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A recent article in an educational research journal reports a correlation of +0.8+0.8 between math achievement and overall math aptitude. It also reports a correlation of −0.8−0.8 between math achievement and math anxiety.

Which of the following interpretations is the most correct?
a) It is impossible to tell which correlation is stronger.
b) The correlation of +0.8 indicates a stronger relationship than the correlation of −0.8.
c) The correlation of +0.8 is just as strong as the correlation of −0.8.

User Van
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Final answer:

The correlation of +0.8 between math achievement and math aptitude is just as strong as the correlation of -0.8 between math achievement and math anxiety, as both have the same absolute value.

Step-by-step explanation:

A recent article in an educational research journal reports a correlation of +0.8 between math achievement and overall math aptitude. It also reports a correlation of −0.8 between math achievement and math anxiety. Considering the interpretation of correlation coefficients, the most correct interpretation is c) The correlation of +0.8 is just as strong as the correlation of −0.8.

The correlation coefficient reflects the strength and direction of a linear relationship between two variables. A correlation coefficient of +0.8 indicates a strong positive relationship, meaning as one variable increases, so does the other. Conversely, a correlation coefficient of -0.8 indicates a strong negative relationship, implying that as one variable increases, the other decreases. The strength of the relationship is determined by the absolute value of the correlation coefficient, which is 0.8 in both cases. Thus, both correlations are equally strong, just opposite in direction.

User Michael Daum
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