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