Chapter 5: z-Scores - Location of Scores and Standardized Distributions

Vocabulary flashcards covering key concepts, formulas, standardizations, and inferential applications from Chapter 5 z-Scores.

z-Score

A standard score that identifies and describes the exact location of a score within a distribution; its sign indicates whether the score is above ($+$) or below ($-$) the mean, and its numerical value specifies the distance from the mean in standard deviation units.

Population z-Score Formula

The mathematical formula $z = \frac{X - \mu}{\sigma}$, where the numerator represents the deviation score ($X - \mu$) and the denominator expresses that deviation in standard deviation units ($\sigma$).

Raw Score Formula

The formula $X = \mu + z\sigma$, used to calculate a raw score ($X$) by taking the population mean ($\mu$) and adding or subtracting the product of the z-score ($z$) and population standard deviation ($\sigma$).

Deviation Score

The numerator in the z-score formula ($X - \mu$), which specifies the direction and distance of a raw score ($X$) from the population mean ($\mu$).

Standardized Distribution

A distribution of scores that has been transformed into standardized values (such as z-scores) to make it directly comparable to other distributions; a z-score distribution always has a mean of $0$ and a standard deviation of $1.00$.

Standardized Scores in Comparison

Converted scores (z-scores) that allow direct comparison of scores originating from different distributions because all transformed scores are placed on the exact same scale.

Two-Step Standardization Process

A procedure used to establish a new standardized distribution with a predetermined mean ($\mu$) and standard deviation ($\sigma$) by first converting original raw scores into z-scores, and then converting those z-scores into new $X$ values.

Inferential Statistics

Statistical methods that utilize sample data to draw conclusions and answer research questions about larger populations.

Extreme Individuals

Individuals with scores located in the outer tails of a distribution (typically with z-scores beyond $+2.00$ or $-2.00$), which suggests that a treatment or effect has made the sample noticeably different from the untreated population.

Sample z-Score Characteristics

Transforming a sample distribution into z-scores maintains the exact shape of the original distribution, with relative positions defined by distance from the sample mean $M$ in units of sample standard deviation $s$.