z scores

Question 1

Normal Curve

Answer 1

theoretical distribution of population scores

Question 2

z-score

Answer 2

how many standard deviations above or below the mean a raw score is

unitless; z is italicized

provide standardization among scales with different units, means, and standard deviations
eg, different GPA systems, different scales measuring depression

Question 3

How do you convert raw scores to z-scores

Answer 3

(X - mean) / standard deviation

Question 4

How do you convert z-scores to areas (eg, how unusual is the score)

Answer 4

• sketch out distribution, and shade the area you’re trying to find
• use the table (areas under the normal curve) to find the shaded area
  column B: area between mean and z
  column C: area beyond z

if area is between two scores & one is below the mean:
- find area B for z1
- find area B for z2
- add areas together

if area is between two scores & both are on the same side of the mean:
- find area C for z1
- find area C for z2
- subtract the smaller area from the larger area

Question 5

Composite Measure

Answer 5

a combination of two or more individual measures in a single measure that results in a single score

average z-scores rather than raw scores to ensure equal weighting of differently measured data

Question 6

How do you convert z-scores to raw scores?

Answer 6

if z = (x - mean) / standard deviation, then

x = mean plus (z * standard deviation)

Question 7

How do you convert between areas, z-scores, and raw scores?

Answer 7

Question 8

Linear Transformation

Answer 8

the transformation of a set of raw data using an equation that involves addition, subtraction, multiplication, or division with a constant

adding or subtracting:
- mean is increased/decreased by that constant
- standard deviation is unchanges

multiplying or dividing:
- mean is multiplied/divided by that constant
- standard deviation is multiplied/divided by that constant