Scatter plots can be used to analyze your GRE Examination, or to evaluate your own test preparation strategies and the information you present to your GRE teachers and classmates. A plot that shows the mean average score (MAS) of students who took the GRE examination in the past four years, for example, is a good indicator of how your scores have changed over time. This information can help you determine how well you prepared for the exam, and whether your current approach and tactics are yielding results that meet your expectations.
Of course, a plot that demonstrates a significant deviation from the mean (which is what a Scatter plot for a GRE examination would indicate) is not necessarily indicative of cheating. The difference in the values of a random variable (i.e., a uniform distribution) and a distribution that deviate from its mean value is not random. The deviation is not random either. It is the result of some underlying pattern. The random variable distribution that shows an extreme deviation from its mean value is actually a “distribution” of a statistically-defined statistical process (e.g., binomial random variable).
There are a few basic elements that you should look for when evaluating your GRE Examination results and using scatter plots to analyze your performance. First, you should determine if the distribution of the data (i.e., MAS distribution) deviates from the means (the sample mean) of other students who have taken the exam. If there is a significant deviation, it can be used to assess whether your approach is yielding consistent positive results. For example, if the MAS distribution for a particular study session deviates from the mean by five percent, this is an indication that a different student is probably having a significantly different experience from the mean. However, it doesn’t necessarily mean that the other students who took the examination are cheating, especially if there isn’t a clear difference in their results over the course of the study session.
Second, you should be careful in interpreting the meaning of “significant deviations” as there may be two or more other factors that could explain why the distribution deviates in question, such as multiple testing sessions, a student’s personality and/or a student’s practice and knowledge. Since the distribution may have significant deviations due to several variables, there is a strong possibility that a significant amount of variation is left unaddressed. For example, a large deviation from the mean for one particular test could mean that a different student performed worse than average because he has poor test taking skills. A very large deviation from the mean could mean that the opposite is true.
Another concern when interpreting scatter plots for your GRE examination is the possibility that a significant deviation from the mean (i.e., the sample mean) will indicate that the test taker does not prepare adequately for the examination. The distribution may not have any real meaning, but if it seems too high (as it sometimes does) then it may be because the student is using too many strategies to boost his/her performance. Therefore, it may be better to avoid using scatter plots on a test score (especially if your teacher suggests using them). If the results of your exam is very close to zero, there may not be enough information to show a significant deviation, and a small deviation could mean that the student is not as prepared as he/she might have been. If your instructor has suggested using scatter plots, however, you should still avoid analyzing the data using them unless it is appropriate.
One other thing to keep in mind is that a distribution can be plotted without considering all of the important aspects of the distribution itself, such as the distribution’s standard deviation. By considering only the mean and standard deviation (which is easy to analyze with other methods), you will not receive a valid estimate of the distribution’s reliability. There are also other ways to get an idea of a distribution’s reliability, such as calculating its kurtosis (a measure of its dispersion), but the former methods are much easier to interpret and obtain an accurate value from.
In conclusion, while scatter plots can be helpful for students who are preparing for the GRE, they are not a reliable indicator of whether or not the student is really ready for the examination. When you need more solid information on the GRE test, such as data based on multiple-choice tests (and particularly when you need to compare data across multiple testing sessions), you should use kurtosis or other non scatter plots to provide an accurate reading on the performance of students.
