Eva Young wrote: > I've never had a statistics class, but I have had calculus, through > differential equations, and I'm not sure what Atherton is refering to with > his reference to "regression models" and "variances." It kind of reminds > me of how computer techies talk -- and when you ask questions -- rather > than being afraid of sounding "stupid" -- a few follow up questions reveal > the person doesn't know what they are talking about.
I've had calculus, though not through differential equations, and when I became an education major I was shocked at the complexity of the statistics courses (even after having had statistics courses in psychology and computer science). Regression models and variance components are conceptually complex, but absolutely necessary for understanding educational research and making educational policy decisions, but it is not surprising that people outside of the field are unfamiliar with the terminology. I'll try to give a quick overview so that we can all be on the same page and we can continue to discuss these issues intelligently. "Models" in mathematics and statistics (generally) refer to equations that describe something about the real world. For example the equation, distance = rate X time, tells you how far you'll travel if you drive at a specific speed for a given amount of time. It allows an accurate prediction of the distance from your starting point. In statistics we also create models to describe situations and make predictions. The idea of a regression model is to derive a formula to describe the relationship between one factor and given a number of other factors that one collects data about. For example, if we were interested in knowing what factors contributed to heart attacks, we could go collect data and then use a computer program to create a formula that would describe the influence of each factor on heart attacks. This formula would actually allow us to predict how likely an individual would be to have a heart attack, given say their age, weight, sex, amount of exercise, etc. Now let's consider the specific model that Ms. Johnson cited. This model was designed to describe and predict student achievement based on parent involvement, teacher quality, and class size. First point: It is the researcher who gets to pick the factors. In this case the researcher picked parent involvement, teacher quality, and class size; they could have just as easily picked student intelligence, socioeconomic status, ethic background, or any other set of factors. Usually, a research has some notion of what might be the most important factors and picks those. Second point: The factors that you select never completely describe or fully predict the factor that you are interested in. SO, in this student achievement model, parent involvement, teacher quality, and class size cannot fully account for everything that contributes to achievement. There is always some, "portion of the variance" unaccounted for by the model. That is why the numbers didn't make any didn't make any sense. When Ms. Johnson originally reported them. She said, research shows that "...student achievement can be accurately measured as follows: 49% attributed to parent involvement, about 42% teacher quality, and about 8% to class size." Well if you sum up these percentages the result is 99%, leaving only 1% is account for by any other factors that might reasonably contribute to achievement. Well then, when I check the article it turned out that the numbers were really 49%, 43%, and 8% which sums to 100%, and that makes even less sense. So here is the problem. Ms. Johnson most likely got her numbers from a pie chart on page 9, which divides the pie into only three pieces, the three factors mentioned above. The pie chart is titled, "Influence of Teacher Qualifications on Student Achievement." Then, in really small print it says "Proportion of Explained Variance in Math Test Scores Gains." Well, it's true that if you only included these three factors in your model, they will account for 100% of the EXPLAINED variance, because they are the only factors that you included in your model. What is not mentioned is how much of the variance is not accounted for by the model. In other words, the three variables (parent involvement, teacher quality, and class size) may account for say 20% of the total variance, leaving 80% of the variance unaccounted for by this model, but we don't know because this article never reports what amount of the influence on student MATH achievement was not accounted for by their model. This is really important because without knowing the influence of the unknown factors you can't truly calculate the influence of the known factors. The upshot of this is that this report is very misleading (be it intentional or otherwise), thus it is reasonable that Ms. Johnson could have misinterpreted the data. And, it's true when Ms. Young says, "figures don't lie, but liars figure." The upshot of this is that we can't expect to improve the schools and help students using lies and false data. This is why it's so important for school administrators be able to evaluate the research. I don't fault anyone for not knowing statistics when they are elected to the school board, but they better get up to speed before they start making decisions that are going to impact our children. Michael Atherton Prospect Park _______________________________________ Minneapolis Issues Forum - A Civil City Civic Discussion - Mn E-Democracy Post messages to: [EMAIL PROTECTED] Subscribe, Unsubscribe, Digest option, and more: http://e-democracy.org/mpls
