Measuring Day-to-Day Variability in
Travel Behavior Using GPS Data

EXPLORATORY COMPARISON OF MEAN TRAVEL
CHARACTERISTICS BY DAY

Comparison by Day

The first analysis performed in this study is an exploratory comparison of sample-wide mean travel characteristics across the days for which travel data was collected. The survey entailed drivers using the GPS equipment and recording travel information for about a six-day period, with several households providing additional days of information and several providing a little less than six days of usable information. For comparison purposes, seven days of travel information was considered in the context of this study.

Table 2 shows a comparison of mean travel characteristics across seven days. The first day on which a coherent trip record is found is considered "day 1" and then all of the subsequent days for which coherent travel information is available are numbered consecutively. As the sample size varies from one day to the next, it should be noted that the comparison is not being done for exactly the same sample of individuals. There are individuals in one day's sample who are not in another day's sample. The table provides sample sizes corresponding to each day and to each measure of travel considered in the comparison. This sample size corresponds to the number of drivers for whom complete information was available for that day and that travel measure.

The comparison includes the result of a one-way analysis of variance performed on the sample to statistically compare means across multiple days. The last column includes the F-statistic that tests the null hypothesis that the multiple means across all days are equal. If the F-statistic is greater than a critical value (at the appropriate degrees of freedom and desired confidence level), then the null hypothesis can be rejected and the means may be considered significantly different from one another at the chosen confidence level. However, the F-test provided here must be interpreted as only an approximation. In reality, analysis of variance to compare multiple means should be applied in comparing independent samples (i.e., samples drawn from independent populations). Clearly, that condition is violated here as the samples are not independent of one another from one day to the next. Therefore, the F-statistic should be interpreted with considerable caution.

The first three variables represent trip frequencies. Mid-day non-work trips refers to trips made for non-work purposes during the period of 10 AM to 3 PM (trip must begin and end in this period). In general, sample wide averages of trip frequencies are found to be quite similar across the seven days included here. None of the F-statistics are statistically significant indicating that the hypothesis of equality of means can not be rejected at the 95 percent confidence level. The next two variables examine daily travel times reported by individuals in the PDA device and as recorded by the GPS device. In general, the PDA device travel time is found to consistently exceed the GPS recorded travel time. This is because the PDA device would start recording time information prior to the GPS receiver. Whereas the PDA device would start recording time as soon as the respondent hit "start trip", the GPS receiver would start recording time a little bit later after it identified a starting position. Thus, this difference is purely a hardware issue. While the PDA device time shows total travel time a little more than one hour per day, the GPS device time shows total travel time to be a little less than one hour. Regardless of the measure, their averages are quite similar across the days.

The two variables measuring travel distance are obtained through the information recorded in the GPS device. One measure is directly obtained from the GPS positional information while the other is obtained by plotting the information within a GIS. As expected, both of these values are quite comparable at about 25 miles per day. Once again, sample wide averages show considerable similarity across days of reporting. The final three variables examine variability in temporal events. The first time of departure from home is found to be the only variable that has a significant F-statistic. On average, the first time of departure from home for this sample is at about 10:45 AM with day 7 showing the greatest deviation. On average, final arrival at home (that is, the time at which an individual returns home for the day) is a little before 6:30 PM. Final departure times from work (for the workers in the sample) are found to be about 4:15 PM.

Table 2. Comparison of Mean Travel Characteristics Across Reported Days

Characteristic	Day 1		Day 2		Day 3		Day 4		Day 5		Day 6		Day 7		Wtd Avg	F-test
	Mean	N	Mean	N	Mean	N	Mean	N	Mean	N	Mean	N	Mean	N
Total trips	5.3	98	5.2	97	5.1	91	5.4	79	4.7	64	5.3	36	5.3	19	5.2	0.29
Non-work trips	4.5	98	4.6	97	4.0	91	4.7	79	4.0	64	4.6	36	4.7	19	4.4	0.58
Mid-day non-work trips	1.5	98	1.5	97	1.1	91	1.7	79	1.2	64	1.8	36	1.1	19	1.4	1.37
PDA travel time (min)	64.7	98	74.0	97	83.5	91	70.3	79	64.9	64	73.0	36	66.5	19	71.7	0.85
GPS travel time (min)	52.5	65	56.6	75	61.2	71	60.6	63	55.8	49	61.5	27	61.4	12	57.9	0.36
GPS travel distance (miles)	23.2	65	27.2	75	30.8	71	27.1	63	23.4	49	25.8	27	21.5	12	26.4	0.37
GIS travel distance (miles)	21.0	65	23.3	75	28.0	71	24.2	63	23.5	49	24.1	27	21.5	12	24.0	0.45
First departure from home	12:40	98	10:41	97	10:15	90	10:08	79	10:35	64	10:02	36	8:13	20	10:47	4.40a
Final arrival at home	18:38	98	18:18	97	18:25	91	17:54	79	18:23	64	18:16	36	17:39	19	18:18	0.45
Final departure time from work	15:39	43	16:13	38	16:59	42	16:14	34	15:57	25	16:32	17	16:31	7	16:15	0.49

a - significant at the 95% confidence level

Comparison by Day-of-Week

Murakami and Wagner [1999] point out that it would be preferable to control for day-of-week effects when assessing variability in travel characteristics over multiple days. To this end, a comparison across weekdays is provided in Table 3 and a comparison across weekend days is provided in Table 4. In Table 3, it is found that Thursday is different from other days. The number of trips, travel times, and travel distances are all considerably larger on Thursday than other days. Whether this is a simple data issue or a true behavioral phenomenon should be investigated further. Also, it is interesting to note that Friday depicts the lowest trip rates but reasonably comparable travel times and distances. This finding is consistent with that reported by Zhou and Golledge [2000] who found that Fridays are different from other days of the week with respect to trip making behavior.

In Table 4, it is found that the two weekend days are quite similar to one another. The F-statistic comparing the two weekend days is not statistically significant at the 95 percent confidence level for any travel characteristic considered. This finding is in contrast to that reported by Zhou and Golledge [2000] who found significant differences in trip making between Saturday and Sunday.

Table 3. Comparison of Mean Travel Characteristics Across Weekdays

Characteristic	Monday		Tuesday		Wednesday		Thursday		Friday		Wtd Avg	Weekday F-test
	Mean	N	Mean	N	Mean	N	Mean	N	Mean	N
Total trips	5.2	70	5.4	73	5.5	75	6.3	72	4.6	66	5.4	2.22b
Non-work trips	4.6	70	4.4	73	4.4	75	5.2	72	3.8	66	4.5	1.52
Mid-day non-work trips	1.4	70	1.7	73	1.3	75	1.8	72	1.1	66	1.5	0.05
PDA travel time(min)	67.0	70	71.0	71	70.5	76	89.1	72	72.3	69	74.0	1.27
GPS travel time(min)	52.8	49	69.0	54	55.3	59	68.2	58	58.0	56	60.8	0.95
GPS travel distance (miles)	20.0	49	28.0	54	19.9	59	40.4	58	23.4	56	26.5	3.95a
GIS travel distance (miles)	20.0	49	26.1	54	20.1	59	29.1	58	23.4	55	23.8	1.66
First departure from home	10:31	70	9:36	73	10:52	76	10:20	72	10:47	69	10:25	0.90
Final arrival at home	18:50	70	18:22	73	18:46	76	18:20	72	18:25	69	18:32	0.41
Final departure time from work	15:49	28	15:22	39	16:47	40	17:20	37	15:23	32	16:11	2.10b

a - significant at the 95% confidence level

b - significant at the 90% confidence level

Table 4. Comparison of Mean Travel Characteristics Across Weekend Days

a - significant at the 95% confidence level

This is possibly because Zhou and Golledge [2000] examined differences in trip making with respect to specific trip purposes. Thus, while trip making with respect to specific activity categories may differ between Saturday and Sunday, the overall travel characteristics (aggregated over all trip purposes) are quite similar. In addition, the different criteria used to identify the primary driver sample in this study may also be contributing to the differing results between this study and that of Zhou and Golledge [2000].

A comparison of weekday averages (from Table 3) and weekend averages is also provided in the last column of this table. Note that when comparisons of two means is done, the F-statistic is simply the square of the t-statistic that would have been obtained in a comparison of two means.

Significant differences between weekdays and weekends are found in total trips, first departure time from home, and final arrival at home. All other measures including non-work trips, mid-day non-work trips, and travel times and distances are not significantly different between weekdays and weekends. Considering that this is not a purely commuter sample, this result is generally consistent with expectations. Overall, it is found that total trip frequency on weekends is less than that on weekdays, presumably because of the absence of work trips. The first time of departure from home on weekends is a little after 12 noon as opposed to the average 10:25 AM departure time found on weekdays. With respect to final arrival at home, the weekend average is about 5:45 PM as opposed to the weekday average of about 6:30 PM.

In summary, the aggregate sample-wide comparison of averages presented in this section shows considerable similarities in travel characteristics across multiple days. However, when one controls for the day-of-week, some differences are found, particularly towards the end of the week on Thursday and Friday. Considerable similarities were also found between the two weekend-days, though this result may be due to the fact that comparisons are not made here for specific trip purposes and activity categories. Also, differences between weekday and weekend averages were found to exist for selected travel characteristics. It is possible that differences between weekday and weekend travel characteristics would be greater for commuters than for non-commuters. Performing a comparison while controlling for commuting status is a task for future research as the small sample data set used in this study would not fully support such a comparison.

The aggregate and average nature of the analysis presented in this chapter may have masked some of the more disaggregate variability present in the data set. The next two chapters focus on a more disaggregate analysis of day-to-day variability in travel.

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