Hypotheses 2

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HYPOTHESES

REAR WINDOW DEFOGGERS REDUCE RELEVANT CRASHES AND THE EFFECTS ARE INDEPENDENT AND ADDITIVE FOR THE THREE ADVERSE CONDITIONS
and
REAR WINDOW DEFOGGERS REDUCE RELEVANT CRASHES ALL THE TIME

The analysis was repeated to see if the individual adverse conditions when defoggers are most likely used reduce relevant crashes. This analysis tests three hypotheses:

rear window defoggers reduce relevant crashes when raining or snowing,
rear window defoggers reduce relevant crashes during the early morning, and
rear window defoggers reduce relevant crashes during the winter.

The model included three individual interaction variables, DEFADW, DEFMORN, and DEFWIN, instead of DEF_USED and USED.

DEFADW has the value of DEF if it is snowing or raining. DEFADW = DEF * ADWEA . For example, if 1989 Ford Taurus (89.7 percent had rear window defoggers) had a collision when it was raining, then DEF = 89.7 and DEFADW = 89.7. DEFADW has the value of zero if it was not raining or not snowing. It also has the value of zero if the make-model was not equipped with any defoggers in that model year.

DEFMORN has the value of DEF if it is during the early morning, particularly between 6:00 am and 9:59 am. DEFMORN = DEF * MORN. DEFMORN has the value of zero when the crash occurred before 6:00 am or after 10:00am.

DEFWIN has the value of DEF if it is during winter: November through April. DEFWIN = DEF * WINTER. DEFWIN has the value of zero when the crash occurred in the months May through October.

DEFADW will indicate if rear window defoggers reduce relevant crashes when it is raining or snowing. DEFMORN will indicate if rear window defoggers reduce relevant crashes during 6:00 am and 10:00 am. DEFWIN will indicate if rear window defoggers reduce relevant crashes during the winter.

Similar to the previous model, DEF must be included in the model because logistic regression requires the main effect to be included in the model when interaction terms are included. If our hypothesis is correct that rear window defoggers reduce relevant crashes under these three conditions, then DEFADW, DEFMORN, and DEFWIN coefficients should be negative. The regression model considers the effects to be linear and additive. If the effects are intrinsically not linear and not additive (e.g., if our second hypothesis is correct that the full benefit of defogger is achieved from any one adverse condition), then the model may spuriously calibrate some coefficients positive and others negative.

Table 12 shows the results and in fact, some of the coefficients are positive and some are negative. When raining or snowing, the coefficients are negative but not statistically significant. During the early morning, the coefficients are positive indicating an increase in relevant crashes. Michigan’s coefficient is statistically significant, but Florida’s is not. The coefficients for rear window defoggers during the winter are mixed. Michigan’s coefficient is negative and Florida’s is positive, but neither is significant. In any case, none of the coefficients is significant in the “right” direction, and we cannot conclude that rear window defoggers reduce relevant crashes when it is raining or snowing, during the early morning, or during the winter.

Table 12

DEFADW, DEFMORN, DEFWIN And DEF Coefficients And Percent Reduction By State

State	DEFADW		DEFMORN		DEFWIN		DEF
State	Coeff	% Reduced	Coeff	% Reduced	Coeff	% Reduced	Coeff	% Reduced
MI	-0.00044	4%	0.00153	-17%*	0.000323	-3%	0.000122	-1%
FL	-0.00094	9%	0.000668	-7%	-0.00006	1%	-0.00061	6%

* Significant