Technical Brief on the 1999 Statistical Model

A Visualization of the RI Model

While we can not draw a graph for multivariate analysis like one can do with simple regression models; perhaps a virtual (spatial) image of the RI model would be helpful. Imagine a large empty room with transparent walls. Inside the room is a set of thousands of small balls suspended in space and stretching unevenly across the room. These balls represent the actual scores of all students in one particular grade who took one of the state tests. When you look into the room from the North (SES) side you notice that the balls spread across the room are variously tinged with red ranging from brilliant red (very poor) to very light, almost non-existent red (very wealthy). You note that most of the brilliant red balls are concentrated in one end of the room and most of the very light, almost non-existent red balls are concentrated in the far other end of the room. However, you do note a few brilliant red balls scattered here and there throughout the room, including even the far end where the very light balls hold sway.

Similarly, as you move to the West (Special Education) wall and peer into the room, you now notice that the balls viewed from this angle are tinged with two types of blue The deep blue balls represent students receiving services under special education law and the light blue represents students not receiving any special education services. Once again you note that most of the deep blue balls are near the same location in the room although there are exceptions. Some light blue balls can be found throughout the room, but most are concentrated toward one end of the room.

Now you move to the East (bilingual and LEP programs) wall and notice that there are two kinds of purple balls - dark purple (receiving services) and light purple (non-recipients). You note dispersal patterns among the purple balls similar to what you have noted with the previous colors.

As you now move to a platform to peer down into the room from the top, you now see that all the balls are colored from a bright yellow (very high achievement score) to clear (a zero). However, you note a crucial difference from what you have seen in the room from the other two walls. All of the bright yellow balls are in one end of the room and all of the clear balls in the other. In fact, balls with identical or very similar shades of yellow are uniformly found in the same approximate location within the room.

A person now opens the door into the room with a large transparent cube with colored balls in it speckled with the blue and red hues you have already observed. Each ball is also uniformly colored green (to represent the fact that these are all students from the same school). He releases the balls into the room from the cube and they magically head to various locations within the room. You note from your vantage point at the top of the room that they all have arranged themselves at varying places within the room with some concentrated at particular places and some existing solely by themselves with no other green balls anywhere near them. As you descend to the West (special education) wall, you see that nearly all the deep blue balls just released into the room have arrayed themselves in the end of the room where most of the deep blue balls are concentrated. Similarly, as you move to the North (SES) wall you notice that most of the brilliant red balls from this school have arrayed themselves with their counterparts (other very poor students from across the state) and the East (bilingual/LEP) wall similarly. Finally, as you move to the South (school) wall, you notice clearly that you can easily pick out where all the green balls are within the room. In fact you discover that you can count how many are in each section of the room. The majority of balls representing student achievement scores on this particular test from this particular school are concentrated within a given area of the room. The person who released the balls now explains to you that what you have seen is a statistical model of last year's student performance for the state. Each time they release colored balls representing an individual school within the room, 95 times out of a hundred, the balls end up in the approximate location where you now see them. "Is it chance, or just coincidence?," he asks you. You reply, "I will have to go to that school and see what I can find out."

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