Chapter 5

Why do you convert scores into Z-scores?

Z-scores (standardized scores) allow the direct comparison of scores from 2 different distributions because they have converted to the same scale

What is the formula to find z-score?

z = (x - μ)/σ

A sample with a mean of and a standard deviation of is being transformed into z-scores. After the transformation, what is the standard deviation for the sample of z-scores?

1 b/c any variate is a standard normal variate when it follows a normal distribution with Mean=0 and standard deviation=1. So that's why transforming any variable into standard normal variable changes the standard deviation of that variable into 1.

T/F 1. Transforming an entire distribution of scores into z-scores will not change the shape of the distribution 2. If a sample of n=10 scores is transformed into z-scores, there will be 5 positive z-scores and 5 negative z-scores

1. True 2. False; # of z-scores above/below mean will be exactly the same as # of original scores above/below mean

T/F 1. A negative z-score always indicates a location below the mean 2. A score close to the mean has a z-score close to 1

1. True 2. False; scores quite close to mean have z-scores close to 0

Z-scores

Exact location is described by this Sign tells whether score is located above or below mean Number tells distance between score and mean in standard deviation units

What does z-score establish a relationship between?

Raw score, mean and standard deviation

What are the characteristics of z-score transformation?

Same shape as original distribution Mean of z-score distribution always 0 Standard deviation always 1

What location in a distribution corresponds to? A. Above the mean by 2 points B. Above the mean by a distance equal to 2 standard deviations C. Below the mean by 2 points D. Below the mean by a distance equal to 2 standard deviations

D

A z-score of z = +1.00 indicates a position in a distribution ____. A. Above the mean by 1 point B. Above the mean by a distance equal to 1 standard deviation C. Below mean by 1 point D. Below the mean by a distance equal to 1 standard deviation

B

A population with μ and σ is transformed into z-scores. After the transformation, what is the mean for the population of z-scores? A. μ=80 B. μ=1 C. μ=0 Cannot be determined from the information given

C

Under what circumstances would a score that is 15 points above the mean be considered an extreme score? A. When the mean is much larger than 15 B. When the standard deviation is much larger than 15 C. When the mean is much smaller than 15 D. When the standard deviation is much smaller than 15

D

What is z-score distribution also called?

Standardized distribution