PSYC*1010 Chapter 5: Z-Scores

Question 1

What is a z-score?

Answer 1

A type of standardized score

Question 2

What does the sign of a z-score indicate?

Answer 2

• Whether it’s located above or below the mean
• (+) is above the mean
• (-) is below the mean

Question 3

What does the numerical value of a z-score indicate?

Answer 3

The number of standard deviations between the mean and the score

Question 4

T or F: The location identified by z-scores are the same for all distributions, regardless of the mean or standard deviation for that distribution.

Answer 4

True

Question 5

When calculating z-scores, what does the numerator (X-μ) in the equation measure?

Answer 5

• (X-μ) is the deviation score
• Measures the distance in points between the score and the mean

Question 6

When calculating z-scores, why is the numerator/ deviation score (X-μ) divided by the standard deviation?

Answer 6

So the distance between the mean and the score is in terms of the number of standard deviation units

Question 7

What is the equation for calculating a z-score in a population?

Answer 7

z= (X-μ)/σ

Question 8

How can a raw score be determined from a z-score?

Answer 8

By rearranging the z-score equation

Question 9

What is the equation for transforming a z-score into a raw score from a population?

Answer 9

X= μ + zσ

Question 10

If every X value is transformed into a z-score, how will the shape of the distribution change?

Answer 10

The distribution of z-scores will have exactly the same shape as the original distribution

Question 11

If every X value is transformed into a z-score, how will the mean of the distribution change?

Answer 11

The z-score distribution will always have a mean of zero

Question 12

If every X value is transformed into a z-score, how will the standard deviation of the distribution change?

Answer 12

The z-score distribution will always have a standard deviation of one

Question 13

What is a standardized distribution?

Answer 13

A distribution composed of scores that have been transformed to create predetermined values for μ and σ

Question 14

Why does a standardized deviation always have a standard deviation of one?

Answer 14

Because the numerical value of a z-score is exactly the same as the number of standard deviations it is from the mean

Question 15

Why are two raw scores from different distributions unable to be compared, but two z-scores from different distributions can be?

Answer 15

• Raw scores from two different distributions likely have different means and standard deviations
• All z-scores have the same mean and standard deviation, so they can be compared across distributions

Question 16

What is a standardized score?

Answer 16

A score that has been transformed into a standard form

Question 17

What is the procedure for standardizing a distribution to create new values for μ and σ?

Answer 17

1. Transform raw scores (X) into z-scores
2. Transform z-score back into a raw score/X value using the predetermined μ and σ

Question 18

What is the difference between the z-score equation for a score from a population and the z-score equation for a score from a sample?

Answer 18

The equation is identical, but the notation is different

Question 19

What is the equation for calculating a z-score in a sample?

Answer 19

z= (X-M)/s

Question 20

What is the equation for transforming a z-score into a raw score from a sample?

Answer 20

X= M + zs

Question 21

T or F: If all scores in a sample are transformed into z-scores, their distribution will have the same properties that exist when all scores in a population are transformed into z-scores.

Answer 21

True