Ratio measures of the gender gap fluctuate more than percentage measures and can distort long-term trends

Female percentage and female-to-male ratio of aggravated assault by solo offenders

Note: Aggravated assault offenses are perpetrated in (male-dominated) groups as often as by solo offender.  See also, figure 2, panel a in Schwartz et al. 2009, which shows offsetting multiple offender incident trends and overall offending trends for aggravated assault.         

Calculating and Interpreting Gender Gap Measures

Female Percentage = Female Rate / (Female Rate + Male Rate) * 100

Interpretation:  the share of offenders who are female, after adjusting for sex composition of the population (Schwartz et al. 2009)  For example, a five unit increase means the gender composition of offenders contains five percent more female (or there are 5 more females per 100 offenders).  This measure ranges from 0 to 100, with 50% indicating gender-equal involvement.    

Female-to-Male Ratio = Female Rate / Male Rate

Interpretation: female-to-male population-adjusted rate ratios of offending (Lauritsen et al. 2009)
This measure ranges from zero to infinity; a value of 1 indicates gender equal involvement.

Q&A about using percentage-based gender gap measure

Q.  Why use a percentage-based rather than a ratio-based gender gap measure?

A.  Ratios are extremely unstable when the number of events is small, as in female serious violence.  Female rates from the NCVS are often based on fewer than 30 incidents involving women.  Year-to-year changes are exaggerated by the ratio method (e.g., compare changes in the percentage and ratio measures from 1993 to 1994 or 1996 to 1997).  Also note how these more extreme outliers distort the long-term regression trend.

See: Anderson and Zelditch 1968, A Basic Course in Statistics. NY: Holt, Rinehart & Winston.

Q.  Why do short-term fluctuations matter when theories are about long-term patterns of social change?