PSYC 243 - Chp. 5: Z-scores
What happens when sample distribution is transformed into z-scores?
- Same shape as OG distribution - Same mean (M) and standard deviation (s)
What are some characteristics of z-score transformation?
- Same shape as the OG distribution - Mean of a z-score distribution is always 0 - STD is always 1.00 (units)
Purpose of z-Scores
-Identify and describe location of every score in the distribution -Standardize an entire distribution -Take different distributions and make them equivalent and comparable
How is it possible to compute z-scores for samples
-Indicates relative position of score in sample -Indicates distance from sample mean
What are the steps in standardizing a distribution?
-Original raw scores transformed to z-scores -The z-scores are transformed to new X values so that the specific predetermined μ and σ are attained.
Characteristics of z-score transformation
-Same shape as original distribution -Mean of z-score distribution is always 0. -Standard deviation is always 1.00
Sample distribution can be transformed into z-scores how?
-Same shape as original distribution -Same mean M and standard deviation s
How many steps does standardizing a distribution have? What are they?
2 steps - OG raw scores transformed to z-scores - The z scores are transformed to a X values so that the specific predetermined mean and STD are attained
Numerator of a z score is what?
A deviation score
A z-score distribution is called what?
A standardized distribution
Every X value can be transformed into what?
A z score
A z-score of z = +1.00 indicates a position in a distribution....
Above the mean by a distance equal to 1 standard deviation
Z-scores (standardized scores)
Allow the direct comparison of scores from two different distributions BECAUSE they have been converted to the same scale
z-scores (standardized scores)
Allow the direct comparison of scores from two different distributions because they have been converted to the same scale
All z-scores are what to each other?
Comparable
Scores from different distributions can be...?
Converted to z-scores
Interpretation of research results depends on what?
Determining if (treated) a sample is noticeably different from the population
All z-scores are comparable to what?
Each other
What can be transformed to a z-score?
Every X value
True or False: A score close to the mean has a z score close to 1.00
False
True or False: • If a sample of n = 10 scores is transformed into z-scores, there will be five positive zscores and five negative z-scores.
False. # of z-scores above/below mean will be exactly the same as # of OG scores above/below mean
Raw score
Is the population mean plus (or minus if z is below the mean) z multiplied by population the standard deviation
Denominator of a z score is what?
It expresses deviation in standard deviation units
What is the most common context for computing z-scores?
Populations
What were the abilities that were measured by the Binet & Simon tests?
Q's that 60 - 90% of kid of a given age could answer easily = "normal" ability for that age - memory of word meaning - color - music - thinking abstractly
Process of standardization is widely used in what things?
SAT and IQ scores
True or false: A negative z score always indicates a location below the mean
True
True or False: The process of standardization is widely used
True (i.e SAT and IQ scores)
Is the =/- sign required for z-score?
YES!! Indicates whether it's above or below the mean!
Is a z-score a standardized score?
Yes
Is it possible to compute z-scores for samples?
Yes - Indicates relative position of score in sample - indicates distance from sample mean
Scores from different distributions can be converted into what?
Z scores
What will always be the mean of a z-score distribution?
ZERO
Standardized distribution
a z-score distribution
What did William Stern do?
created the ratio of mental age to chronological age multiplied by 100 to provide "Mental Quotient" now called Intelligence Quotient or IQ
Number of z score tells what?
distance between score and mean in standard deviation units
What did Alfred Binet do?
w/ Simon - developed assessed "natural" intelligence with 30 questions of increasing complexity
Sign of z score tells what?
whether score is located above or below the mean
How to determine a row score
x = mean + or - (z*STD) - Sign depends on the z score value
Equation for Z-Score
z = (x-mean)/standard deviation
