0
$\begingroup$

I have a question for an exam:

You read a journal article on TOTAL-cholesterol, HDL-cholesterol and LDL-cholesterol from a study of n=100 patients where TOTAL-cholesterol = HDL + LDL cholesterol. Assume that for HDL, LDL and TOTAL cholesterol, the distributions are iid multivariate normal.
The article reports for:

HDL: sample-mean = 145 and p-value for the population mean to be 150 is 0.10
LDL: sample-mean = 48 and p-value for the population mean to be 50 is 0.05
TOTAL: sample-mean = 193 and p-value for the population mean to be 200 is 0.05 All P-values are Two-Sided

You must derive the standard deviations and covariances for HDL-cholesterol and LDL-cholesterol in a single observation from this information

A. Work backwards from the p-values for the population means be equal to the specified values based on the observed sample means to obtain the standard deviations for both HDL-cholesterol and LDL-cholesterol in a single observation?

B. What is the covariance of HDL and LDL cholesterol in a single observation?

How does one figure out the standard deviation with only the information given is the mean and p-value?

$\endgroup$
  • $\begingroup$ You'd also need sample size. $\endgroup$ – Glen_b Nov 30 '18 at 4:00
  • $\begingroup$ @Glen_b He said the sample size is 100 in Question. $\endgroup$ – user158565 Nov 30 '18 at 22:45
  • $\begingroup$ @user158565 Thanks, though I was responding to the explicit question in the title which seems to propose ignoring that information. $\endgroup$ – Glen_b Dec 1 '18 at 1:27
1
$\begingroup$

Hints:

Suppose p-values were got from t-test.

A: Step 1: from sample size and p-value, you can get t value

step 2: from Sample mean, population means, and t value, you can get standard error

Step 3: From standard error and sample size, you can get estimated variance, then standard deviation.

B: Total = HDL +LDL, so Var(Total) = Var(HDL) + Var(LDL) +2Cov(HDL,LDL)

$\endgroup$
  • $\begingroup$ From step 2, do u mean t value=sample mean / sd/sqrt(n) ? if so, why does this equality hold? $\endgroup$ – SEUNG HOON JUNG Nov 30 '18 at 4:44
  • 1
    $\begingroup$ $|\bar Y - \mu|/se = t$ $\endgroup$ – user158565 Nov 30 '18 at 4:46

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.