Understanding Different Types of Correlations

Business Drivers The correlation between two variables is the degree to which the variables move in the same direction. A positive correlation means that the variables both move in the same direction, and if they are correlated that a movement in one will result in a movement by the other. For example, the number of students who need school lunches and the funding that the school receives for lunches will have a positive correlation. This is because the funding formula is based on how many students need lunches.

There is basically a variable cost element to that, where each student is worth x amount of money, so every student that needs a school lunch increases the funding that is made available to the school to provide that lunch. A negative correlation means that as one variable moves up, the other variables goes in the opposite direction. For example, the age of the student when the subsidy is received will be negatively correlated with the impact of the subsidy.

The reason for this is that the subsidy for school lunch will have a greater impact on younger students. Those younger students are in a position where a school lunch affects their growth, both physically and mentally. The older a kid gets, the less this effect will be. So basically, a student in the first grade will benefit more from the school lunch than a student in the twelfth grade.

A student in the twelfth grade probably still has some benefit, but the costs associated with skipping a meal are not as bad for someone of that age, whereas they can be quite disastrous for someone who is very young. So the negative correlation here is that the impact of the subsidy declines as the age of the student increases. A minimal correlation is when there is little relationship at all between the variables.

For example, there might not be much correlation between the number of classrooms connected to the Internet and the student performance on the exams. In order for there to be a relationship, the computers would need to be used to study material that is one those exams, and in fact for a positive relationship the computers would have to be better than whatever analog method is currently being used. So there may or may not be a correlation.

There will, however, be a positive correlation between the teachers' comfort level with the Internet and the ability of the teacher to use the Internet effectively with the students. If the teacher is not comfortable, they might not put much emphasis on the Internet, they might be inefficient or they might just be really bad at teaching with it. Overall, there is going to be a positive correlation between the more comfortable the teacher is, the more effective he/she will be.

But there are lots of examples of things that are not correlated, unless there is some weird butterfly effect. For example, there is no correlation between how many times a lioness licks her cub's head and the chance of rain in Philadelphia. Even if the lioness is in the local zoo there, there is still no correlation. In the Goolsbee and Guryan study, there were a few correlations examined. They noted that the use of E-Rate was positively correlated with the percentage of students who required school lunches.

What this meant was that the subsidy program.