Science Buddies: "Ask an Expert"

The project is to determine if background stimuli affect performance on math test. The 50 math problems are the same on all tests. The environment changes (music, TV, "silence"). The MEAN values are 24.71, 20.03 and 22.36. The STANDARD DEVIATION values are 9.78, 10.12 and 8.71. I am not sure what to do with these values. There are terms I have read about but do not understand if they apply to my project. For instance, do I want to find if I have STATISTCAL SIGNIFICANCE? Do I want to find what is the STATISTICAL CORRELATION of the tests? And if I do, how do I do it.

Hi jbrock,

Great to see someone concerned with doing statistics right on a science fair project! Sounds like the start of a great report.

I think "statistical significance" will be a good keyword to describe what you're after. Some other keywords you may find useful are "student's t test" and "significance test."

Basically, the question you want to ask (or at least one of the questions you can ask) is "what are the chances that you could get differences as big as the ones you saw if the environmental changes had *no* real effect on test scores." The answer won't be zero. Since there's some scatter in test scores even without changing conditions, there's always going to be some chance that what you've observed is just a coincidence. The value of 1 minus the chance that what you've seen is a coincidence is generally considered an estimate of how likely it is the differences you've seen are real. Often that's called a "confidence level." Someone will say, for example, "the results are significant at the 95% confidence level," meaning that there's less than a 5% chance that the differences were just a coincidence.

(A subtle point that you can probably ignore: what that result actually tells you is the chance that *something* was different. Whether or not the different thing is what you are interested in depends on how well the experiment was designed.)

There are a few different approaches one can take to trying to answer that question. The usual method is to assume (or show) that the variation in scores on tests under a single condition are Gaussian. (If it isn't clear what that means, you can probably skip it for now. "Gaussian distribution" and "probability density function" or "gaussian pdf" are good keywords for more info if you have time and interest.) Assuming that condition is satisfied, which is often true, then you can apply some cookbook statistics formulas to estimate the chances that the differences observed are real. There are some tests best suited to small data sets, which are probably most appropriate for your experiment.

I'm sure I or someone else here can offer some more tips to get you started if you find it hard to know where to begin. There are also a number of good books on the subject which you might be able to find in a local library. It would probably help to know what math class you're in and how long you have to work on the project, so as to recommend suitable material.

Good luck,
Erik