Regression, Correlation: Effect of IQ on GPA
Effective teaching begins with understanding the thinking and reasoning abilities of one's students and devising ways to ensure that the classroom setting is accommodative of the inherent differences in cognitive capabilities and that all students get to benefit from the learning process. One way of measuring a child's intellectual ability is by administering the Wechsler Intelligence Scale for Children -- Forth Edition (WISC-IV), which measures IQ on the basis of a child's processing speed, working memory, perceptual reasoning, and verbal comprehension skills. Children 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 class activities with therapeutic interventions to ensure that they remain at par with the rest of the class. This text 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. Towards this end:
H1: there is a direct and positive relationship between a child's IQ and their GPA
In this case, IQ is the independent variable, and GPA, the dependent variable. In other words, a child's GPA depends, and is determined by the level of their IQ. Both variables are continuous in nature, with an infinite number of potential values. Further, both are quantitative (expressed in significant numerical measures). However, IQ is a quantitative interval variable, given that higher values would signify higher levels of smartness, but a value of 0 would have no meaning; whereas GPA is a quantitative ratio variable -- higher values symbolize higher levels of academic achievement, and a value of zero is significant as it would symbolize that a student earned no points in a particular element.
The dependent variable (GPA) yields a mean index of 2.73; a median of 2.85; and a modal score of 2.90. The independent variable (IQ), on the other hand, yields a mean of 85.1; a median score of 82.0; and a modal value of 66.0. The researcher acknowledges that there were multiple modal values, and that the lowest values were selected for reporting purposes. According to Thorndike and Thorndike-Christ (2010), the degree of skewness of a distribution depends on the difference in the values of the three measures above -- the greater the difference, the higher the degree of skewness. The modal value in the case of the IQ measure differs significantly from that of the mean, and the median (19.1 units from the mean, and 16.0 units from the median), implying that the distribution is skewed. The direction and strength of skewness are obtained from the positive 0.374 skewness index. This implies that if a frequency curve were drawn, joining the topmost points of the IQ histogram bars, its tail would run up to the high scores -- more than half of the sampled children have an IQ index less than the mean index of 85.1 and only very few surpass the mean.
In the case of GPA, the three measures do not differ substantially, implying that the distribution is more uniformly-scattered around the mean. The 0.012 skewness index, which can rightly be rounded off to 0.0 goes to show that the distribution is almost balanced -- the number of students with GPA points less than...
Apart from the differences in skewness, the two distributions also differ in terms of variability, with the IQ distribution depicting a smaller degree of variability.
Conventionally, the WISC-IV scale yields an SD of 15 and a mean equaling 100, implying that any IQ score between 85 and 115 can be regarded as normal. The sample used in this particular investigation yielded a mean of 85 and a standard deviation of 16. The assumption in this case is that IQ scores falling between 69 and 101 are normal; whereas those below 61 and those above 101 represent outliers. The mean score of 81 and the higher boundary of 101 fall within the WISC-IV's conventional indices; the difference in the values of the lower boundary can be attributed to errors caused by the small sample size. Towards this end, the test can be deemed suitable for the sampled group, although the results would have been more accurate had a larger sample been used. Thus:
i) 13 children, out of the sampled forty, are within 1 SD below the mean of the test (between 85 and 70)
ii) 22 children are within 2 SDs below the mean of the test
iii) 22.5% of the sampled students possess an IQ score that happens to be below (or equivalent to) 70 (9/40 of 100)
iv) 22.5% of the sampled students reported IQ scores that exceeded 100 (9/40 of 100)
According to Jackson (2011), correlation measures i) the strength of the relationship between two variables, and ii) the direction of the relationship between two variables. The direction of the relationship is predicted by the sign preceding the correlation index (r). According to the author, a positive r value indicates a positive correlation, and hence, "a direct relationship between variables" (Jackson, 2011, p. 68). A negative r value, on the other hand, indicates a negative correlation, and consequently, an inverse relationship between the variables under investigation. The strength of the relationship is depicted by the value of the correlation coefficient (Jackson, 2011). The strongest possible correlation would yield a value of 1(if positive) and -1 (if negative); towards this end, positive correlation coefficients are considered stronger if they are greater than 0.5, and vice versa.
The results in this case indicate a strong, positive correlation (r = 0.608) between IQ and GPA, implying that, in line with hypothesis H1, students with higher levels of IQ are likely to be better academic performers (as measured by the GPA), compared to their peers with lower IQ levels. The results can be regarded as being statistically significant, given that p < 0.01. The scatterplot diagram shows a cloud of points moving outwards from the origin, implying that if a line of best fit were to be drawn joining the same, it would yield a positive slope, in which case the slope would be taken to represent the direction of the relationship between IQ and GPA; and it would imply that at higher IQ indices, GPA points are concurrently high.
Further, the relationship between the two is relatively strong, depicting a consistent pattern, and consequently, a high possibility that the relationship will always be positive (Jackson, 2011). Towards this end, we can expect students with higher GPA points to always demonstrate higher reasoning, thinking, and understanding abilities, compared to their peers with lower GPA points. However, in as much as we can rightly draw the conclusion that GPA will always be directly related to IQ level, we cannot argue that variations in GPA are solely due to differences in IQ levels -- other factors, for instance a child's self-disciple and academic background also have a hand in their performance (Duckworth & Seligman, 2005). A child who attends a good school right from their formative years is likely to perform better than one who attends a not-so-good formative facility, even if the latter has a higher IQ index. In this regard, IQ alone cannot be used to effectively predict GPA or overall academic performance.
Moreover, we cannot rely fully on the study results owing the validity and reliability issues characteristic of such research studies, both of which give rise to errors that impede on accuracy. Validity has to do with…
prediction so we have to assume that the research question is nondirectional. In this case the research question is that there will be a difference in the rate of people to get the flu depending on whether or not they get the nasal spray or the shot. In terms of the null and alternative hypotheses we could state them as: H0: There will no difference in flu rates between groups