviving from a food-induced coma the various daughters had other plans. Jennifer was heading out to a club to catch up with some friends. I was surprised that any place would be open on Thanksgiving Day, but Jenn pointed out that plenty of people don’t have families, and other people have families that drive them to drink.
So, I went back to some notes I was writing on matrices and realized that I am also extremely thankful for people who take the time and effort to make their knowledge freely available on the web. I was extremely skeptical of the announcement this week that President Obama is supporting STEM (science, technology, engineering & mathematics) education. I picked this link out of the 500+ on the web because it included the interesting comment that most parents would rather talk to their children about drugs than mathematics and science.
While I wish the best of luck to President Obama and all of his corporate cheerleaders, I think the preceding statement is one half of the reason I suspect nothing will come of this. The other half is that the vast majority of teachers I have met don’t want to teach STEM and don’t want to learn it.
This makes me doubly thankful for those who are good teachers and generous enough to share themselves. Let’s take a simple tour of some nice websites with a topic, say, matrices.
Start with onlinemathlearning.com – the videos are excellent for a student who already has some interest in math and perhaps a basic understanding. There are no animated leaping leopards from rain forests here. You know, I am not sure those help. At worst, they give students the message that math in itself is not inherently interesting enough to learn. The onlinemathlearning site gives this explanation of a singular matrix:
“If the determinant of a matrix is 0 then the matrix has no inverse. It is called a singular matrix.”
This is followed by a very understandable video which shows that to invert a matrix one needs to multiply by 1 divided by the determinant. If the determinant is zero, it can’t be done. For those who did not know what a determinant is, that is explained in an earlier page. (Really, you should take a look at the video. It is quite a nice explanation.)
Somewhat surprisingly, given all the dissing it gets in academic quarters, wikipedia has some great math and statistics articles. For example, this one on positive definite matrices gives the following definition,
followed by some equally understandable examples. [Note: For those of you who are shaking your heads and saying, 'THAT'S understandable?' , trust me that I left out a lot of websites that seemed to be written with the attitude that if you didn't already understand everything about mathematics it was your own damn fault and too bad.
A symmetric matrix by the way, is not, like you might suppose, simply one where it has the same number of rows and columns. No, rather it is a particular KIND of square matrix where the matrix equals its transpose. ]
If you would like to know a little bit more about positive definite matrices than you get from wikipedia, you can check out this page on “Not positive definite matrices, causes and cures ” . This is a link from Ed Rigdon’s SEM FAQ page. (It might be said that frequently asked questions about structural equation modeling is an oxymoron, unless the question is ‘What the hell is structural equation modeling?’ )
Now, it no doubt represents a failure in my education that I do not know who Ed Rigdon is. On the other hand, I’m pretty sure he doesn’t know who I am either. Regardless of our mutual non-acquaintance, he gets major kudos from me for the following statement (emphasis added) wherein he touches on one of the major flaws in much use of statistical software today:
“Now, some programs include the option of proceeding with analysis even if the input matrix is not positive definite–with Amos, for example, this is done by invoking the $nonpositive command–but it is unwise to proceed without an understanding of the reason why the matrix is not positive definite. … Sample covariance matrices are supposed to be positive definite. For that matter, so should Pearson and polychoric correlation matrices. That is because the population matrices they are supposedly approximating *are* positive definite, except under certain conditions. So the failure of a matrix to be positive definite may indicate a problem with the input matrix.”
Just because you can do something doesn’t mean you should. LISREL quite sensibly quits under the circumstance when the covariance matrix is not positive definite, and issues you a message to that effect, at which point you should feel shame.
My point, which I do have buried in here, is that STEM education is not about “making science cool”, it is about understanding stuff.
Here is what I am going to do right now for STEM education. I had a talk with my 11-year-old last week about possible questions that could be answered because we can tap into the high performance computing cluster from home and there are all sorts of enormous datasets, including census data. I suggested perhaps her class would like to come up with some questions. Julia made an A in math and did okay on her standardized tests (defined as not nearly as above average as I consider acceptable) and her lowest score was in ‘data interpretation’. Since I haven’t heard back from her teacher, Julia and I are going to hypothesize about such things as the number of 11-year-olds in the country and how many of them live in different regions, the average income, standard deviation of income, where she stands relative to that. Then, I am going to write a program to find all of the answers and run it on SAS 9.2 which we are still testing (no bugs so far) . Since I am still testing it and haven’t used the map library, this will be a nice thing for the university that I am working for free on Thanksgiving weekend and Julia’s knowledge of data interpretation and hypothesis testing will improve.
Whether she thinks it is cool or not.
So, I am loving my new computer – 12 GB RAM, dual quad-core and a terabyte of space. Mac OS 10.6 (Snow Leopard) plus four VMs with Vista 32, Vista 64, Office 32 and Office 64, plus two enormous monitors so I can run Unix programs on our cluster and monitor that while I am programming in the Windows environment or running SPSS on the Mac on the other side. Learning JMP keeps moving up my to-do list, so I got the SAS download manager for JMP, downloaded it to my computer and got this message:
JVM not found.
I suspected immediately it had something to do with Snow Leopard and the fact that I was right about this helped me not at all in fixing it. I could not find any mention of this problem on the JMP site or anything specific to the SAS download manager or JMP anywhere. However, I did find quite a number of explanations of why one might get a JVM not found error and what to do about it.
I found a number of sites with fixes, all relating to installing Java 1.5 on Snow Leopard, some of which were absolute Greek to me (and I have three graduate degrees, including a doctorate with a specialization in statistics where we are used to Greek! )
This one http://chxor.chxo.com/post/183013153/installing-java-1-5-on-snow-leopard from CHXO Internets was absolutely simple to follow and fixed my problem immediately. Hurray.
[Note to self, as soon as I get a spare minute, as in first thing tomorrow, send $20 for shareware fee to Pacifist , I already have another use for this. ]
When I followed the few steps outlined in the blog post above, the SAS download manager installed, then I installed JMP and all was wonderful.
Not being able to move much, I have spent a lot more time lately in the company of my 11-year-old daughter, and that is not a bad thing. She started Algebra this year and she commented to me,
“You know, when I read this stuff, like Y = 3x +5 and what is Y if x is 2, I get it now, but I know if I went back to myself as a kindergartener, or if I said it to a kindergartener now, they wouldn’t understand it. Did you know that math is like a language? I feel like I have learned to speak Alien language or something.”
I stopped what I was doing, which was installing the SAS software depot on the Linux computer in the living room, and said,
“You’re right and it gets better and better from here on out. You got done with the boring part of math where you have to memorize your times tables and stuff and now it is the fun part. There’s lots of other languages you can learn and every time you learn one the next one gets easier. Some day, you’ll be able to do things and say things in that language you can’t even imagine now.”
So, I feel like she made a major breakthough this week, all on her own. At some point, we will have to have the opposite talk, which is that no matter how good you are at math there is going to come a point where you just don’t get it and you have to struggle through. For years now, when I have looked back on having won the world judo championships in my twenties, it has struck me odd in retrospect that at the time it all seemed perfectly natural, being best in the world. Now, even older, when I look back at graduating from college at 19 or my graduate courses in statistics and realize that two of my professors gave me an A+ in courses when the grading scale only went up to a 4.0 for an A, that is all quite odd, too. One of them explained that I had not only had the highest grade, but was a standard deviation above the next student, so he felt he had to do something. At the time, it seemed like just what I did, though and I did not think of myself as particularly good at math or statistics, it was just something I happened to like and the university offered graduate courses in it, I lived a few miles away and had three babies, so it was something to do. In retrospect, I run into my old classmates and they all still remember me as “Oh, you were the statistics BRAIN!”
AND YET, there have been so many times when I read something not just once but two or three times before I got it.
There are times to this day when I attend a presentation on say, multiple imputation, and I have a general idea, but I don’t feel like I completely understand it, so I read an article on it, and then another, and it gels. There are other times when I feel completely at sea. The first time I read an article on LISREL (probably the first program that came out on structural equation modeling) and I understood about 10% of it. So, I got Leslie Hayduk’s book on structural equation modeling and read the whole thing and still didn’t understand half of it. I took a course from Keith Widaman, at UCR and then I felt like I understood a good bit, which I am now trying to remember as I get more SEM questions these days.
My point, and I do have one, is that no matter how good you are in math, there are always those bumps in the road. You just have to barrel through. To read the book over and over, read a different book, take a class, be determined to understand it, and you will. You need to learn not to give up. Then, when you move from matrix algebra to Linux, you learn to keep trying, if
doesn’t work, try
Eventually, you’ll find yourself talking to the aliens as if you’ve known them all your life.
Whether you are a statistician, SPSS guru, SAS programmer or professor and world-renowned expert on re-incarceration, odds are great that you are susceptible to bubble-vision. You work, breathe and socialize within one or two very narrow bubbles.
This is bad and unhealthy. You’ll miss much of life that is beautiful, exciting, dramatic, interesting, tragic and delightfully fun. You’ll also focus too much on things that are not particularly important because you are looking only at whether your colleague in the Study of Very Important Flagellum Department unfairly criticized your latest conference presentation, who voted for you as Treasurer of the SVIF Society and what that editor of the Journal of SVIF said about your latest article submitted.
Be like Julia (the eponym for The Julia Group), live life large, interested and happy. In the interest of that goal, here are some interesting links to follow that relate to the world outside of my personal bubble:
The Disease Management Care Blog – is unfortunately named because, contrary to what you might think, it is far more interesting than a rectal exam. The latest post was on Comparative Effectiveness Research. I don’t wholly agree with the point cited that CER doesn’t take into account co-existing conditions, personal preferences, etc. It may not in all cases but that is no reason it couldn’t. The author discusses both sides of the issue of CER funding, whether we are spending too much on it, too little and does it do any good in the end? These are pretty general questions of life.
I love the New York Times because their coverage is intelligent and thought-provoking. This series on social class in America is even more the case than usual. My family certainly lives in a different class than the one I grew up in. When Julia was about four, I asked her if someone she had mentioned was her friend’s mother and she answered contemptuously,
“No, she’s him’s ‘anny !”
After all, who could be so dumb as to not know it is your NANNY that takes you to the park, not your mommy. Your mommy is probably working on a documentary or writing a blog on statistics or at the hospital delivering a baby.
When I was eight years old, I walked a mile home from school with my brothers and sister. During the summers, we watched ourselves, made ourselves lunch and solved our own fights, by means best not shared with my mother to this day. Let me just say that the broken front window, the broken down bathroom door and the scars on my second brother’s forehead – none of those were me. My oldest brother’s broken finger or the drainpipe inexplicably pulling away from the second floor, well, I plead the fifth.
Their discussion of class was fascinating to me in part because, being over-involved in judo (I am the president of the United States Judo Association) in my copious spare time, of which I have none, I meet people from all possible strata of American society, most of whom haven’t a clue what a stratum is. Some are absolutely infuriated that I do not do as I am told. What the New York Times articles highlighted was the class differences in the value placed on doing what one is told versus finding the right answer. It never even occurred to me that blind obedience could even be considered a virtue.
Wiki-books is an interesting concept. Free textbooks. Not great in quantity, but hey, if you want to contribute, go ahead, or read whatever happens to be there. Every now and then I go just to read at random. Today, I read How to Do Nothing. As anyone who has ever met me can tell you, it is a textbook I sorely need to read.
Speaking of the judo association, another good site to check out is the page on Social Capital from bettertogether.org . This Internet thing is pretty cool. Where else could you read original research by people from Harvard University while sitting in your massage chair? Or find 150 ways to increase your social capital.
Right now, I think I am going to do #86, log off and go to the park, even though I am not, in fact, a nanny.
Logistic regression is based on logarithms. Ordinary Least Squares regression and analysis of variance uses the actual values as the dependent and independent variables in an equation. Logistic regression does not.
What is a log, anyway?
Let’s start with the very basics. First we learned to add:
5+5+5+5 = 20
After about eight years of age, we realized that was pretty inefficient so we started multiplying
5 x 4 = 20
We got a few years older, thought, why stop there, and got into exponents
5 x 5 x 5 x 5 became 5 to the fourth power = 625
Then we get into logarithms, where the log to the base 5 of 625 = 4
Think about this. Really think about it. Go to the wikipedia page that has a good explanation of logarithms and read that.
Calculate the logs of several numbers to different bases, just for the heck of it. I have noticed that, so often, students skip over topics like logarithms thinking, “I don’t need to know that.”
This is wrong on a whole lot of fronts, just one of those reasons being it is a really bad habit to get into. I don’t know how many reports I read in the newspaper of people losing their homes that included the statement,
“Mr & Mrs John Q Public said that they did not understand the mortgage papers, that they just trusted the real estate agent, the banks or the ad they watched on TV at 2 a.m.”
So, whose fault is that. Understand what you are doing! Start with logarithms. It’s as good a place as anywhere else.
I was going to write about the log of odds ratios and explain logarithms. This is the very, very odd fact I have noticed in most of social science – people in doctoral programs are often thrust into statistics course for which they really don’t have the basic mathematical foundation. This is because if they were really into mathematics they probably would have gone into that in the first place, but they didn’t. They majored in history or liberal studies or something else. They became teachers or social workers or counselors. In doing so, they took the one (count ‘em, ONE) required mathematics course to get a college degree. Further dismaying news, the one mathematics course has been changed dramatically since I was in college – now, you can get a degree with a C- in College Algebra – whatever that is. It definitely does not involve logarithms. When I went to college, Algebra was something you were supposed to have had in high school. But I digress. This whole post is a digression so now I have digressed squared.
So, what did I do all day if not write about logarithms?
Downloaded a dataset from the Interuniversity Consortium for Political and Social Research, which is a site I truly love. What a great idea! Finished with your data? Upload it to the Internet and let anyone else use it for whatever they can find.
Spent an hour (I am embarrassed to confess this) trying to find the error in my SPSS syntax and could not figure out why the HELL it kept saying “file not found” when I could clearly see it there. Finally, as a last resort, went to the c:\ prompt, listed the files and realized that Windows, designed by Machiavelli, hides part of the file name so that my file was actually named college.txt.txt . AAAGH !
Monir, the travel lady, stopped by and took care of my reservations and registration for SAS Global Forum.
Worked on the PowerPoint for my Enterprise Guide class next week. For once, did not waste time rotating the charts in space to see how my bar chart would look sideways (oh, don’t pretend you never did it!)
Enterprise Guide runs pretty slow on my old computer with only 1 G RAM, and EVERYTHING runs really slow with the size of some of the datasets I have been using. My Mac desktop only has 512M RAM (I know, I am deprived) and I was kind of tired of using my laptop and the Unix server for everything.
Today, Justin a.k.a., our hardware guy, came by and told me he had a new computer for me. Like everywhere else, we are watching the budget but somehow he came up with one. So far, I have installed SPSS 17, run a factor analysis with 191,000 subjects and it ran in less time than it took me to type this sentence. I am very happy. Installing the applications I need took a good bit of time, but it will be well worth it in the end in saved time and aggravation. I decided to try something different, so I installed Seamonkey as my browser and downloaded Open Office and Gimp instead of Microsoft Office and Photoshop.
Speaking of sea monkeys, I thought this would be a good example of how statistics can be applied to everything. Even though I work about a block from the museums and Exposition Park, I have only been there once in the last year. So, Tuesday, I walked over to the science museum shop and bought a sea monkey kit. My idea was that I would have it on my desk, collect data and use it in different statistical analyses.
This could also be an example of creativity in analysis in trying to come up with different variables. My original thought was perhaps I could begin with the number of sea monkeys hatched. Unfortunately, statistics for the day are :
Specks floating around that could possibly be sea monkeys – somewhat less than a zillion. I would give a close approximation as 1,000.
Matter which can be definitely distinguished as sea monkeys- 0.
I probably should re-read that code on break point analysis before the meeting tomorrow. I should finish editing the on-line ethics course. Instead, though, I am sitting here with Jenn watching episodes of Numbers on DVD.
She wanted to know, “Is that really true? Can you tell that someone cheated by random numbers? That doesn’t make sense.”
I told her that it was exactly true. It’s like the old Sherlock Holmes story, the Curious Case of the Dog in the Night Time – what was significant was what you DIDN’T see. Sometimes, the telling evidence in an evaluation is that relationships don’t exist where they should, because the numbers were just made up and entered in the database, because, after all, who would ever know?
Yes, I am the F-word – a feminist. I was at a faculty meeting this weekend and one of the presenters began by saying, pointing to a colleague in the audience,
“I am sure Dr. Y knows more about this than me.”
Several times in her presentation on analysis of assessment data she would pause and make comments such as,
“Well, I am not very good at statistics, but this is pretty easy to understand.”
I was a bit annoyed at her self-deprecating manner. I wanted to walk up to her and say,
“You understand this perfectly well and I know Dr. Y, who is very smart and competent, but no more so than you.”
Even more annoying was another presenter, also a woman, also very competent, who gave a very good presentation on assessment. Near the end of it, she said,
“You don’t have to use numbers. For those of you who don’t do math, you can put your students in categories as having exceeded criterion, met criterion or failed. You can just put it in bullet points.”
For those of you who don’t do math …. ????
What the hell? This is a university faculty meeting; 99% of the people in the room have graduate degrees and at least three-fourths of them have Ph.D.’s.
Since when has it become acceptable to not be competent, particularly in math??? Would that same presenter have started a sentence with,
“For those of you who can’t read, I have recorded this presentation as a podcast?”
There may be some people who can’t read because they are visually impaired or have a learning disability, but we consider this a disability, not a lifestyle choice.
This particular department is overwhelmingly female, and I could not help but wonder if the same sort of statements would be made in a predominantly male department? In my admittedly non-random and non-representative experience, the answer is, “No.”
So, first of all, for all of you women (and men), who say you aren’t good at math – cut it out! That’s a lot of nonsense that some people are naturally good at math and some aren’t. It’s a lot like swimming. You aren’t born knowing how to swim and, yes, very few people will become Olympic swimmers, but the vast majority of people can learn to dive in a pool and swim a few laps. It just takes time and effort to practice.
Let’s start with the phi coefficient. I blatantly stole this table from the Children’s Mercy Hospital website because I thought it was very well-explained and easy to understand – until I realized that it wasn’t and I only understood it because I already knew exactly how to calculate a phi coefficient. However, not one to let any act of larceny go to waste, I used it anyway.
The formula for Phi is
Notice that Phi compares the product of the diagonal cells (a*d) to the product of the off-diagonal cells (b*c). The denominator is an adjustment that ensures that Phi is always between -1 and +1.
Let me explain this a little better. We have two categorical variables, gender – coded 1 =female, 2= male, and “Did you eat today?” – coded 0 = no , 1 = yes
In our table below, you can see that there is zero correlation between gender and if you ate today, as males and females are both equally likely to have had something to eat.
Gender \Ate today? NO YES TOTAL
Female 10 90 100
Male 10 90 100
Total 20 180 200
When we subtract (10*90) – (10*90) — obviously, the numbers are the same, so we get zero. There is zero relationship. In the formula above, a, b, c & d are the numbers in each cell.
So, we have mathematically shown that there is no relationship between gender and whether one eats or not. Let’s try another question, “Did you do the dishes?” This time, we get the following results:
Gender \Washed Dishes? NO YES TOTAL
Female 10 90 100
Male 90 10 100
Total 100 100 200
Let’s look at the phi coefficient again.
10*10 – 90*90 = 100 – 8100 = -8,000
100*100*100*100 = 100,000,000 and the square root of that is 10,000
So, our phi coefficient is -8,000/ 10,0000 or -.80. That is a pretty high correlation, considering that the coefficient ranges from -1 to +1.0 . A negative coefficient means that those who are lower on one variable (1= female, 2= male) are more likely to be higher on the other variable (0 = did not do the dishes, 1 = washed dishes).
So, our conclusion is that, while women are no more likely to eat each day than men, they are significantly more likely to do the dishes with data that I just made up to prove it. My daughter, Maria, tells me that any married woman knows that without the need for statistics.
Why did I just go into this in such detail and all about one coefficient? Because I think that is a big part of the reason that many people don’t learn math is that there are so many assumptions that we can “just skip over this”. In fact, the reason I liked the Mercy Hospital site is it did not start out with n10n21 – n21n10 / √(n0+n1+n+1n+2)
and assume that everyone knew what marginal distributions and array subscripts meant, because, I can guarantee you, that they don’t.
Sheila Tobias wrote a really interesting book about teaching and learning science, the title of which is “They’re not dumb, they’re different”.
Maybe, but I guarantee you that part of the problem is that they’re not clairvoyant. No one was born knowing that n10 means the number in the cell where the row value =1 and the column value = 0. It doesn’t help that at other times that same cell would be represented as n11 as the first row and first column.
If you can make that switch in your mind easily, it is no doubt because you, like me, have looked at thousands of matrices and had that notation explained to you so long ago that it is probably like learning to swim, you can’t even remember it. The secret to being good at math is the same as being good at swimming – practice!
Completely random fact – in my misspent youth, I was the first American to win the world championships in judo. If you type judo blog into google, the first of 3,000,000+ pages that comes up is mine. And my most recent judo blog was on outliers and practice. Rather unusual when the two halves of my split personality come together.
As to odds ratios, I have more to say about those, but it is 1:30 a.m. and I have to get up in 7 1/2 hours to go to work, so that will have to wait until another day.