Question

The paper "Digit Ratio as an Indicator of Numeracy Relative to Literacy in 7-Year-Old British Schoolchildren" (British Journal of Psychology [2008]: \(75-85\) ) investigated a possible relationship between \(x=\) digit ratio (the ratio of the length of the second finger to the length of the fourth finger) and \(y=\) difference between numeracy score and literacy score on a national assessment. (The digit ratio is thought to be inversely related to the level of prenatal testosterone exposure.) The authors concluded that children with smaller digit ratios tended to have larger differences in test scores, meaning that they tended to have a higher numeracy score than literacy score. This conclusion was based on a correlation coefficient of \(r=-0.22 .\) Does the value of the correlation coefficient indicate that there is a strong linear relationship? Explain why or why not.

Short answer

No, the correlation coefficient of -0.22 does not indicate a strong linear relationship. It suggests only a weak negative linear relationship between the digit ratio and the difference in numeracy and literacy scores.

Step-by-step solution

Understand the Scale of Correlation Coefficient

Correlation coefficient values range between -1 and 1. The closer the value is to 1 or -1, the stronger the linear relationship. A positive correlation (closer to 1) means as one variable increases, so does the other, while a negative correlation (clother to -1) means as one variable increases, the other decreases.

Interpretation of the Given Correlation Coefficient

The given correlation coefficient value is -0.22. This value lies somewhat close to 0. This indicates that there is a weak negative linear relationship between the digit ratio and the difference between numeracy and literacy scores. In essence, as the digit ratio (x) decreases, the difference in test scores (y) tends to slightly increase, but this relationship is weak.

Concluding Remarks

Negative correlation of -0.22 does not indicate a strong linear relationship because it is not close to 1 or -1. It means there is only a weak inverse relationship between the digit ratio and the difference in test scores. Therefore, the conclusion that children with smaller digit ratios tend to have larger differences in test scores is not derived from a strong correlation.