Ch. 5 Z-Scores

for a population with u=80 and o=12, what is the z-score corresponding to x=92?

+1.00 (92-80)/12

for a population with u=80 and o=10, what is the z-score corresponding to x=95?

+1.50 (95-80)/10

for a population with u=80 and o=12, what is the z-score corresponding to x=71?

-0.75 (71-80)/12

z-scores for comparisons

-all z-scores are comparable to each other -score from differential distributions can be converted to z-scores -the z-scores (standardized scores) allow the comparison of scores from two different distributions along

raw score (X)

-gives little information -changing ___ into z-score describes the exact location in a distribution

computing z-scores for samples

-populations are most common context for computing z-scores -it is possible to compute z-scores for samples (indicates relative position of score in sample, indicates distance from sample mean) -sample distribution can be transformed into z-scores (same shape as original distribution, same mean and standard deviation)

z-score transformation

-same shape as original distribution -mean of z-score distribution is always o -standard deviation is always 1.00

inferential statistics

-techniques that use the information from samples to answer questions about populations -also used to help interpret results from a research study -the interpretation of the research results depends on whether the sample is noticeably different from the population -using z-scores you can decide that an individual with a z-score near o is located in the center of the population and would be considered to be a fairly typical or representative individual of the population

sign

-tells location -above mean (+) -below mean (-)

numerical value

-tells number of standard deviation between X and the mean of the distribution

standardizing distribution

1. original raw scores transformed to z-scores 2. the z-scores are transformed to new x values so that the specific U and O are attained

for a population with u=100 and o=20, what is the X value corresponding to z=0.25?

105 x=100+(0.25)(20) x=100+5=105

for a population with u=100 and o=20, what is the X value corresponding to z=-0.50?

90 x=100+(-0.50)(20) x=100+(-10)=90

standardization

AT has u=500 and o=100 IQ has u=100 and o=15 point

a z-score of z=-2.00 indicates a position in a distribution _________

below the mean by a distance equal to 2 standard deviations

z-scores

identify and describe the exact location of every score in a distribution

by itself, a ________ or x-value provides very _____________ information about how that particular score compares with other values in the distribution

raw score, little

if the _________ is transformed into a _______, it tells exactly where the score is ____________ relative to all the other scores in the distribution

raw score, z-score, located

th z-score combines the ____, the _____, and the ________ into a single number that describes the location of a particular score relative to the other scores in the distribution

score, mean, standard deviation

in a sample with s=8, a score of z=-0.50, with m=60 what is the raw score?

x=m+zs x=60+(-0.50)(8) x=60+(-4.0) x=56

standardized distribution

z-score distribution

z-score for a sample

z=(X-m)/s

determining raw score from z-score for a sample

z=(x-m)/s SO x=m+zs

z-score for a population

z=(x-u)/o

determining raw score from z-score for a population

z=(x-u)/o SO X=u+zo

for a distribution of scores, which of the following z-score values represents the location closest to the mean?

z=+0.50

for a distribution of scores, which of the following z-score values represents the most extreme location on the left-hand side of the distribution?

z=-2.00

What is the z score for x=46 from a sample where m=40 and s=12?

z=X-m/s z=(46-40)/12 z=6/12=0.50