I probably last saw this in the last century but I’ll put it in anyway!

#### Details #

Essentially another standardisation method but transforms raw scores so their mean is 50 and one standard deviation is 10. So the equation is:

$$x^{‘}=50 + \frac{10(x – mean_{x})}{SD_{x}}$$

To give a silly example, if the raw data are 1, 2, 3, 4 and 5 then they have mean of 3 and SD of 1.581139. The t-score transformation converts these data to 55, 60, 65, 70 and 75 which have mean 50 and SD 10.

As ever with these transformations/standardisations, that’s using the mean and SD from the data, usually the transformation would use some referential mean and SD.

Apparently this scoring/transformation is used quite a lot in Japanese education.

#### Try also #

Mean (arithmetic mean/average)

Standard deviation (SD)

Standardisation/normalisation

Transforming/transformation

z-scores/z-transforming

#### Chapters #

Not in the OMbook!

#### Online resources #

None currently.

#### Dates #

First created 2.iv.24, tweaks 3.iv.24.