Appendix C. GES Technical Notes

Standard Errors

The national estimates produced from GES data may differ from the true values, because they are based on a probability sample of crashes and not a census of all crashes. The size of these differences may vary depending on which sample of crashes was selected. [For a complete description of the GES sampling design, see National Accident Sampling System General Estimates System Technical Note (DOT HS 807 796) available from NCSA.] The standard error of an estimate is a measure of the precision or reliability with which an estimate from this particular GES sample approximates the results of a census.

In a report of this size, it is impractical to provide standard errors for each estimate. Instead, generalized standard errors for estimates of totals are provided in the following table. Generalized errors were calculated separately for the crash, vehicle, and people characteristics. The values for the GES estimates and an estimate of one standard error are given in Table C1 on the following page. By adding and subtracting two standard errors, a 95 percent confidence interval can be created for the GES estimates in this report. For example, the estimated number of injury crashes that occurred in the month of February is given in Table 23 as 144,000. To calculate one standard error for this crash estimate, use Table C1. Since 144,000 does not appear in the Crash Estimate column of Table C1, use linear interpolation from the standard error values for 100,000 (8,000) and 200,000 (14,600). One standard error would be approximately 10,900. The 95 percent confidence interval for this estimate would be 144,000 ± 2 × 10,900 or 122,200 to 165,800.

Table C1. 2004 GES Estimates and Standard Errors

Crash Estimate (x)	Crash Standard Error (SE)*	Vehicle Estimate (x)	Vehicle Standard Error (SE)**	Person Estimate (x)	Person Standard Error (SE)***
1,000	400	1,000	400	1,000	400
5,000	900	5,000	900	5,000	900
6,000	1,000	10,000	1,400	10,000	1,400
7,000	1,100	20,000	2,300	20,000	2,100
8,000	1,200	30,000	3,100	30,000	2,800
9,000	1,300	40,000	3,800	40,000	3,500
10,000	1,400	50,000	4,500	50,000	4,100
20,000	2,300	60,000	5,200	60,000	4,700
30,000	3,100	70,000	5,900	70,000	5,300
40,000	3,800	80,000	6,600	80,000	5,800
50,000	4,600	90,000	7,200	90,000	6,400
60,000	5,300	100,000	7,900	100,000	6,900
70,000	6,000	200,000	14,200	200,000	12,200
80,000	6,700	300,000	20,300	300,000	17,200
90,000	7,300	400,000	26,300	400,000	22,200
100,000	8,000	500,000	32,400	500,000	27,100
200,000	14,600	600,000	38,500	600,000	31,900
300,000	21,000	700,000	44,600	700,000	36,800
400,000	27,400	800,000	50,700	800,000	41,600
500,000	33,800	900,000	56,900	900,000	46,500
600,000	40,300	1,000,000	63,100	1,000,000	51,400
700,000	46,900	2,000,000	127,200	2,000,000	100,700
800,000	53,400	3,000,000	194,700	3,000,000	151,700
900,000	60,100	4,000,000	265,200	4,000,000	204,200
1,000,000	66,700	5,000,000	338,500	5,000,000	258,100
2,000,000	136,300	6,000,000	414,200	6,000,000	313,400
3,000,000	210,300	7,000,000	492,200	7,000,000	370,000
4,000,000	288,100	8,000,000	572,400	8,000,000	427,800
5,000,000	369,400	9,000,000	654,500	9,000,000	486,600
6,000,000	453,800	10,000,000	738,600	10,000,000	546,600
6,500,000	497,100	11,000,000	824,400	11,000,000	607,500
7,000,000	541,000	12,000,000	912,000	12,000,000	669,400
*SE   =   e a + b (ln x) 2, where a = 4.168580 b = 0.036360		**SE   =   e a + b (ln x) 2, where a = 4.240450 b = 0.035690		***SE   =   e a + b (ln x) 2, where a = 4.297920 b = 0.034310

Unknowns

GES data are obtained either directly from an item on the PAR or by interpreting the information provided in the report through reviewing the crash diagram, the Officer’s written summary of the crash, or combinations of variables on the PAR. Because of this interpretation, and because the police officer may not have entered some item of information or provide complete information, data can be missing. Two different statistical procedures are used on GES data to complete values for unknown data. These procedures, univariate and hotdeck imputation, are described in a technical report available from NCSA, Imputation in the General Estimates System (DOT HS 807 985). Table C2 below gives the reader the proportion of unknown values prior to imputation for variables with imputed values that were used in this report.

Table C2. Percent of Unknowns for 2004 GES Data Elements