Chapter 5

Question 1

z-scores

Answer 1

z-scores use the mean as a reference point to determine whether the score is above or below average. A z-score also uses the standard deviation as a yardstick for describing how much an individual score differs from average

• a z-score will tell you if your score is above the mean by a distance equal to two standard deviations, or below the mean by one-half of a standard deviation

Question 2

raw scores

Answer 2

original, unchanged scores that are the direct result of measurement are called raw scores

Question 3

purposes of z-scores

Answer 3

• Each z-score tells the exact location of the original X value within the distribution.
• The z-scores form a standardized distribution that can be directly compared to other distributions that also have been transformed into z-scores.

Question 4

The z-score accomplishes describing the position of a score by transforming each X value into a signed number (+ or −) so that…

Answer 4

• the sign tells whether the score is located above (+) or below (−) the mean, and
• the number tells the distance between the score and the mean in terms of the number of standard deviations.

Question 4

z-score

Answer 4

A z-score specifies the precise location of each X value within a distribution. The sign of the z-score (+ or −) signifies whether the score is above the mean (positive) or below the mean (negative). The numerical value of the z-score specifies the distance from the mean by counting the number of standard deviations between X and mu

Question 5

formula for transforming scores into z-scores

Answer 5

z = X-mu / standard deviation (o)

The deviation score (X-mu) is then divided by o because we want the z-score to measure distance in terms of standard deviation units.

Question 6

deviation score

Answer 6

X-mu

• it measures the distance in points between X and μ and indicates whether X is located above or below the mean

Question 7

z-score transformation

Answer 7

A transformation that changes raw scores (X values) into z-scores.

Question 8

standardized distribution

Answer 8

A standardized distribution is composed of scores that have been transformed to create predetermined values for μ and o (standard deviation). Standardized distributions are used to make dissimilar distributions comparable.

Question 9

Standardized scores

Answer 9

A score that has been transformed into a standard form.

Question 10

The procedure for standardizing a distribution to create new values for
μ and o is a two-step process:

Answer 10

The original raw scores are transformed into z-scores.

The z-scores are then transformed into new X values so that the specific
μ and o are attained.

Question 11

for a sample, each X value is transformed into a z-score so that

Answer 11

• The sign of the z-score indicates whether the X value is above (+) or below (−) the sample mean, and
• The numerical value of the z-score identifies the distance from the sample mean by measuring the number of sample standard deviations between the score (X) and the sample mean (M).

Question 12

The transformed distribution of z-scores will have the same properties that exist when a population of X values is transformed into z-scores. Specifically,

Answer 12

• The sample of z-scores will have the same shape as the original sample of scores.
• The sample of z-scores will have a mean of M=0.
• The sample of z-scores will have a standard deviation of s=1 .