Hypotheses 1

Hypotheses 1 | Hypotheses 2 | Hypotheses 3 |

HYPOTHESES –

REAR WINDOW DEFOGGERS REDUCE RELEVANT CRASHES IN THE PRESENCE OF ANY ONE OR MORE CONDITIONS WHEN THEY ARE MOST LIKELY USED (but the effect does not increase if there is more than one adverse condition)
and
REAR WINDOW DEFOGGERS REDUCE RELEVANT CRASHES ALL THE TIME

This model contained two independent variables that indicate if rear window defoggers are effective. DEF_USED indicates if the presence of rear window defoggers when they are most likely to be used affects the rate of changing lane and backing crashes. DEF indicates if the mere presence of rear window defoggers affects the rate of changing lane and backing crashes. In other words, DEF will indicate if rear window defoggers are effective all of the time and DEF_USED will indicate if rear window defoggers are effective in the conditions when they are most likely to be used. Thus, the DEF_USED coefficient in the model will test our hypothesis that defoggers reduce relevant crashes when they are most likely used. But the DEF coefficient must also be included in the logistic regression (because interaction terms such as DEF_USED should not be included without also including the main effects DEF and USED). DEF will indicate if defoggers when present affect relevant crashes. We believe that just the presence of rear window defoggers should not have an effect on relevant crashes. If our hypothesis is correct that defoggers reduce relevant crashes when used and they have no effect when they are not used, then the DEF_USED coefficient should be negative and significant and the DEF coefficient should be close to zero. In fact, even if the DEF coefficient were substantial, we suspect it more likely indicates a possible bias in the model or data than a real effect of defoggers. We believe DEF_USED is the more important coefficient.

Table 10 shows the results of the logistic regression for the 1986-1999 Florida data. The coefficient for DEF_USED is –0.00002, in the “right” direction but not statistically significant (Chi-Square = 0.002).

Technically, the DEF_USED coefficient represents the change in the log odds ratio of relevant (changing lanes and backing) to non-relevant (stopped) crashes when defoggers are most likely used for a 1 percent increase in the percentage of cars with rear window defoggers. A negative coefficient represents a reduction that is associated with the presence of rear window defoggers when most likely used. Thus, a 100 percent increase in the percentage of cars with rear window defoggers is associated with 0.002 reduction in the log of relevant crash rate when defoggers are most likely used. The coefficient can be translated into the percentage change in the expected number of relevant crashes in the following way:

Expected percentage effectiveness = 100*[1-exp (DEF coefficient*100)].

In other words, cars with rear window defoggers when they are most likely used have 100 * [1- (exp (.002))] = 0.2 percent reduction in changing lanes and backing crashes relative to crashes where the vehicle was stopped. Rear window defoggers when most likely used have no effect on relevant crash, since the chi-square value is 0.002 and chi-square needs to be at least 3.89 for statistical significance at the 0.05 level.

The coefficient for DEF is 0.00162, in the “wrong” direction but also non-significant (Chi-Square = 3.184). Thus, the Florida data do not show any statistically significant effect for defoggers.

Table 10

1986-1999 Florida

Cars With Rear Impacts That Were Changing Lanes, Backing Up, Slowing, Stopped, Or Stalled

Parameter	Estimate	Standard Error	Wald Chi-Square	Pr > ChiSq
Intercept	-1.6579	0.1343	152.2927	<.0001
DEF	0.00162	0.000909	3.184	0.0744
DEF_USED	-0.00002	0.000435	0.002	0.9647
USED	-0.1511	0.0416	13.1992	0.0003
ADWEA	-0.7571	0.0234	1051.1949	<.0001
WINTER	0.0518	0.0233	4.9489	0.0261
MORN	-0.0985	0.0196	25.165	<.0001
VEHAGE	0.0173	0.00427	16.3514	<.0001
VEHAGE2	0.000608	0.000225	7.3093	0.0069
CY86	0.0273	0.0448	0.3715	0.5422
CY87	-0.1325	0.0426	9.6577	0.0019
CY88	-0.1503	0.0399	14.2253	0.0002
CY89	-0.1073	0.0373	8.2893	0.004
CY90	-0.1011	0.0361	7.83	0.0051
CY91	-0.0766	0.0347	4.8868	0.0271
CY92	-0.0459	0.0327	1.9701	0.1604
CY93	-0.0979	0.0319	9.4068	0.0022
CY94	-0.1121	0.0306	13.4317	0.0002
CY95	0.013	0.028	0.2165	0.6417
CY96	-0.2027	0.0284	50.9083	<.0001
CY97	-0.0186	0.0264	0.4957	0.4814
CY98	0.0373	0.0254	2.1556	0.142
DRVMALE	-0.0285	0.0296	0.9264	0.3358
M14_30	0.0502	0.0022	521.6789	<.0001
M30_50	0.0175	0.00151	134.1712	<.0001
M50_70	0.0276	0.00168	269.659	<.0001
M70_96	0.0996	0.00282	1243.4684	<.0001
F14_30	0.0549	0.0024	520.9121	<.0001
F30_50	0.000669	0.0016	0.1753	0.6755
F50_70	0.0471	0.00182	671.5062	<.0001
F70_96	0.0886	0.00359	609.8991	<.0001
CAVALIER1	-0.8086	0.1146	49.7464	<.0001
ESCORT1	-0.8556	0.1179	52.6484	<.0001
CAPRICE1	0.0319	0.1123	0.0805	0.7766
TAURUS1	-0.6526	0.1212	28.979	<.0001
TEMPO	-0.6629	0.1172	31.9908	<.0001

CELEBRITY	-0.7663	0.1196	41.0775	<.0001
GRANDAM	-0.8848	0.1185	55.708	<.0001
CIERA	-0.8502	0.12	50.1573	<.0001
CUTLASS1	-0.5913	0.1166	25.7121	<.0001
CHEVETTE	-0.4266	0.1243	11.7865	0.0006
CENTURY1	-0.845	0.1217	48.2322	<.0001
MUSTANG	-0.6024	0.1145	27.6735	<.0001
RELIANT	-0.8532	0.1263	45.6675	<.0001
CORSICA	-0.6775	0.1247	29.5101	<.0001
SUNBIRD	-0.8745	0.1272	47.2302	<.0001
ESCORT2	-0.8156	0.1234	43.6733	<.0001
MONTE1	-0.5853	0.1183	24.4601	<.0001
CROWNVIC	0.3289	0.1175	7.8379	0.0051
LUMINA	-0.6828	0.1272	28.8221	<.0001
CITATION	-0.5525	0.141	15.3483	<.0001
ARIES	-0.8317	0.1248	44.4337	<.0001
FAIRMONT	-0.4133	0.12	11.8572	0.0006
MALIBU	-0.5068	0.124	16.6945	<.0001
ACCORD1	-0.8565	0.1264	45.8754	<.0001
REGAL	-0.5897	0.1188	24.6408	<.0001
P6000	-0.638	0.1287	24.574	<.0001
DELTA1	-0.1761	0.1193	2.1787	0.1399
GMARQUIS	-0.5362	0.1215	19.4728	<.0001
OMNI4DR	-0.7307	0.163	20.0868	<.0001
SABLE	-0.7579	0.1309	33.5421	<.0001
LESABRE1	-0.9783	0.1276	58.7781	<.0001
TOPAZ	-0.6658	0.1337	24.7831	<.0001
SHADOW	-0.8883	0.1365	42.3473	<.0001
SUNDANCE	-0.8107	0.1395	33.7796	<.0001
DEVILLE1	-0.3088	0.1219	6.4152	0.0113
DEVILLE2	-0.4892	0.1261	15.0633	0.0001
BERETTA	-0.5711	0.1292	19.5558	<.0001
THUNDER1	-0.6749	0.1272	28.1715	<.0001
COUGAR1	-0.6792	0.1297	27.4176	<.0001
SKYLARK1	-0.592	0.138	18.399	<.0001
DEVILLE3	-0.6975	0.1208	33.3294	<.0001
HORIZON	-0.6784	0.1704	15.8464	<.0001
SATURN	-1.1415	0.1323	74.4713	<.0001
CAVALIER2	-1.107	0.1426	60.27	<.0001
SKYLARK2	-0.943	0.1324	50.7292	<.0001
CALAIS	-0.9328	0.1331	49.0969	<.0001
DELTA2	-0.8705	0.1318	43.6156	<.0001
GRANDPRIX1	-0.8488	0.1348	39.6177	<.0001

Table 10 – Continued

Parameter	Estimate	Standard Error	Wald Chi-Square	Pr > ChiSq
CIVIC1	-0.9198	0.1254	53.8029	<.0001
LESABRE2	-0.3507	0.1229	8.1429	0.0043
GRANADA	-0.1958	0.1293	2.2906	0.1302
TOWNCAR	-0.4348	0.1223	12.6429	0.0004
ACCORD2	-1.0276	0.1292	63.2644	<.0001
ACCORD3	-0.791	0.1275	38.4732	<.0001
SENTRA1	-1.1258	0.127	78.6326	<.0001
CAMRY1	-0.8883	0.1268	49.0939	<.0001
LTD	0.0808	0.1248	0.4191	0.5174
VOLARE	-0.2067	0.129	2.5661	0.1092
CAPRICE2	-0.0625	0.1284	0.2372	0.6262
CIVIC2	-1.1626	0.1349	74.2177	<.0001
ACCLAIM	-0.7761	0.1489	27.1552	<.0001
GRANDPRIX2	-0.339	0.1216	7.7791	0.0053
CUTLASS2	-0.0547	0.1281	0.1827	0.6691
SUPREME1	-0.6846	0.1463	21.8879	<.0001
SKYHAWK	-0.7723	0.156	24.5135	<.0001
ELECTRA	-1.14	0.1385	67.7382	<.0001
HORNET	-0.0827	0.1386	0.3563	0.5506
MONTE2	-0.1587	0.136	1.3605	0.2435
BONNEVILLE	-0.1353	0.1315	1.0581	0.3037
PARISIENNE	-0.3587	0.1503	5.6926	0.017
NOVA1	-0.2251	0.1257	3.2076	0.0733
CAMARO	-0.4467	0.1218	13.4537	0.0002
PINTO	-0.019	0.1439	0.0175	0.8948
LEBARON1	-0.8419	0.1371	37.7211	<.0001
CAMRY2	-0.6545	0.1312	24.881	<.0001
ASPEN	-0.3034	0.129	5.5308	0.0187
TAURUS2	-0.7342	0.1473	24.8572	<.0001
ALTIMA	-0.921	0.1314	49.1283	<.0001
DAYTONA	-0.8438	0.1475	32.7431	<.0001
THUNDER2	-0.3195	0.1313	5.9238	0.0149
CHEVELLE	0.1859	0.1463	1.6149	0.2038
SPIRIT	-0.7976	0.1496	28.432	<.0001
LEGACY	-1.1856	0.2229	28.2828	<.0001
PROBE	-0.8096	0.1453	31.0575	<.0001
OLDS98	-0.9531	0.1377	47.9346	<.0001
LEBARON2	-0.6259	0.139	20.2716	<.0001
DYNASTY	-0.819	0.1529	28.7071	<.0001
MONZA	-0.4225	0.1687	6.2762	0.0122
EAGLE	-0.1943	0.338	0.3304	0.5654
OMEGA	-0.4624	0.1804	6.5732	0.0104
NEONPLY	-0.7177	0.1925	13.9012	0.0002

NEONDOD	-0.8636	0.1769	23.8328	<.0001
ZEPHYR	-0.4222	0.1492	8.0099	0.0047
FIREBIRD	-0.4837	0.1298	13.8907	0.0002
CENTURY2	-0.3467	0.1546	5.0307	0.0249
THUNDER3	-0.855	0.1361	39.4743	<.0001
INTREPID	-0.5406	0.1558	12.0399	0.0005
MARQUIS	-0.5115	0.1399	13.37	0.0003
COUGAR2	-0.753	0.1433	27.5981	<.0001
LEBARON3	-0.2955	0.1508	3.8413	0.05
CORDOBA	-0.2765	0.1558	3.1491	0.076
NEWYORKER	-0.899	0.1519	35.033	<.0001
DART	-0.1866	0.1528	1.4905	0.2221
DIPLOMAT	0.3079	0.1245	6.111	0.0134
CONTOUR	-0.8677	0.1639	28.0303	<.0001
FIRENZA	-0.7187	0.1702	17.8207	<.0001
SUPREME2	-0.5465	0.1229	19.7705	<.0001
LEGACY1	-0.6543	0.3883	2.839	0.092
NOVA2	-0.8272	0.1522	29.5268	<.0001
COUGAR3	-0.1681	0.143	1.382	0.2398
VALIANT	-0.2049	0.2075	0.9752	0.3234
GREMLIN	-0.3648	0.1803	4.094	0.043
JETTA	-1.0479	0.1388	56.9669	<.0001
COROLLA	-1.0354	0.1256	67.916	<.0001
LOYALE	-0.9161	0.1702	28.9677	<.0001
ACCORD4	-0.9514	0.1339	50.4566	<.0001
VOL240	-1.068	0.1382	59.7267	<.0001
EXCEL	-0.9987	0.1326	56.6941	<.0001
MAXIMA1	-0.8257	0.1376	36.0173	<.0001
SUBARU	-0.8949	0.1716	27.2023	<.0001
SPECTRUM	-1.0584	0.1526	48.0771	<.0001
GOLF	-1.0393	0.161	41.6642	<.0001
TERCEL	-1.0464	0.195	28.7966	<.0001
SENTRA2	-0.9259	0.1374	45.4432	<.0001
RABBIT	-1.1188	0.1591	49.4222	<.0001
MAXIMA2	-0.8316	0.1391	35.7504	<.0001
CELICA	-0.6559	0.1372	22.8457	<.0001

The regression coefficient (0.0173) for VEHAGE shows that changing lanes and backing crashes increase relative to stopped involvements, as cars get older. Changing lanes and backing crashes increase 2 percent for every year a car gets older. The negative regression coefficient for almost all of the CY terms implies that changing lanes and backing crashes were less common in the past than in recent years. VEHAGE, VEHAGE2, and most of the CY terms are included in the model because they are significant.

The coefficients of the other independent variables seem reasonable. The positive coefficients for M14_30, M70+, F14_30, and F70+ show that the youngest and oldest drivers are especially prone to backing up or changing lane crashes. ADWEA and MORN are negative, indicating that changing lanes and backing crashes decrease relative to stopped involvements during adverse weather and early morning. USED is also negative, indicating the relevant crashes decrease during conditions when rear window defoggers are most likely used.

The make-model indicator variables are used only as control variables in the model. Some will have high or low coefficient values by chance alone indicating more or fewer changing lane and backing crashes than the average. We could reduce the number of these variables, if we grouped several make-models together. But there is no basis to group them. For example, not all small cars are driven in such a manner that they have fewer (or more) relevant crashes than large cars. Thus, all the individual make-model terms are included in the model and it is irrelevant if certain make-model terms are significant and others are not.

A similar model was run on the Michigan database. The adverse weather indicator variable for Michigan also had a value of 1 if the crash occurred when it was snowing, sleeting, hailing or freezing rain. Michigan’s model included 34 additional make-models not included in the Florida model that had at least 750 crashes in Michigan.

The only other difference in the model was the number of individual CY terms. Since 1981-1991 Michigan data were analyzed, the model had 10 individual CY terms: CY81, CY82, …, CY90.

Table 11 shows the DEF_USED and DEF coefficients, percent reduction, and significance for the model by State. All of the results are non-significant indicating that rear window defoggers have no effect on changing lane and backing crashes, in all conditions and in conditions when they are most likely used. The DEF_USED coefficient in Michigan is in the “wrong” direction, corresponding to a 5 percent increase in changing lane and backing crashes, but this effect is not statistically significant.

Table 11

DEF_USED And DEF Coefficients And Percent Reduction By State

State	DEF_USED		DEF
State	Coeff	Percent Reduction	Coeff	Percent Reduction
Michigan	0.00047	-5%	0.00015	-2%
Florida	-0.00002	0.2%	0.00162	-18%