CORRECTING THE SAMPLING ERROR CALCULATION FOR A MULTI-DAY LONGITUDINAL STUDY

With the increasing use of GPS to collect travel data over multiple days (Itsubo, 2006; Oliveira et al., 2006; Marchal et al., 2008; Bohte and Maat, 2009; Schussler and Axhausen, 2009; Feng and Timmermans, 2012; Rasmussen et al., 2013; Stopher et al., 2013, inter alia ), transport planners are facing a new issue that has not arisen in the past. With conventional diary or interview data, the data have generally been limited to a single day for each respondent. Although it is probable that people living in the same household do not make choices about their travel independently of other members of the household, whatever dependence exists has generally been ignored. Thus, when calculating sampling errors and other statistics that relate to conventional surveys, it has been assumed that observations on each respondent are independent events. However, when multi-day data are collected, the assumption of independence is clearly violated. The travel that a person makes on one day is likely to be influenced by the travel he or she made on the previous day or days, and will also be influenced by the travel he or she plans to do in the coming days. As a simple example, in a household where grocery shopping is done once a week, if grocery shopping was done on Wednesday, there is almost no likelihood that another grocery shopping trip will occur on Thursday. Likewise, if a person goes to work or school on Monday through Friday, they are unlikely to go to work or school again on Saturday or Sunday. Decisions on the mode of travel are also not independent, nor are decisions on route, and location of the destination. In general, if the GPS data are collected for a single point in time, the issue of lack of independence in the observations is usually ignored. However, it becomes of much greater importance if the data are collected from a panel (Stopher et al., 2013). The reason for the increased importance now is that the benefits of a panel stem from reduction in the errors associated with changes between the panel waves (Kish, 1965). If the multi-day observations on each respondent are treated as being independent, then the variance in the data is underestimated. Because sampling errors are proportional to the square root of variance, underestimating the variance will mean that sampling errors are also underestimated. The issue at hand then is that, in a multi-day survey, the observations for each day of the survey are not independent of one another, as is commonly assumed in calculating sampling errors and related statistics from surveys. Stopher et al. (2008) explored the issue of this lack of independence in observations of one person over multiple days. However, their paper looked solely at the issue of sample size requirements from such a multi-day survey. In this paper, a corrected sampling error for two or more multi-day panel waves is calculated using the notation from the paper by Stopher et al. (2008).  Two statistics, the within-group sum of squares (WSS) and the between-group sum of squares (BSS), which respectively represent the intrapersonal sum of squares and the interpersonal sums of squares are used in the analysis to calculate the correct variances for each wave and the covariance between waves. An application of this calculation is also provided in the paper and compared with the “naive” sampling error that is usually used currently to show the impact of multiple days on a panel survey of multiple waves. A comparison is also made to the equivalent sampling error from a one-day survey of the same sample size, to determine the extent of the gain of undertaking multiple day measurements. References Bohte, W. and K. Maat (2009). 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