Question

The scholar wants to collapse a scale into four ordinal categories: low egalitarianism, assigned to respondents with Z scores of less than −1; medium-low egalitarianism, assigned to respondents with Z scores in the range between −1 through 0; medium-high egalitarianism, for Z scores of greater than 0 through +1; and high egalitarianism, assigned to respondents with Z scores of greater than +1. What are the raw-score ranges for each of the four ordinal categories?”

Answer 1

Solution:

Let the scaling has been done on a 0 to 100 scale.

Now using the "NORM.S.DIST" function of excel we get,

P(Z < -1) = 0.1587

(0.1587 × 100) = 15.87

Hence, the raw score ranges from 0 to 15.87 for low egalitarianism category.

Using the "NORM.S.DIST" function of excel we get,

P(Z < 0) = 0.50

(0.50 × 100) = 50  

Hence, the raw score ranges from 15.88 to 50 for medium-low egalitarianism category.

Using the "NORM.S.DIST" function of excel we get,

P(Z < 1) = 0.8413

(0.8413 × 100) = 84.13

Hence, the raw score ranges from 51 to 84.13 for medium-high egalitarianism category.

And the raw score ranges from 84.14 to 100 for high egalitarianism category.

Category	Range
Low egalitarianism	from 0 to 15.87
Medium-low egalitarianism	from 15.88 to 50
Medium-high egalitarianism	from 51 to 84.13
High egalitarianism	from 84.14 to 100