Question

The paper "School Achievement Strongly Predicts Midlife IQ" (Intelligence [2007]: \(563-567\) ) examined the relationship between school achievement test scores in grades 3 to 8 and IQ measured many years later. The authors reported an association between school achievement test score and midlife IQ, with a correlation coefficient of \(r=0.64\) a. Interpret the value of the correlation coefficient. b. A science writer commenting on this paper (Livescience, April 16,2007\()\) said that the correlation between school achievement test scores and IQ was very strong - even stronger than the correlation between height and weight in adults. Which of the following values for correlation between height and weight in adults is consistent with this statement? Justify your choice. \(\begin{array}{lllll}r=-0.8 & r=-0.3 & r=0.0 & r=0.6 & r=0.8\end{array}\)

Short answer

a. The value of the correlation coefficient, \(r=0.64\), indicates a fairly strong positive correlation between school achievement test scores and midlife IQ, meaning as one increases, the other is likely to increase as well.\nb. The correlation coefficient consistent with the given statement is \(r=0.8\). This value signifies a stronger relationship compared to \(r=0.64\) as indicated by the science writer.

Step-by-step solution

Interpreting Correlation Coefficient

The correlation coefficient \(r\) is a measure that demonstrates the extent of interdependency of variable quantities. Its value lies between -1 and +1. Negative values represent inverse correlation while positive values represent direct correlation. The magnitude of the value represents the strength of the correlation, with 1 being the maximum. The correlation coefficient of \(r=0.64\) for midlife IQ and school achievement test scores signifies a strong positive correlation - as school achievement test scores increase, midlife IQ also likely increases.

Comparison of Correlation Coefficients

Correlation coefficients denote the strength and direction of a linear relationship between two variables. The correlation between school achievement test scores and IQ is said to be stronger than the correlation between height and weight in adults. Keeping in mind the possible values ranged from -1 to +1, any coefficient less than \(r=0.64\) would imply a weaker correlation. Therefore, any values such as \(r=-0.8, r=-0.3, r=0.0, r=0.6\) would be ruled out, leaving only \(r=0.8\) as the suitable choice to be consistent with the statement.

Key concepts

School Achievement and IQ Relationship

Understanding the connection between school performance in early years and intelligence later in life is an intriguing topic. Research, like the example paper referenced, investigates this relationship through statistical means. The study's reported correlation coefficient of

\r\(r=0.64\)

\ris indicative of how closely related these two variables are. In educational research, this correlation is significant, as it suggest that performance in school could be a strong predictor of intellectual ability as an adult. It's crucial to note that a positive correlation coefficient points to a direct relationship; in this case, as school achievement scores go up, so typically does the midlife IQ.

\rWhile this offers a valuable indicator for educators and policy makers, we should be cautious not to overstate these findings. Correlations do not imply causation, meaning we cannot definitively state that good grades cause higher IQs later in life, but rather that there is an observable link between the two.

Interpreting Correlation

When scrutinizing a correlation coefficient, a grasp of its implications is fundamental. As seen in our example, the value of

\r\(r=0.64\)

\rsignals a strong, positive correlation. But what does that really mean? A coefficient closer to +1 or -1 signifies a stronger relationship between the two variables studied.

\rPositive values imply that as one variable increases, so does the other, which is the case for school achievement and midlife IQ. In contrast, a negative value would mean that as one variable increases, the other tends to decrease. If the correlation coefficient was 0, it would indicate no relationship.

\rInterpreting the magnitude is also essential; values above +0.5 or below -0.5 are generally considered to be strong correlations. In educational settings, this interpretation can help identify the strength of various factors related to academic success.

Comparing Correlation Strengths

To compare different correlation coefficients, it is necessary to understand their magnitudes in context. The claim made by the science writer about the strength of the correlation between school achievement and IQ being greater than that between adult height and weight prompts us to examine the provided options.

\rA coefficient of

\r\(r=0.8\)

\rwould indeed suggest a stronger correlation than our study's

\r\(r=0.64\)

\rvalue. To justify the comparison, one must consider real-life variability; heights and weights can vary vastly among adults with minimal impact on each other, whereas early academic success and later intellectual prowess might be more tightly linked. Therefore, when assessing, any correlation weaker than

\r\(r=0.64\)

\rwould not support the writer's claim. This example illuminates how broad, seemingly unrelated facets such as stature can be contrasted with more nuanced developmental aspects like intelligence and achievement.