A Beautiful Chart

In the monthly Customer Opinion Panel (join here!), we added a bus replacement module (an extra set of questions pertaining specifically to replacement buses for out of service rail lines) in the months of June and July and then a follow up in October. The module asked riders about their experiences when a commuter rail or subway trip is temporarily replaced by a shuttle bus. After receiving feedback from riders in June and July, some questions were added and modified in October to better understand the responses.

One specific question aimed at determining optimum frequency of replacement shuttles asked, “What level of convenience would you experience if shuttle buses replacing subway service came at the following time intervals during a scheduled service interruption?” In June-July, the options we gave were frequencies of every 5, 8, 10, and 12 minutes, on the scale of “Convenient, Inconvenient, and Unacceptable”.

Unsurprisingly, respondents found higher frequencies to be preferable. However, we were not sure whether riders were choosing their levels of convenience based on the frequencies themselves, or whether the interval options were encouraging biased responses. For example, we found that only 30% of respondents find 8-minute frequencies convenient, but is that because they also had the much more attractive 5-minute option available, and compared to 5 minutes, 8 does not seem as convenient?

So in October, we asked the same question; however, we changed the frequencies to every 7, 9, and 11 minutes. These frequencies, which fit between the June-July options, allowed us to see if the responders were influenced by the time intervals presented in the survey. We can see whether the new “best case” of 7 minutes more closely resembles the previous choices of 8 minutes, which would mean that riders are responding based on the listed frequency, or closer to the previous choice of 5 minutes, implying that people are responding positively to the first available choice.

Animated GIF cycling through four different chart designs showing percent of respondents who would find the suggested frequencies convenient.
Animated GIF cycling through four different chart designs showing percent of respondents who would find the suggested frequencies unacceptable.

The animation above displays three sets of data:

  1. The “Initial Convenience” charts display data from June-July, with convenience of and inconvenience of bus shuttle frequency of every 5, 8, 10, 12 minutes. As the frequency of the replacement shuttle bus decreases, so does the percent of people that find it convenient. The chart clearly shows that the majority of respondents find having a bus arrive at every 5 minutes the most convenient. 12-minute headways are considered an unacceptable wait time by the majority of respondents.
  2. The second set of charts, with blue and green bars, show the additional data from October with the initial data from June/July. The additional data strongly suggests that respondents were not unduly influenced by the survey design. The level of convenience at 7 minutes fits precisely in the pattern between 5 and 8 minutes; placing 7 minutes as the first option did not encourage riders to find that frequency convenient.
  3. The third set of data shows the responses broken out by mode of the riders’; most recent trips. The darkest columns represent respondents whose last trip was bus only, and the lighter ones show rapid transit only, then bus and rapid transit, and the lightest are the responses from commuter rail riders. This breakdown shows the differences between modes: it seems that at almost every frequency level, Bus Only riders are the most likely to find it convenient, while Commuter Rail riders are the least sensitive to decreases in frequency. This breakdown also shows that the pattern persisted across survey instruments: the October mode patterns are very similar to the June/July mode patterns.

Below are the final “beautiful” charts.

Clustered bar chart titled 'Subway Replacement: Convenient.' The X axis shows different frequency options for subway; every 5 minutes, every 7 minutes, every 8 minutes, every 9 minutes, every 10 minutes, every 11 minutes, every 12 minutes. The Y axis is the percent of customers who find each frequency convenient, ranging from 0% to 80%. At each frequency is a cluster of bars varying in color intensity to represent each mode. The darkest is bus, next is Rapid Transit, next is Bus and Rapid Transit, and the lightest is Commuter Rail. Most customers found every 5 minutes acceptable, although there is some variation between modes with Rapid Transit and Commuter Rail finding it less convenient than bus. There is a sharp drop between 5 and 7 minutes, 7 and 8 minutes, and 8 and 9 minutes. Few customers considered every 10, 11, or 12 minutes convenient.
Clustered bar chart titled 'Subway Replacement: Unacceptable.' This is a very similar chart to Convenient but it shows a reverse trend with few customers considering every 5 minutes or every 7 minutes unacceptable, the percent of customers rising and most customers considering every 11 or every 12 minutes unacceptable.


One of the most important take aways from these charts is that Bus Only riders are most likely to take shuttle bus replacements at any frequency, and Commuter Rail riders are least sensitive to decreases in frequency. Bus Only riders are the largest group in each time interval in the convenience chart by mode. For Commuter Rail riders, the initial level of convenience is lower than other modes at the 5-minute frequency, but the level of convenience decrease in each time interval is quite small. Commuter Rail riders are more likely than other riders to find the entire experience of shuttle bus replacement inconvenient, but those that find it convenient are not as influenced by increasing frequencies as riders of other modes.

Another important takeaway is the non-linear nature of convenience at increasing frequencies. Matching a binomial trendline to the convenience values allows us to estimate the frequency of bus shuttle replacement service that practically all riders would find convenient (when y=100% in the “convenient” chart), as well as the frequency which practically no riders would find unacceptable (when y=0% in the “unacceptable” chart). The trendline produced the following results (the R2 values are impressively high only because of the few datapoints in the trend):

Scatterplot with trendline showing how the percentage of respondents who said 'Convenient' dropped as the wait time increased.
Scatterplot with trendline showing how the percentage of respondents who said 'Unacceptable' rose as the wait time increased.

Assuming the trendline continues matching predictions, at about 3.66 minutes everyone (when y=100%) would find the wait time convenient. For the second chart, about 3.82 minutes would be when the lowest percentage of the respondents would the wait time unacceptable. For practical purposes, rounding to four minutes predicts that 93% of the riders would find service convenient and only 4% of the riders would find the wait time unacceptable [1].

In practice how often shuttle buses arrive during scheduled rail replacement service is subject to multiple factors. The MBTA has to balance these trade-offs, but this analysis gives us a range for scheduled bus shuttle replacement service frequency from 4 minutes, where almost 100% of riders would find it convenient, to 6.5 minutes, where the majority of riders would still find it convenient.

This analysis allows us to better plan replacement bus shuttles for when we have to shut down rail service for maintenance and construction projects. It also helps inform our survey methodology by identifying question designs that have the least influence on responses, ensuring that the results are more likely to be reflecting real opinions than biases due to survey design.

1 Caveats: With only seven data points collected, the trendline extrapolated cannot be considered particularly reliable. We know, for example, from earlier modal breakdown, that there will likely be some groups of people that will not find any frequency convenient. In addition, the shortest frequency convenience data point collected was at 5 minutes, so estimates much lower than this level are likely to be unreliable, while the estimates of in-between time points like 6 minutes are less suspect. [Back]