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 the following table. 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 the table on the following page. Since 144,000 does not appear in the Crash Estimate column, use linear interpolation from the standard error values for 100,000 (8,000) and 200,000 (14,500). 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.

2003 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	1,500	10,000	1,400
7,000	1,100	20,000	2,300	20,000	2,200
8,000	1,200	30,000	3,100	30,000	2,900
9,000	1,300	40,000	3,900	40,000	3,500
10,000	1,400	50,000	4,600	50,000	4,200
20,000	2,300	60,000	5,300	60,000	4,800
30,000	3,100	70,000	6,000	70,000	5,400
40,000	3,900	80,000	6,600	80,000	5,900
50,000	4,600	90,000	7,300	90,000	6,500
60,000	5,300	100,000	8,000	100,000	7,100
70,000	6,000	200,000	14,300	200,000	12,300
80,000	6,700	300,000	20,400	300,000	17,400
90,000	7,400	400,000	26,500	400,000	22,300
100,000	8,000	500,000	32,600	500,000	27,200
200,000	14,500	600,000	38,600	600,000	32,000
300,000	20,900	700,000	44,700	700,000	36,800
400,000	27,200	800,000	50,900	800,000	41,600
500,000	33,500	900,000	57,000	900,000	46,500
600,000	39,900	1,000,000	63,200	1,000,000	51,300
700,000	46,300	2,000,000	126,900	2,000,000	99,900
800,000	52,700	3,000,000	194,000	3,000,000	149,900
900,000	59,200	4,000,000	263,900	4,000,000	201,200
1,000,000	65,700	5,000,000	336,400	5,000,000	253,800
2,000,000	133,500	6,000,000	411,300	6,000,000	307,600
3,000,000	205,200	7,000,000	488,400	7,000,000	362,600
4,000,000	280,500	8,000,000	567,500	8,000,000	418,600
5,000,000	359,000	9,000,000	648,600	9,000,000	475,700
6,000,000	440,200	10,000,000	731,500	10,000,000	533,700
6,500,000	481,900	11,000,000	816,100	11,000,000	592,600
7,000,000	524,100	12,000,000	902,400	12,000,000	652,400
*SE   =   e a + b (ln x) 2, where a = 4.208860 b = 0.036070		**SE   =   e a + b (ln x) 2, where a = 4.272400 b = 0.035530		***SE   =   e a + b (ln x) 2, where a = 4.357200 b = 0.033990

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). The table below gives the reader the proportion of unknown values prior to imputation for variables with imputed values that were used in this report.

Percent of Unknowns for 2003 GES Data Elements