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Statistical Bulletin Transport Series Trn/2003/2 Bus and Coach Statistics: 2001-02

6. The Public Service Vehicle Operator annual returns

6.1 General information

The basis for most of the statistics in this Bulletin is the annual returns which a sample of Public Service Vehicle operators across Great Britain make to the Department for Transport (DfT). Further information is contained in the DfT publications Transport Statistics Great Britain, Focus on Public Transport and Bulletin of Public Transport Statistics. Enquiries regarding the statistics should be made to Paul O'Hara of DfT (tel: 0207 944 3076).

The sample is stratified by size of operator, based on the numbers of vehicles that they are licenced to run (their numbers of licence discs). With effect from the 1997-98 survey, it includes all operators with 30+ vehicles, and a random sample of smaller operators (who are selected with probabilities depending upon their numbers of discs). The survey design and sampling fractions are a compromise between the optimal designs for local and other (non-local) services. As the table below shows, large operators are responsible for the major share of local work, so a smaller sample of small and medium sized operators would be acceptable for the purposes of producing figures for local services alone. However, the small and medium-sized operators provide the majority of non-local services, and therefore the sample must include enough of them to produce reasonable estimates for non-local services.

Sampling fractions and 2001/02 distributions by numbers of discs(GB figures )

* See section 6.3. The actual "grossing-up" factors for each size band depend on the level of response. The factors shown here assume 100% response rates, but the factors actually used are higher, because of non-response.

** Small operators, in particular, enter or leave the industry throughout the year.

For Scottish operators, the method of selecting the sample is based purely upon the number of discs: there is no "area within Scotland stratification" to take account of where the operator is based. (From 2000-01, the sampling frame for England was modified to stratify it by disc size and by Government Office Region, to give a more even coverage across all the regions of England). For each survey, in order to improve the estimates for Scotland as a whole, DfT scrutinised the randomly-selected sample for Scotland and, for each size band, compared the number who had been selected for inclusion in the sample with the number of Scottish operators shown in the sampling frame. In cases where the sample appeared to contain too few (or too many) operators in a particular size-band in Scotland as a whole, DfT changed the composition of the sample, adding (or removing) operators in that size-band who were based in Scotland. However, the "luck of the draw" could lead to the sample of operators which was selected for an area within Scotland being unrepresentative of the operators in that area. For example, the sample for an area might have contained significantly more (or significantly fewer) operators in a particular size-band than would have been expected from knowledge of the sampling percentage and of the "population" number of operators in that size-band in that area.

It is not possible for DfT to ensure that the sample for an area within Scotland is representative. For example, suppose that a particular area has only one operator in a particular size-band (eg "20-29 discs", for which the sampling fraction is 60%). Clearly, all DfT can do is to include that operator in the sample in some years, and exclude it from the sample in other years: DfT cannot include 60% of the operator in the sample in every year. A further complication is a "survey holiday" voucher scheme, which is designed to reduce the burden on small businesses by giving periods of exemption from surveys. The first such "survey holiday" applies to operators with nine or fewer staff who were sampled in 1997-98, who were not eligible for selection again until the survey for 2000-01. This scheme limits the number of smaller operators who are available for selection in each year, and hence limits the DfT's ability to choose samples which are as representative as possible for each area within Scotland for every year.

Finally, it should be noted that small operators enter and leave the industry each year, which makes consistency of sampling in the smaller fleet size groups more difficult.

The figures for Scotland for non-local services are derived from the returns made by the operators who are based in Scotland, and so will include services into England which are run by operators based in Scotland, and will exclude services into Scotland which are run by operators based in England. (NB: a large group, such as Stagecoach, is not treated as a single operator: there will be a separate statistical return for each of its subsidiary companies.)

6.2 Estimation of certain breakdowns, in cases where the survey does not collect information for smaller operators

In order to reduce the burden on respondents to the survey, the smaller operators receive a simplified questionnaire, which does not ask for certain pieces of information. For example, smaller operators supply only an overall total figure for their income from local services: unlike the larger operators, they do not provide a breakdown between "passenger receipts", "public transport support", "concessionary fare reimbursement", "contract payments" and "Bus Service Operators Grant" (formerly known as the fuel duty rebate).

In order to produce overall totals for the different types of income from local services, DfT must estimate the breakdown of local service income between these headings for the smaller operators. DfT does this by assuming that, for each small operator which responds to the survey, the percentage breakdown of income between these headings is the same as the overall Scotland percentage breakdown of such income for all the large operators taken together. Thus, if "passenger receipts" accounted for (say) 80% of the total local service income of all large operators in Scotland, DfT would assume (for the purposes of estimating the overall totals) that passenger receipts accounted for 80% of the local service income of each of the smaller operators who responded to the survey.

The survey obtains, from the larger operators, information about their expenditure (operating expenditure on local services and on other services, administration expenditure and depreciation). It does not ask the smaller operators to provide this, but the effect of this on the calculation of costs per vehicle kilometre and per passenger journey is thought to be small.

6.3 Estimation of totals for all smaller operators, by "grossing-up" the returns from the smaller operators

The figures for each smaller operator (including those income breakdown figures which DfT estimated - see above) are "grossed-up" using a grossing-up factor which is the inverse of the achieved sampling fraction, and therefore makes an allowance for any non-responding small operators (as the grossing-up factors are based upon the numbers of responses obtained for each fleet size group). For example, as roughly 5% of the smallest operators respond to the survey, the grossing-up factor for them will be about 20. (While the aim may be to sample 1-in-20 of the smallest operators, the survey is unlikely to obtain returns from exactly 1 in 20 of them: for example, if there were 250 such operators, and 12 of them were chosen for the survey and made returns, the grossing-up factor would be 250 divided by 12, which is about 20.8). DfT calculates the "grossing-up" factors separately for Scotland, Wales and each government office region in England: the Scottish grossing-up factor for a particular size-band is simply the total number of Scottish operators in that size-band divided by the number of them who made returns.

6.4 Estimation of figures for areas within Scotland

The larger operators (those with over 1 million vehicle-miles run on local services) are asked to split their local service passenger numbers, vehicle miles and income of various kinds between the local government areas in which they operate. Up to and including the 1996-97 returns, the breakdown was requested in terms of the former Regions and Island Areas; from the 1997-98 returns it is in terms of the present Councils. (In order to provide a time-series, the present Councils have been grouped together on the basis of the former Regions for the purpose of producing Tables 9.1 and 9.2.)

The methods that operators use to split their totals between areas will depend upon the kind of information that is available from their businesses' records, and may vary from operator to operator: some may have administrative systems that provide breakdowns of passenger numbers etc by area that are more detailed than those of other operators. There is no recommended method: all that the instructions for the completion of the return ask is that "if exact figures are not available, please give the approximate proportion or percentage in each [area]". In some cases, therefore, an operator might only be able to provide a rough estimate of the breakdown (eg 60% in area A, 30% in area B, 10% in area C). It may be that, from time to time, an operator changes the way in which it estimates or calculates the split of its figures between the areas which it serves - if so, this may cause a discontinuity in the time-series for those areas.

The smaller operators are not asked to provide such a breakdown. Instead, DfT assumes that all a small operator's activity is in the area in which the operator's office is situated. As each small operator's figures are grossed-up as part of the process of producing estimates which cover all small operators, it follows that the grossed-up estimates based upon a small operator's return are counted wholly against the one area.

6.5 DfT's rules on the possible disclosure of figures for an area

When the data are collected from Scottish operators, an undertaking is given that (unless they give written permission) access to their figures will be restricted to the DfT and Scottish Executive staff who deal with public service vehicle statistics. Therefore, the need to protect the confidentiality of the information which is provided in the statistical returns may prevent the disclosure of the totals for an area without the permission of the larger operators in that area. For example, if the two largest operators in an area together account for a very large proportion of the total patronage, one of them might be able to deduce the approximate size of the other's business from any totals that were published for that area. In such a case, therefore, one would need the permission of both large operators before one could disclose the totals for that area. DfT uses the following rule to determine whether or not the totals for an area may be disclosed without the permission of the larger operators in the area:

a total for an area is NOT disclosable (without the permission of the larger operators in the area) if

either i. the largest operator accounts for over 60% of the total for the area

or ii. the second largest operator accounts for over 60% of the rest

These rules mean that figures for several parts of Scotland cannot be disclosed without the permission of the larger operators in those areas. Therefore, as the collector of the statistics, DfT kindly wrote to the largest operators in Scotland, asking if they would agree to the figures from their statistical returns being used to produce totals for areas within Scotland which the Scottish Executive would publish. We are very grateful to all the major operators who agreed that the Scottish Executive could use their figures in this way.

6.6 The uncertainties about the estimates for parts of Scotland

It will be seen that there are some large year-to-year changes in the estimates for some areas, and that occasionally one year's figure stands out as unusually high or unusually low. It must always be remembered that the survey is not designed to produce reliable figures for areas within Scotland (such as the former regions or the current councils) - for example, the sample is not stratified on the basis of the areas within Scotland in which the operators are located. Therefore, the estimates for any areas which have only a few operators may be subject to what could occasionally be considerable sampling errors, if those operators are small operators, since the "luck of the draw" could occasionally include most of the operators in that area in the sample in one year (leading to the grossed-up estimates being far too high) and there could occasionally be few or none of them in the sample in another year (leading to the grossed-up estimates being too low). And, even if the selected sample happened to be representative of each area, this would not guarantee that the results for each area would be reliable. For example, the figures for an area would be too low if returns were made by fewer operators than would be expected for that area, which could happen due to non-response to the survey by a higher than average proportion of the operators in that area.

Unreliability may also be an inevitable consequence of an area having only a small number of operators. For example, suppose that a particular area has only one operator with 20-29 discs. The sampling fraction for that size-band is 60%. In the years in which that operator responds to the survey, its figures will be multiplied by the grossing-up factor for the "20-29 discs" size-band (i.e. 1.67 - or more, if there was non-response by some Scottish operators in that band), and therefore the survey's estimate of the total for the area will be too high (all else being equal). In the years in which that operator is not selected for inclusion in the sample (and in any years in which the operator is included in the sample but fails to respond), the operator will make no contribution to the survey's estimate of the total for the area, which will therefore be too low (all else being equal). For this reason, it may be impossible for the survey ever to provide the correct figures for some areas.

It follows that some of the estimates that are provided in Tables 9.1 and 9.2 may be subject to considerable uncertainty. For example, an area could appear to have a particularly large increase in its estimate in one year because:

that year, the survey obtained returns from disproportionately more of the operators who are based in that area;

or the previous year, the survey obtained returns from disproportionately few of the operators who are based in that area;

or one of the larger companies which operates in that area changed the way in which it split its totals between the areas in which it operates, with the result that a much greater percentage of its total was counted against that area;

or a smaller company, which operates in that area but is based in another area, has now become large enough to be required to split its totals between the areas in which it operates, and therefore provides figures for this area for the first time ever;

or a combination of some of the above factors, and other factors, produces that result.

The estimates for different parts of Scotland provided in Tables 9.1 and 9.2 are therefore a general guide to the way in which the levels of patronage and service have changed in each of these areas over the past 10-or-so years. The "hiccups" in the series are a reminder that the estimates may be affected by sampling quirks etc, and so are not necessarily reliable. In order to see better the overall trends in local bus service provision and patronage in some areas, users of the statistics could take (say) three-year moving averages of the estimates for those areas, as moving averages should be less affected by sampling and estimation problems.

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