PSY201: Chapter 5 - z-Scores

Question 1

Z Score

Answer 1

Mean + standard deviation describe entire distribution of scores
Z-scores describe exact location of individual scores in distribution

Question 2

Z Score

Answer 2

By itself, X provides very little info about how particular score compares with other values in distribution

Question 3

Z Score

Answer 3

uses the mean + standard deviation to transform each X-value so we know where score is located relative to other scores, without needing to know about original scale

Question 4

Z Score

Answer 4

one way to standardize distribution so we make diff distributions equivalent, thus comparable

Question 5

z-scores and Location

Answer 5

sign of the z-score (+/–): above/below mean

numerical value = # of standard deviations betw X + mean

Question 6

z-scores and Location

Answer 6

2 standard deviations above mean = +2.00

Question 7

z-scores and Location

Answer 7

z=X−μ/σ

expressing the deviation from mean in standard deviation units

Question 8

z-scores and Location

Answer 8

X = μ + zσ

zσ is the deviation of X - # of points away from mean

Question 9

Using z-Scores to Standardize a Distribution

Answer 9

transform every X-value into a z-score ⇒ new z-score distribution:
shape same as the original X-value distribution - not changing relative distance from mean

Question 10

Using z-Scores to Standardize a Distribution

Answer 10

mean of z-score distribution always 0 + standard deviation always 1

Question 11

Using z-Scores to Standardize a Distribution

Answer 11

Because all z-score transformations have same mean + standard deviation ⇒ standardized distributions
μ=0 ⇒ easy to identify relative locations

Question 12

Using z-Scores to Standardize a Distribution

Answer 12

σ = 1 ⇒ numerical value of z-score = number of standard deviations from mean

Question 13

Using z-Scores to Standardize a Distribution

Answer 13

useful to visualize z-scores as locations in a distribution
z = 0 is in the centre + extreme tails correspond to z-scores of approximately – 2 on left + +2 on the right
most of distribution is contained between z = –2 + z = +2

Question 14

Using z-Scores to Standardize a Distribution

Answer 14

Advantage of standardizing distributions: 2/more diff distributions can be made the same, can be directly compared

Question 15

Using z-Scores to Standardize a Distribution

Answer 15

can be used as descriptive statistics + inferential statistics
descriptive statistics: describe exactly where each individual is located

Question 16

Using z-Scores to Standardize a Distribution

Answer 16

inferential statistics: determine whether specific sample representative of pop/or extreme + unrepresentative

Question 17

Z Scores and Samples

Answer 17

possible to calculate z-scores for samples
definition of a z-score same for sample + pop
formulas same except sample mean + standard deviation used in place of pop mean + standard deviation

Question 18

Z Scores and Samples

Answer 18

shape of distribution stays the same

Mean of z-scores will be 0

Question 19

Z Scores and Samples

Answer 19

Standard deviation will be 1.00

standard deviation computed using sample formula: dividing by n – 1 instead of n

Question 20

Other Standardized Distributions Based on Z Scores

Answer 20

many people find z-scores burdensome - consist of many decimal values + negative numbers
often more convenient to standardize distribution into numerical values simpler than z-scores

Question 21

Other Standardized Distributions Based on Z Scores

Answer 21

1. select mean + standard deviation you would like for new distribution
2. z-scores used to identify each individual’s position in original distribution
3. compute individual’s position in the new distribution.