Determining a Relationship Between Two Variables

¶ … reach significance, one can conclude from the analysis that there is no correlation between GRE and GPAs at the end of the graduate program for electrical engineering in the Ivy League university between 2000 and 2013. In other words, when one variable changes, it does not reflect in the change of the other variable in a linear way (Lecture 5 Notes, n.d., p. 1).

For significance to be shown, it would have to be seen that the variables' values were statistically correlated in a manner that could be "represented in a linear equation" (Lecture 5 Notes, n.d., p. 1). No consistency in change signifies that there is no correlation. Thus, if one's GPA is 3.5, a reasonable guess cannot be made regarding what that individual's GRE score would be.

Or if one's GRE score at the start of the program is x, one cannot make a reasonable guess as to what that person's GPA would be at the end of the program. The GRE, as indicated by the data, is not a strong indicator of GPA. While correlations "are never perfect" one should still expect correlating variables to allow for accurate predictions (Lecture 5 Notes, n.d., p. 1). Variables do not necessarily have to move in the same direction (positive correlation) -- they can move in opposite directions (negative correlation).

The point is, however, that for variables to be correlating, there has to be consistent movement over a period of time indicating that there is a significant relationship between the variables. In the case of GRE scores and GPAs at the end of the program, the data does not signify any consistent movement in either direction. Thus, it can be determined that there is no correlation/relationship between the two variables, and that the one is not a good predictor of the other and vice versa.

The results cannot be generalized to all graduate students in electrical engineering master's programs across the U.S. because they are specific only to this particular data group, and alternate data could possibly show a stronger correlation that is not apparent in this subset. 2. These are valid hypotheses for the research question based on what the researcher is attempting to identify, i.e., whether there is a relationship between GRE total scores and GPAs in the master's programs in electrical engineering.

As Lecture 4 Notes (n.d.) indicate, "If the researcher is interested in a simple contrast of certain variables, observing group differences may be the natural hypothesis" (p. 1). For this particular question, the researcher is looking to see if either variable is an indicator or predictor of the other. A correlational analysis therefore would be appropriate and the questions to ask for such an analysis can be based on whether there is positive correlation, negative correlation or no correlation.