# False Alarm Ratio: Definition

A false alarm ratio, generally abbreviated FAR, is the number of false alarms per the total number of warnings or alarms in a given study or situation.

The false alarm ratio is often confused with the false alarm rate, which shares the same abbreviation (FAR). The definitions are different, however; a false alarm rate is defined as the number of false alarms (in which an alarm, or warning, is given in spite of a non-event) per the total number of ‘non-events’ (times the event didn’t happen). A false alarm rate is also known as the probability of false detection.

## Examples of False Alarm Ratios

For an autism screening test, the false alarm ratio would be the number of false positives (test subjects who do not have autism receiving a false diagnosis) vs the total number of positive diagnoses. Let’s say you had 20 children flagged as autistic in a particular run of the screening test, but only 12 are actually autistic. The FAR would be:
number of false alarms / the total number of warnings or alarms:
8/20 = 0.40.

In weather reporting, the false alarm ratio for tornado warnings is the number of false tornado warnings per total number of tornado warnings. In 2003, there were reported to be four tornado warnings and one turned out to be an actual tornado, so the FAR was 3/4 or 0.76.

If, in any context, there were 10 valid alarms per 50 false alarms, the FAR would be 50/(10+50)= 0.833.

The study of false alarm ratios is important in weather forecasting, as forecasters seek the balance between over reporting possible danger vs. the danger of not making the alarm when actual catastrophic danger will happen. Low false alarm ratios are always preferred, but not at the cost of under-reporting actual danger.

## References

Barnes, L. R., E. C. Gruntfest, M. H. Hayden, D. M. Schultz, and C. Benight, 2007: False Alarms and Close Calls: A Conceptual Model of Warning Accuracy
Also: 2009: CORRIGENDUM: False Alarm Rate or False Alarm Ratio? Wea. Forecasting, 22, 1140–1147& 24 1140-1147