Center for Problem-Oriented Policing

Appendix B: Formulas for the WDQ and TNE to Measure Displacement and Diffusion

An innovative team of crime scientists in the United Kingdom has developed a series of formulas to precisely measure displacement and diffusion effects in relation to response effects.35 These consist of the gross effect (GE), net effect (NE), weighted displacement quotient (WDQ), and the total net effect (TNE). Each of these is determined as presented in the following four steps:

The gross effect (GE) and the net effect (NE) are defined as

(1)       GE = Rb - Ra

where Ra is the crime count in the response area post intervention, and Rb is the crime count in the response area before the intervention.

(2)       NE = (Rb/Cb) - (Ra/Ca)

where Ca is the crime count in the comparison area post intervention, Cb is the crime count in the comparison area before the intervention.

The weighted distribution quotient, or WDQ, used to determine displacement or diffusion effects and is designated as

(3)      

WDQ = Da/Ca – Db/Cb
Ra/Ca – Rb/Cb

where Da is the crime count in the buffer area post intervention, Db is the crime rate in the buffer area before the intervention.

The WDQ can also be broken down into separate measures of response success and displacement/diffusion, such as:

Success Measure (WDQ denominator) = Ra/Ca – Rb/Cb

Buffer Displacement Measure (WDQ numerator) = Da/Ca – Db/Cb

Additionally, the overall impact of the project can be determined using the TNE or "total net effects" model, which is defined by the relationship

(4)       TNE= [Rb(Ca/Cb)-Ra] + [Db(Ca/Cb)-Da]

These computations can be used for measuring any form of displacement as long as the three criteria for the selection of the areas are followed (e.g., logical interrelatedness/ proximity, proportionality, and contamination free). If you use multiple measures to assess your project, you need to use these four formulas for each of the types of measures that you collect or create a single composite measure from all or some of the measures taken. If before and after measures are taken at repeated intervals over time, the average of the before and after data periods can be computed and used in the equations. You can also use rates of crime for the computation of the net effect (NE) and weighted displacement quotient (WDQ), but not for the gross effect (GE) and total net effect (TNE) as these require the use of raw counts of crime or problem behavior. They require counts because they provide measures of the number of crimes or problem behaviors prevented, and, therefore, the resulting number can be interpreted as such (i.e., a TNE = 50 would mean that overall the project resulted in the prevention of 50 crimes).

† If the time period following the response is long enough it may be possible to use a statistical procedure called ARIMA to assess displacement and diffusion effects. To use this procedure you need to contact an expert in evaluation or statistics such as a crime analyst from your agency or one from your local university for assistance.