Question

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. The correlation of + 0.8 +0.8 indicates a stronger relationship than the correlation of − 0.8 . −0.8. B. It is impossible to tell which correlation is stronger. C. The correlation of + 0.8 +0.8 is just as strong as the correlation of − 0.8 .

Answer 1

C. The correlation of + 0.8 +0.8 is just as strong as the correlation of − 0.8 .

Correct. Both correlation coefficients+0.8 and -0.8 indicates strong relationship, the only difference is that the +0.8 is associated to a proportional relation and the value of -0.8 to an inverse proportional relation. But when we want to see if a correlation value is strong we need to analyze the absolute value and if we satisfy that the absolute value is near to 1 we have strong relationship.

Explanation:

Previous concepts

The correlation coefficient is a "statistical measure that calculates the strength of the relationship between the relative movements of two variables". It's denoted by r and its always between -1 and 1.

And in order to calculate the correlation coefficient we can use this formula:

`r=(n(\sum xy)-(\sum x)(\sum y))/(√([n\sum x^2 -(\sum x)^2][n\sum y^2 -(\sum y)^2]))`

Solution to the problem

A. The correlation of + 0.8 indicates a stronger relationship than the correlation of − 0.8 .

False both correlation coefficients +0.8 and -0.8 indicates strong relationship, the only difference is that the +0.8 is associated to a proportional relation and the value of -0.8 to an inverse proportional relation. But when we want to see if a correlation value is strong we need to analyze the absolute value and if we satisfy that the absolute value is near to 1 we have strong relationship.

B. It is impossible to tell which correlation is stronger.

False we can conclude soomething about the statement.

C. The correlation of + 0.8 +0.8 is just as strong as the correlation of − 0.8 .

Correct. Both correlation coefficients+0.8 and -0.8 indicates strong relationship, the only difference is that the +0.8 is associated to a proportional relation and the value of -0.8 to an inverse proportional relation. But when we want to see if a correlation value is strong we need to analyze the absolute value and if we satisfy that the absolute value is near to 1 we have strong relationship.