methosds and statistics in psychology?

Question

I am developing a Prejudice Against Professors (PAP) scale. I've given the scale to 1000 students and found that they have a mean score on the scale of 26.5 with a standard deviation of 3.5. If Kara gets a score of 19.5 on this scale, fill in the blanks below so that her score would be equivalent in each case:
a. mean of X scores=100, s=15, X=__
b. mean of X scores=__, s=2, X=-9
c. mean of X scores=60, s=__, X=45
d. mean of X scores=10, s=20, X=__
e. mean of X scores=100, s=__, X=90

Answer 1

First of all, you seem to be assuming a Gaussian distribution on the original data. Under most circumstances involving people, this is not the distribution you really get.

The primary reason people assume the Gaussian distribution is that it has some very nice mathematical properties. One of those properties is that scaling it, shifting it, etc. still leaves you with a Gaussian distribution.

That means that the only important piece of information in an individual datum is the number of standard deviations away from the mean it is.

That is, suppose M0 is the mean of a Gaussian distribution with standard deviation S0. Then a datum X0 can be normalized to

N = (X0 - M0)/S0

Since you know M0 (26.5), S0 (3.5) and X0, you can compute N.

In all of the other cases, you know N and two of M, S, and X so you can compute the third.