Go to standardisation for the full background on this but z-scores, z-transforming is one of a set of ways of converting raw scores to a different score range. In the z-transform scores are standardised using the mean and SD so a score equal to the mean becomes zero and each score change of SD from the mean converts to a change of 1 (+1 if up from the mean and -1 if down!). If using the mean and SD of the dataset the equation is this.

$$x^{‘}=\frac{(x – mean(x))}{SD(x)}$$

In that case the mean from the dataset must become zero and the SD of the standardised dataset will have an SD of 1. That’s fine if the standardised data are only being used within the study but very often the point of standardisation is for comparison across data sets. In that case standardisation is generally done using referential values for the mean and SD:

$$x^{‘}=\frac{(x – mean_{referential})}{SD_{referential}}$$

#### Details #

See standardisation for the full story.

#### Try also #

Centring/centering

Composite scores/variables

Gaussian (“Normal”) distribution

Percentiles: see quantiles!

Population

Quantiles

Sample

Sampling and sample frame

t-scores

Transforming

#### Chapters #

Not mentioned in the book.

#### Online resources #

Not yet.

#### Dates #

First created 3.iv.24