Effect of IQ on GPA: Regression and Correlation Analysis

Introduction

Effective teaching begins with understanding the thinking and reasoning abilities of one's students and devising ways to ensure that the classroom setting is accommodating of the inherent differences in cognitive capabilities, so that all students benefit from the learning process. One way of measuring a child's intellectual ability is by administering the Wechsler Intelligence Scale for Children – Fourth Edition (WISC-IV), which measures IQ on the basis of a child's processing speed, working memory, perceptual reasoning, and verbal comprehension skills. Children who score below the average range in IQ are thought to have lower understanding, thinking, and reasoning abilities compared to their peers. It is the instructor's duty to follow up such children's classroom activities with targeted interventions to ensure they remain at par with the rest of the class. This paper presents the hypotheses, regression results, and descriptive statistics of a study that sought to determine the relationship between IQ and GPA by administering the WISC-IV to forty 14-year-old ninth-graders.

Numerous studies have shown that, ceteris paribus, children with higher cognitive abilities are likely to be better academic achievers than their peers with lower cognitive abilities. Accordingly:

H1: There is a direct and positive relationship between a child's IQ and their GPA.

Hypothesis and Variables

In this study, IQ is the independent variable and GPA is the dependent variable. In other words, a child's GPA depends on, and is determined by, the level of their IQ. Both variables are continuous in nature, with an infinite number of potential values, and both are quantitative — expressed in meaningful numerical measures. However, IQ is a quantitative interval variable: higher values signify greater intelligence, but a value of 0 has no meaningful interpretation. GPA, by contrast, is a quantitative ratio variable: higher values symbolize higher levels of academic achievement, and a value of zero is meaningful because it indicates that a student earned no points in a given element.

The dependent variable (GPA) yields a mean of 2.73, a median of 2.85, and a modal score of 2.90. The independent variable (IQ) yields a mean of 85.1, a median of 82.0, and a modal value of 66.0. The researcher acknowledges that there were multiple modal values and that the lowest value was selected for reporting purposes. According to Thorndike and Thorndike-Christ (2010), the degree of skewness of a distribution depends on the difference among the three measures of central tendency — the greater the difference, the higher the degree of skewness. The modal value for IQ differs significantly from both the mean and the median (19.1 units from the mean and 16.0 units from the median), implying that the IQ distribution is skewed. The direction and strength of that skewness are indicated by the positive skewness index of 0.374. This means that if a frequency curve were drawn through the tops of the IQ histogram bars, its tail would extend toward the higher scores — more than half of the sampled children have an IQ below the mean of 85.1, and only very few exceed it.

In the case of GPA, the three measures of central tendency do not differ substantially, implying that the distribution is more uniformly scattered around the mean. The skewness index of 0.012 — which can rightly be rounded to 0.0 — indicates that the GPA distribution is nearly balanced: the number of students with GPA points below 2.73 is almost equal to the number whose GPA exceeds the mean. Beyond differences in skewness, the two distributions also differ in terms of variability, with the IQ distribution exhibiting a smaller degree of variability.

Descriptive Statistics

Conventionally, the WISC-IV scale yields a standard deviation (SD) of 15 and a mean of 100, meaning that any IQ score between 85 and 115 can be regarded as normal. The sample used in this investigation yielded a mean of 85 and a standard deviation of 16. Under these sample parameters, IQ scores between 69 and 101 are treated as normal, while those below 69 and those above 101 represent outliers. The sample mean of 85 and the upper boundary of 101 fall within the WISC-IV's conventional range; the slight difference in the lower boundary can be attributed to error caused by the small sample size. The test can therefore be deemed suitable for the sampled group, although results would have been more accurate with a larger sample. Specifically:

(i) 13 of the 40 sampled children fall within 1 SD below the test mean (IQ between 70 and 85).

(ii) 22 children fall within 2 SDs below the test mean.

(iii) 22.5% of sampled students have an IQ score at or below 70 (9/40 × 100).

(iv) 22.5% of sampled students reported IQ scores exceeding 100 (9/40 × 100).

According to Jackson (2011), correlation measures both the strength and the direction of the relationship between two variables. The direction is indicated by the sign preceding the correlation index (r). A positive r value indicates a positive — or direct — relationship between the variables, while a negative r value indicates an inverse relationship (Jackson, 2011, p. 68). The strength of the relationship is reflected in the magnitude of the correlation coefficient: the strongest possible values are +1 and −1, and positive coefficients above 0.5 are generally considered strong.

The results in this case indicate a strong, positive correlation (r = 0.608) between IQ and GPA, implying that — consistent with hypothesis H1 — students with higher IQ levels are likely to be better academic performers as measured by GPA. The results are statistically significant at p < 0.01. The scatterplot shows a cloud of points moving outward from the origin, indicating that a line of best fit drawn through those points would have a positive slope, reflecting the direct relationship between IQ and GPA: at higher IQ levels, GPA points are concurrently higher.

Conclusion

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Thorndike, R. M., & Thorndike-Christ, T. (2010). Measurement and evaluation in psychology and education (8th ed.). Pearson Inc.

Walker, I. R. (2011). Reliability in scientific research: Improving the dependability of measurements, calculations, equipment and software. Cambridge University Press.