Theory:

The Standard Deviation Ratio (SDR) was first presented as a technical indicator in the March 1992 edition of Technical Analysis of Stocks & Commodities magazine 'Adapting Moving Averages To Market Volatility'.  The author Tushar S. Chande, Ph.D. used it as the Volatility Index in the original version of his Volatility Index Dynamic Average (VIDYA) or Variable Moving Average (VMA).

Calculating it is as simple as taking the ratio of a Standard Deviation (SD) over one period to that of a longer period where both have the same starting point.  One quirk of the SDR is that because the short term SD can become greater than the longer term SD, the ratio has no upper limit but does tend to remain below 1 most of the time (see the example chart below).  The higher the ratio, the more spread the recent data is from the mean in relation to the past which should indicate a stronger trend.

Usage:

The standard deviation ratio (SDR) on its own can be used in a similar mode as the regular standard deviation - as a measure of current market volatility (ie: it is not a directional indicator and it can not be used for trend direction determination - for that you need some other indicator combined with this one)