29 Sep 2022


Correlation Analysis: Definition, Methods, and Examples

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Academic level: College

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Many researches and educators have pondered about the relationship between Intelligence and academic achievement of students (Angela & Duckworth, 2004). In order to find out if this may be true experiments have been done, to try and correlate the two variables. Hypotheses formulated as a basis for research are that for a particular set of students, there is no external or independent variable that affects the relationship between GPA and IQ. Based on that null hypothesis, an alternative hypothesis can be formulated in that, for a given group of students, it’s possible that there may be a correlation between their grade point average and their intelligence quotient. It is important to note that both these variables are measured using standardized tests with a specific grading criteria. Other variables that cannot be quantified such as self-discipline, working memory and socioeconomic status are not accounted for in the study.

In an educator’s study of a sample of 30 ninth graders, aged fourteen years old, the two variables used were, intelligence quotient and grade point average. GPA was the independent value and IQ was the dependent variable. The ordinal variable was that the students were all 14-year-old ninth graders. The interval variable was the GPA scores as they can be measured according to specific intervals. Intelligence quotient was the nominal value since it can be categorized without having any kind of natural order.

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Based on the results obtained, both the results of the GPA and IQ analysis give normal distribution curves. The GPA results have evenly distributed scores across the GPA intervals. The frequencies with most of the GPA values are very similar and therefore shows that the GPA values across all the 30 students are independent of their IQ levels. The GPA values ranged from 1.80 being the lowest value to 4.00 being the highest value. On the other hand, the IQ values ranged from 75.00 being the lowest value to 105.00 being the highest value. The IQ value with the highest frequency of students was 90.00.

The IQ values show us that most of the students were of normal or average intelligence. However, some of them get very high GPA scores and some get very low GPA scores. The mean GPA was 2.8500 and the mean IQ level was 91.700. Based on these findings, there may be a correlation between GPA and IQ. A further observation of the table of correlation and the scatter plot shows a positive correlation of 0.726 between GPA and IQ. The correlation is not only positive but also significant as the probability of getting such a correlation coefficient by chance is 0.01, indicating the presence of a relationship. Using the scatter plot, it can be deduced that the correlation is positive and since the correlation value is close to +1, the correlation value is strongly positive, supporting the relationship between IQ and GPA.

The statistically obtained values, point towards the fact that GPA scores have a strong correlation with IQ. It therefore supports the null hypotheses, clearly pointing out that external variables do not affect GPA or IQ correlations. It also supports the alternative hypotheses, that there is indeed a relationship between the GPA scores and IQ of a group of students, with a very high probability of reproducing the same results under similar conditions.

In conclusion, it is important to note that there is a strong correlation between grade point average scores of a student and their intelligence quotient. These are independent of any external variables such as self-discipline, socioeconomic backgrounds and working memory. However, it is important to note that this is true for a sample of the population and therefore under different circumstances or under different conditions, the result may vary (Angela & Duckworth, 2004). The correlation was not absolute and some of the students may not have matched up with the correlation study outcome and we cannot conclude undoubtedly that if the environment is changed or the method of assessment is changed, the same results will be obtained. Other variables such as teaching methods, revision and study methods may be added to confirm without a doubt, the correlation between GPA and IQ.


Angela L. & Duckworth, M. E. (2004, December 12). University of Pennsylvania. Retrieved from www.sas.upenn.edu/~duckwort/images/PsychologicalScienceDec2005.pdf

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