New Year's Day is January 1 and it is observed on that day. The length of the holiday period varies depending on what day of the week January 1 falls. It may be 1.25 days long if January 1 falls on a Wednesday; 3.25 days long if January 1 falls on a Friday, Saturday, Sunday, or Monday; or 4.25 days long if January 1 falls on a Tuesday or Thursday.
In 2005, New Year's Day falls on Saturday so the holiday period is 3.25 days and extends from 6:00 p.m. Thursday, December 30, 2004, to 11:59 p.m. Sunday, January 2, 2005.1
The terms used in the traffic fatality discussion were chosen carefully to reflect the level of accuracy of the quantities involved. Estimate is used because the fatality figures are calculated approximately, as opposed to the precision of calculation inferred by the use of the word predict. May is used to indicate the figures express a contingency, whereas will is used to express something that may be expected or is supposed to occur.
The objective is to estimate the number of deaths that will occur in traffic crashes during the New Year holiday period based on data available several weeks before the holiday. The estimate developed here includes all traffic deaths from crashes that occur during the holiday period.2
The general procedure involves three steps. First, historical data are used to determine the average fraction holiday fatalities are of total deaths for the month containing the holiday. Second, total traffic deaths for the coming month in which the holiday falls are estimated using a time series forecasting model. Third, the projected total for the month is multiplied by the fraction to obtain the holiday estimate.
Holiday as percent of month. Total January deaths are the estimates published in Injury Facts® (formerly Accident Facts®) the year after the year of the estimate (e.g., the January 2003 estimate as published in the 2004 edition of Injury Facts®). This figure is used, rather than a revised estimate or the National Center for Health Statistics final count, because it closely approximates the level of accuracy that the time series estimate will give for total monthly deaths in the current year. Fatality Analysis Reporting System (FARS) data were used to obtain deaths during the holiday periods.
Table 1 shows the total traffic fatalities for the month of January and fatalities from crashes that occurred during the six most recent 3.25-day New Year holiday periods. Over those six years, fatalities from crashes during the New Year holiday period averaged 12.12% of the total fatalities in January.
Time series model and projection. A time series model was developed to forecast an estimate of total traffic deaths for January 2005. An Autoregressive Integrated Moving Average (ARIMA) model was constructed based on 48 months of traffic deaths recorded from November 2000 through October 2004. An ARIMA model was chosen because of the seasonal pattern in traffic deaths. The model was developed using the SPSS/PC+ Version 5.0 statistical computer package. The model forecasts total traffic fatalities for January 2005 to be 3,232.
Holiday estimate. Multiplying the projected total fatalities for January 2005 by the fraction obtained in the first step gives an estimate of 392 traffic fatalities from crashes during the holiday period.
There is uncertainty associated with any estimate. The 90% confidence interval for the estimate of total January deaths is 2,959 to 3,530. If we assume that the fraction of January deaths that occur during the New Year period is normally distributed, then the 90% confidence interval for that fraction is 11.42% to 12.82%. Combining these two gives the confidence interval for the New Year period estimate: 338 to 453 traffic deaths.
Based on the current disabling-injury to death ratio of 54:1, and rounded to the nearest hundred, the estimate of the number of nonfatal disabling injuries that will result from crashes during the holiday period is 21,200 with a range of 18,200 to 24,400.
A frequently asked question is "How much more dangerous is travel over the New Year holiday?" There are two aspects of this question that must be considered. First, compared to what? And, second, what about changes in the amount of driving?
For most holidays, we compare the holiday to periods of similar length before and after it. Because New Year's Day is exactly one week after Christmas Day, we chose to compare New Year to periods of similar length one week and two weeks after it. Specifically, from 6:00 p.m. Thursday to 11:59 p.m. Sunday of the two weeks immediately after the New Year holiday. Table 2 shows the fatality data from FARS for comparable periods. The average number of traffic deaths during New Year over those six years was 16.8% greater than the average number of traffic deaths during the comparison periods (383 vs. 328 deaths). The difference between these two means is statistically significant at the 5% level.
The second question concerns changes in the amount of travel, or exposure. We know of no data system that tracks changes in vehicle miles of travel by day of the year on a national basis. Lacking an objective measure of exposure change, we assume that travel is greater on holiday weekends than on nonholiday weekends.
If the assumed travel increase exceeds 16.8%, then the risk of dying in a traffic crash during the New Year holiday period is less than during comparable nonholiday periods. If the travel increase is less than 16.8% or if travel is actually lower, then the risk of dying on the holiday is greater than during comparable periods.
Arnold and Cerrelli (1987) also examined the variation in fatalities during holiday periods.3 They used FARS data for 1975-1985 to determine average daily fatalities for each day of the week in each month (e.g., Mondays in January). For the New Year holiday period, they found that fatalities were about normal on New Year's Eve but were 64% greater than average on New Year's Day.
Table 3 compares the actual FARS counts with the Council's estimates for all holidays for which data are available. Forty-six of the 53 actual counts fall within the 90% confidence interval of the estimate.
1. The National Highway Traffic Safety Administration extends the holiday period to 5:59 a.m. the next morning in its published tabulations of holiday deaths.
2. This differs from holiday estimates published by the Council in 1991 and earlier years. The estimating method described here is entirely different from the method used by the Council through 1991 when estimates were discontinued. Comparisons should not be made between holiday data and estimates shown here and holiday data and estimates published in 1991 and earlier years.
3. Arnold, R., & Cerrelli, E.C. (1987). Holiday Effect on Traffic Fatalities. DOT HS 807 115. Springfield, VA: National Technical Information Service.
Source: Injury Facts®, Accident Facts® and FARS.
Source: FARS.
Source: Estimates from National Safety Council; actual counts from FARS. * = outside of 90% confidence interval.
Kevin T. Fearn Statistics Department National Safety Council November 30, 2004
