In the shower this morning, I was thinking about how seldom true longitudinal designs meet the assumption of sphericity. This is the point where one of my daughters always makes a comment about what other people think about in the shower. I don’t want to hear it.
Sphericity is an assumption that all correlations among the dependent variable in a multivariate design are equal. This is generally a stupid assumption for longitudinal designs because it is saying that the correlation between say, IQ measured at age three years and four years is the same as between IQ measured at three years and six years of age. In other words, all correlations will be equal regardless of the time interval between them, whether the measurements were taken six months apart, a year apart or three years apart. Admit it, you agree with me and are now thinking to yourself,
“What kind of stupid assumption is that?”
Most statistical packages will test the sphericity assumption and then immediately reject it. Your output will also contain a useful few lines that give the mean square and significance with the degrees of freedom adjusted for the violation of the sphericity assumption. The Greenhouse-Geisser adjustment is a popular one.
I’m in a rush today so if you want to read more about this, the absolute best chapter I have ever read on MANOVA with repeated measures is in a wonderful book called Applied Longitudinal Data Analysis for Epidemiology by Jos Twisk. No, it is not the only chapter on MANOVA with repeated measures that I have ever read. Don’t be a smart ass.
I got this book from the central Los Angeles Public Library, which is an amazing place. It is six stories of books – an entire floor on science, a floor on business and technology, another floor for literature, a floor for children and teen books.
It’s beautiful in fact, intent and effect. Every time I go there it restores my faith in humanity. Not only is there an enormous amount of human knowledge stored here free to anyone who walks through the door, but it is also supported by public funds and private donations. Everything in the library is tangible proof that some people cared about society enough to spend their time and energy on making this place possible rather than on buying another iPod or cafe mocha for themselves. Philanthropy is not a dirty word and caring about making the world a better place, yes, even through your taxes, does not make you a communist. And I pay one hell of a lot of taxes. More than General Electric, I can tell you that.
The library is no longer open seven days a week. Due to budget cuts, they now need to close on Sundays and Mondays. I used to buy the argument that we cannot have the library open seven days a week because it is just plain math. We are broke. We keep hearing that, the state is broke, the county is broke, the city is broke. If we take in $X per year and running services the way they are costs $(X +Y) then we have to cut services. It’s basic math.
But there is that assumption again. The unstated assumption is that we will get no more income and that there is no more income to be had. Michael Moore made an insightful comment on the Colbert Report the other night about the trillions of dollars owned by the richest Americans. Before you start screaming that we are punishing the successful, I’d remind you that managers who ran companies that lost billions of dollars received a government bailout and then hundreds of millions of dollars in bonuses. I’m not sure what definition of successful includes having your company lose billions of dollars.
We keep getting told that if we do tax these extraordinarily wealthy individuals and their corporations that it will cost jobs. Actually, it seems to me that those corporations are already creating jobs in India, China and other countries rather than the U.S. – Andy Grove, Intel CEO, noticed the same thing. (Lois Kazakoff has a great post on this topic and Grove’s ideas )
Just like the sphericity assumption is stupid if you stop and think about it, it is just as stupid if you assume that just because some people are making hundreds of millions of dollars that they are the best, brightest and smartest in America and that we will fail and become bankrupt as a society if we make them pay more taxes than they pay now. In fact, the top 1% of earners paid a larger percentage of their income in taxes and there were greater taxes on wealth over thirty years ago and our budget was more balanced and unemployment was lower. Could it possibly be that part of why they are so rich is that they have the wealth and power to change the tax laws and other laws and regulations to benefit themselves?
If we lay off people who work for the government, unemployment will be immediately lower (as those people lose their jobs). The assumption is that corporations will see their taxes being lowered and then hire more people so employment will eventually go up. That assumption has not been born out by the facts. As Jon Stewart noted, not only did General Electric not pay any taxes but they received billions in tax credits, which amounts to a negative tax rate. If you don’t think Jon Stewart is a credible enough source, you could check out articles other places like the New York Times or CNN.
The assumption we are asked to make is that GE would not be globally competitive if they had to pay taxes. General Electric reported a $5.1 billion profit on American operations last year (let’s assume that is fairly reported, another questionable assumption). They paid taxes on none of it.
I paid taxes last year and I kept working, in America, even. I’d like to try a different assumption, and that is that if we closed the loopholes and made GE and its executives and largest shareholders pay the same tax rate as I pay that we’d be able to keep the library open.
Maybe more people would come there and learn about things like applied longitudinal data analysis, apply that knowledge to developing innovative technology and create jobs.
Let’s try that assumption for a while, because the current one isn’t working