PSY201: Chapter 5 - z-Scores Flashcards
Z Score
Mean + standard deviation describe entire distribution of scores
Z-scores describe exact location of individual scores in distribution
Z Score
By itself, X provides very little info about how particular score compares with other values in distribution
Z Score
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
Z Score
one way to standardize distribution so we make diff distributions equivalent, thus comparable
z-scores and Location
sign of the z-score (+/–): above/below mean
numerical value = # of standard deviations betw X + mean
z-scores and Location
2 standard deviations above mean = +2.00
z-scores and Location
z=X−μ/σ
expressing the deviation from mean in standard deviation units
z-scores and Location
X = μ + zσ
zσ is the deviation of X - # of points away from mean
Using z-Scores to Standardize a Distribution
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
Using z-Scores to Standardize a Distribution
mean of z-score distribution always 0 + standard deviation always 1
Using z-Scores to Standardize a Distribution
Because all z-score transformations have same mean + standard deviation ⇒ standardized distributions
μ=0 ⇒ easy to identify relative locations
Using z-Scores to Standardize a Distribution
σ = 1 ⇒ numerical value of z-score = number of standard deviations from mean
Using z-Scores to Standardize a Distribution
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
Using z-Scores to Standardize a Distribution
Advantage of standardizing distributions: 2/more diff distributions can be made the same, can be directly compared
Using z-Scores to Standardize a Distribution
can be used as descriptive statistics + inferential statistics
descriptive statistics: describe exactly where each individual is located
Using z-Scores to Standardize a Distribution
inferential statistics: determine whether specific sample representative of pop/or extreme + unrepresentative
Z Scores and Samples
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
Z Scores and Samples
shape of distribution stays the same
Mean of z-scores will be 0
Z Scores and Samples
Standard deviation will be 1.00
standard deviation computed using sample formula: dividing by n – 1 instead of n
Other Standardized Distributions Based on Z Scores
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
Other Standardized Distributions Based on Z Scores
- select mean + standard deviation you would like for new distribution
- z-scores used to identify each individual’s position in original distribution
- compute individual’s position in the new distribution.