Question

"Assume that an r of 0.8 describes the relationship between daily food intake, measures in ounces, and body weight, measured in pounds, for a group of adults. Would a shift in units of measurement from ounces to grams and from pounds to kilograms change the value of r? Why or why not?"

No. The units of measurement will not affect the means or standard deviations.

No. The value of r depends only on the pattern among pairs of scores, regardless of measurement. The relationship between the variables will be the same.

Yes. The units of measurement affects what the actual means and standard deviations calculations.

Yes. The value of r changes because the measurements increased.

Answer 1

No. The value of r depends only on the pattern among pairs of scores, regardless of measurement. The relationship between the variables will be the same.

Mathematical reason:

Let us consider x an y as two vectors, then the formula for correlation is

Each x and y vectors can be multiplied by constants:

A*x and B*y

Then, the constant factor (A*B) can be taken out of the summations in the numerator.

In the denominator, the first term under the square root would have a constant factor of A^2 and the second term would have a constant term of B ^2.

Hence again a constant = (A*B) would be taken out in the denominator.

These would cancel each other as they are present in both numerator and denominator.

Hence the r is unaffected.