Question

A recent study reported a correlation of 0.68 between scores on an index of depression and scores on an index that measures the amount of saturated fat intake. True or False: You can conclude that if you increase your saturated fat intake by a standard deviation, your degree of depression will increase by more than half a standard deviation.

i.) True

ii.) False

Answer 1

Let us say the index of depression is D and the index of fat is F.

We know that correlation = covariance / (standard deviation of D * standard deviation of F)

Thus , C= Cov (D,F) / [ SD(D) * SD(F) ]

Now, we are told that we increase the S(F) by 1 S(F).

Let us say that the new index of depression is d.

Thus, C= Cov(d,F) / [ SD(d) * 2*SD(F) ]

We know that:

C(with old F) will be the same as C(with new F).

Therefore, we can multiply and divide the RHS with SD(D).

Ultimately, we can subsitute Cov(d,F) / [ SD(D)*SD(F) ] with C.

Therefore, 2C = [C *SD(D) ] / SD(d)

And SD(d) = SD(D) / 2

Therefore, the correct answer is FALSE, as the increase is exactly half and not more than half a standard deviation.

If you have any doubts regarding the answer, please feel free to comment and I will get back to you. Happy learning!