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Scottish Household Survey Travel Diary results

A Notes and Definitions

A1 General notes

A1.1 Totals may appear to differ slightly from the apparent sums of their component parts, in cases where they have been calculated by adding up the "unrounded" values of the components and then rounding each figure independently. Similarly, percentages may appear not to sum to 100%.

A1.2 The underlying sample numbers shown in different tables, or in different parts of the same tables may not be the same. This may be because:

• some people were unable to, or did not want to, answer certain questions; or
• the tables relate to different "populations" (e.g. all adults, all journeys); or
• the SHS only collects some kinds of information in certain circumstances (e.g. the question about the number of occupants is only asked of those who travelled by car, and the information about a person’s occupation, which is used to derive the social class, is sought only from people who are in employment or who had been in paid work in the five years prior to the interview); or
• for some cases, information is not available for some of the variables which were used to produce some of the tables, and therefore those cases cannot be included in tables, or in some parts of them.

A2 The coverage of the SHS Travel Diary

• personal travel for domestic, social or recreational purposes - e.g. driving to and from work, travelling into town to go shopping, and going to see friends;
• journeys in the course of work, provided the purpose of the journey is for the traveller to reach a destination - e.g. taking a bus into town to attend a meeting, flying down to London on business;
• journeys made to take or accompany someone else - e.g. taking the children to school, walking someone home.

A2.2 Journeys made by land, air or water within the United Kingdom are included. Journeys which start or end outwith the UK (e.g. a holiday flight from Spain) are excluded. However, if a respondent were to say that he or she had flown back from a holiday abroad on the previous day, the interviewer should record details of the journey home from the airport (but not record details of the flight to the UK).

A2.3 The SHS Travel Diary does not cover:

• journeys which are made in the course of work by people who are employed (e.g.) as drivers or crew of public transport vehicles; to drive lorries; to deliver letters, parcels, leaflets or goods; as police officers or traffic wardens; etc. However, it does cover their journeys to and from their places of work;
• travel away from public roads or highways, such as taking a dog for a walk across some fields, walking or climbing in the hills, and yachting or flying for pleasure;
• journeys of under a quarter of a mile, or less than five minutes on foot;
• journey stages of under a quarter of a mile, or less than five minutes on foot.

A3 Main definitions

A3.1 Journeys: the basic unit of travel, a journey, is defined as a one-way course of travel having a single main purpose. Outward and return halves of a return journey are treated as two separate journeys. A journey cannot have two separate purposes, and if a single course of travel involves a mid-way change of purpose then it, too, is split into two journeys. However, trivial subsidiary purposes (eg a stop to buy a newspaper) are disregarded.

A3.2 Stages: a journey consists of one or more stages. A new stage is defined when there is a change in the form of transport or when there is a change of vehicle requiring a separate ticket.

A3.3 Journey purpose: the purpose of a journey is normally taken to be the activity at the destination, unless that destination is "home" in which case the purpose is defined by the origin of the journey. A number of purposes are distinguished, such as "place of work", "in the course of work", "educational establishment", "shopping", and so on. Separate categories are used when the traveller has no purpose of his or her own, other than to escort or accompany another person; for example, taking a child to school. Some of the categories which are identified in the survey do not appear separately in the tables, because few journeys were recorded for them.

A3.4 Mode of transport: in the code-lists which are used by the interviewers to record details of the journeys, vans are counted with cars; taxis and minicabs are in a separate category from ordinary cars; and there are separate categories for (i) rail and (ii) underground, and for (a) school bus, (b) works bus and (c) ordinary (service) bus. However, some of these modes of transport do not appear separately in the tables, because few journeys were recorded for them. Therefore, the "other" category includes, for example, motorcycles, ferries, aeroplanes and all other forms of transport which are not shown separately.

A3.5 Main mode of transport: where a journey involves more than one mode of transport (e.g. first a bus and then a train), the main mode of a journey is defined, as in the GB National Travel Survey, as that used for the longest (in distance) stage of the journey. For example, if a journey involved a two mile bus ride followed by a 50 mile train trip, the main mode for the journey would be "rail". It should be noted that this definition does not use the total of the distances travelled by each of the different modes to determine the main mode - for example, a journey involving a 1 mile walk to a bus stop, a 1.5 mile bus ride and a 1 mile walk to the ultimate destination would be classified as "main mode = bus", even though more than half the total distance was covered on foot, because bus was the mode of transport used for the longest stage of the journey. If there is no single longest stage, and the two (or more) longest stages do not involve the same mode of transport, the "main" mode of the journey is defined (as in the NTS) as the mode which was used for the last of the longest stages. In practice, because of the way that the distances are calculated (which produces results which appear to be accurate to about the nearest metre, although they will not be as precise as this - see section A5), it is unlikely that there will be many journeys which have two stages which involve exactly the same distance. In this bulletin, unless indicated otherwise, all analysis by mode of transport is based on the main mode of transport for the journey - so, for example, in the analysis of distance travelled, a journey which involved a two mile bus ride followed by a 50 mile train trip would be counted as 52 miles travelled by "main mode" rail.

A3.6 Highest Income Householder: the household reference person for the first part of the interview. This must be a person in whose name the accommodation is owned or rented, or who is otherwise responsible for the accommodation. In households with joint householders, the person with the highest income is taken as the household reference person (if they have exactly the same income, the older is taken as the household reference person).

A3.7 Social class: the social class categories shown in this bulletin were developed for the analysis of the results of the 1991 Census of Population, and have been used since then. The basis of the groupings is given in the OPCS and Employment Department Standard Occupational Classification, Volume 3 (HMSO, 1991). The method used is designed to group together, as far as possible, people with similar levels of occupational skills. In general, each occupation group is assigned as a whole to one social class, and no account is taken of differences between people within the same occupation group (such as differences in education). However, those who have the employment status of a manager or a foreman may be allocated to a higher class than other people who have the same occupation. The six occupational social classes are as follows, with examples of the occupations in each which are taken from Regional Trends (no. 35 / 2000 edition, pages 242-243):

• professional occupations - includes (e.g.) doctors, solicitors, chemists, professors and clergymen;
• managerial and technical occupations - includes (e.g.) school teachers, computer programmers, personnel managers, nurses, actors and laboratory technicians;
• skilled non-manual occupations - includes (e.g.) typists, clerical workers, photographers, sales representatives and shop assistants;
• skilled manual occupations - includes (e.g.) cooks, bus drivers, railway guards, plasterers, bricklayers, hairdressers and carpenters;
• partly-skilled occupations - includes (e.g.) bar staff, waitresses, gardeners and caretakers;
• unskilled occupations - includes (e.g.) refuse collectors, messengers, lift attendants, cleaners and labourers.

Because the SHS only collects occupational information for people in employment, and for people who are not in work but who have been in paid work in the five years prior to the survey, the social class is not known in many cases (e.g. people who have been retired for many years). For the purposes of classifying households, the social class of the Highest Income Householder is used.

A3.8 Annual net household income: this is the total annual net income (i.e. after taxation and other deductions) from employment, benefits and other sources, which is brought into the household by the highest income householder and/or his/her spouse or partner. This includes any contribution to household finances made by other household members (e.g. for "digs"). Because of refusals or ‘don’t knows’, full information for the main components of household income was not collected from about a third of households. Subsequently, the SHS contractors have imputed the missing components of income for almost all these households, using information that was obtained from other households that appeared similar. Depending upon the component of income, the contractors used either "hot deck" imputation (where the sample is divided into sub-groups based on relevant household characteristics, and the imputed values are obtained from randomly-chosen "donor" cases) or "predictive mean" imputation (where the data are used to construct a statistical model of the relationship between income and other household characteristics, which is then used to "predict" the income in cases where a value is to be imputed). The analyses by income given in this bulletin therefore cover all but a couple of percent of households.

A3.9 Motor vehicles: when the interviewer asks about the motor vehicles that are normally available for the private use of one or more members of the household, the following types of vehicle are covered: car, van, motor cycle, moped, and any other motor vehicle.

A4 The collection and imputation of SHS Travel Diary information about journeys

A4.1 The Travel Diary collects information about journeys that were made on the day before the interview: so, someone interviewed on Sunday will be asked about the journeys he or she made on Saturday. Journeys which start on one day and finish on another should be counted on the basis of the day on which they started: so, if a person interviewed on Sunday went out on Friday evening and returned home in the early hours of Saturday, the journey home on Saturday should be recorded only if it started after midnight (because that would mean that it started on the day before the interview); and if the person went out on Saturday evening, the journey home should be reported provided that it started before midnight.

A4.2 Interviews are not spread evenly across the week, because some types of people are more likely to be found at home, available for interview, on certain days. Therefore, the results are re-weighted using factors, which depend upon the day of the week and the adult's current situation (or economic status), so that, within each category of "current situation", the reweighted number of interviews is spread evenly across the days of the week. The reweighting process covers all interviews, including those with people who had not made any journeys on the day before the interview. Therefore, the reweighted numbers of people who said that they had made journeys, and the reweighted numbers of journeys themselves, are not necessarily evenly spread over the days of the week.

A4.3 The Travel Diary collects information about three different types of journey:

• single stage journeys ( 93.6% ) - such as driving to an out-of-town shopping centre, or going from home to work by bus (assuming that the bus stop is less than a quarter of a mile, or five minutes walk, from home, and therefore that there is no need to record the part of the journey between home and the bus stop as a separate stage; and likewise assuming that the bus stop at the destination is not far from the place of work);
• multi-stage journeys ( 3.7% ) - such as going by bus to the station (the first stage, assuming that the walk to the bus stop is below the threshold) and then catching a train to - say - Manchester (the second stage);
• "series of calls" journeys ( 2.6% ) - in order to reduce the burden on respondents, travel involving a number of stops for the same main purpose and using the same form of transport is treated as one continuous "series of calls" journey from the first such call to the last one. Only shopping and travel in course of work can be treated in this way. Information is collected about the part of the journey to the first call, the total number of calls, and the part of the journey after the last call. In the case of a doctor’s round, for example, the interviewer might ask about the travel from (say) the surgery to the first patient, the total number of calls, and the travel from the final patient back to the surgery (or wherever the doctor went after the last call).

The three types are treated differently to facilitate the interviewing process. There are slight differences in the detailed kinds of information collected about each type of journey, which have implications for the processing and analysis of the data but do not affect the main conclusions that can be drawn.

A4.4 It may be felt that the SHS's results will be biased, tending to over-estimate the number of journeys, because the interviewer asks only about travel on the previous day: for example, people may be more likely to be interviewed on the days on which they made no journeys than on the days on which they made many journeys, since they are more likely to be available for interview on days on which they have not made any journeys. Therefore, the probability of being interviewed on a particular day depends, to some extent, upon the amount of travel on that day. It follows that the day for which the information about journeys is collected (the day before the interview) does not represent a "completely random" choice of day, and therefore that the Travel Diary results may not be properly representative. However, comparisons with the results of the GB National Travel Survey suggest that the SHS Travel Diary actually under-estimates the number of journeys made by adults. One reason for this is that the SHS does not collect information about journeys of less than a quarter of a mile, or of less than five minutes by foot. Another is that details of the previous day's travel are provided "off the top of the head", and therefore some journeys may be overlooked. For example, a person may say that he or she went to work, but may not mention the return journey home, or may overlook a journey in the middle of the day. The way in which the information is recorded by the interviewers' computers does not allow the interviewers to check through the details of the reported journeys in order to identify any errors or omissions. However, some changes have been made to the computer systems to reduce the number of journeys that are overlooked.

A4.5 The Scottish Executive has therefore imputed additional journeys, in cases where it is obvious that they are missing — e.g. if the only journey recorded for the day was to work at 8.00 a.m., a return journey was imputed, using the same mode of transport and with the same duration. The imputation process uses information about the time spent at the destination by other people with the same current situation (economic status) who had reported making both an outward journey and a return journey for the same purpose. The average times spent at the destination, and the distributions of such times, are used to impute the times at which the return journeys would start (unless the imputed time would be after midnight, in which case a return journey is not imputed). The Scottish Executive also split what were recorded as "circular"/"round trip" journeys (such as a two-stage journey from A to B and then back to A) into separate outward and return journeys. Imputation in these, and other, cases has increased the total number of journeys in the database by about 9 %. However, it cannot compensate for the full extent of under-reporting of journeys, because there will be many "overlooked" journeys that cannot possibly be imputed from the information that was recorded (e.g. in a case where two journeys were recorded - to work and back - one would not know if the person had forgotten to mention - say - mid-day journeys from work to some shops and back).

A4.6 Because the imputation process does not compensate fully for the under-reporting of journeys in the SHS, the analyses in this bulletin do not include any estimates of the averages of the total numbers of journeys, or of the total distance travelled, per person per year, as such estimates would undoubtedly be too low. Instead, this bulletin provides information about the characteristics of the journeys which were recorded (such as the percentage made using each mode of transport), which should not be affected greatly by under-reporting (unless, for some reason, the journeys which were reported were markedly atypical of all journeys made by adults).

A4.7 Initial examination of the data collected in the SHS's first few months of interviews identified a number of problems, as a result of which several improvements were made to the interviewers' computer systems, in order to collect better quality data. However, the nature of the SHS is such that it cannot collect travel data of the same quality as are obtained by the GB National Travel Survey (NTS). There are a number of reasons for this:

• the SHS is a multi-purpose survey, which has transport as just one of its three priority topic areas. The NTS is a specialised survey, designed to collect information about travel;
• the SHS collects information about one day's travel by one randomly-chosen adult member of the household. The NTS collects information about seven days' travel by every member of the household, including children;
• the SHS interviewee has to recall, off the top of the head, with no prior warning, details of journeys made on the previous day, during an interview on many topics. In the NTS, each member of the household is asked to record, using a special form, information about journeys which are made in a subsequent period of seven days;
• the SHS does not record journeys of less than a quarter of a mile, or less than five minutes on foot. The NTS includes such journeys. (It should be noted that, in order to reduce the burden on NTS respondents, they are asked to record details of walks of under a mile only on the final day of their travel diary, and these are then "grossed up" to the full seven day period when the data are prepared for analysis);
• the SHS interviewer normally has only one contact with the randomly-chosen adult member of the household. The NTS interviewer makes contact on several occasions (to make an appointment, if necessary; before the seven day period for the travel diaries starts, to explain the procedures to the household; sometimes, a mid-"week" visit to remind and help the household; following the travel diary period, to pick up the completed forms; and, rarely, a telephone call or a further visit if there are outstanding queries);
• the SHS interviewers' computers carry out some simple checks on the information as it is collected (e.g. that the time recorded for the end of the journey is after the time at which it was recorded as starting). The NTS also has computer checks. In addition, at the "pick up" visits, the NTS interviewers check the credibility and completeness of the journeys recorded in the travel diaries, sometimes discovering that some journeys had not been recorded, and obtaining details of them. (Inevitably, such scrutiny of the data, and discussions with respondents about what they did and how they recorded it in the travel diary, will identify errors that could not be detected by any computer check on the details that are keyed in.).

Overall, therefore, the NTS data about travel are undoubtedly more comprehensive and of better quality than those of the SHS. However, the NTS's small sample size in Scotland (only about 300 households per year up to 2001; about 900 households per year from 2002) means that it is not suitable for detailed analyses relating to Scotland, such as looking at the differences in travel patterns between different sub-groups of the population.

A5 Origins and destinations, and distances travelled.

A5.1 Origin and destination: the interviewer asks where the person started from, and where he or she went to, and records the origin and destination of each stage of each journey. "Home" and "work" can be recorded easily; for other origins and destinations the interviewer types in as much detail as possible of the address (e.g. the name of a shop, the street and the town). When appropriate, the interviewer can specify that the previous destination is the origin of the current stage / journey. The contractors determine the relevant postcodes at a later stage in the processing of the data from the survey. In cases where only an approximate location is recorded (e.g. "centre of Edinburgh"), an arbitrary postcode (such as that of the main post office) is assigned. In some cases, the contractors may be unable to allocate a postcode, and can only provide a less "precise" indication of the location, such as a postal district (e.g. "EH10"). Inevitably, there are occasions on which the contractors cannot provide any indication of the location of the origin or the destination of a journey. Since the survey started, the interviewers' computer systems have been improved, to collect better "address" data.

A5.2 The interviewer also records the times at which each stage of each journey started and ended. The recording process will only be accurate to - at best - say the nearest five minutes, for example because many people will not remember precisely, or correctly, the times at which some (or all) of their journeys on the previous day started and finished. Therefore, the estimated durations of some journeys will be subject to possibly large percentage errors.

A5.3 Distance travelled: the length of any journey stage is the estimated distance "as the crow flies", based upon the grid co-ordinates of the "centres" of the postcodes (or whatever types of area were recorded) of the origin and destination of that stage of the journey. Therefore, the estimated distance would be zero in the case of a stage for which exactly the same postcode (or other type of area) was recorded (or derived) for both the origin and the destination. For example, if it was known (or deduced) only that the stage involved travel from (say) "EH10" to "EH10", the estimated distance would be zero. However, if it was known (or deduced) that the journey was from "EH10 6UD" to "EH10 6XE", the "crow flies" distance between the "centres" of the two postcodes would be calculated. Clearly, the percentage error in the estimation of distances will tend to be smaller for longer journeys - such as for a journey from "EH10 6UD to "EH6 6QQ", or for one from "EH1" to "G1". (Because the distances are estimated using grid co-ordinates recorded to the nearest metre, they may appear to be accurate to about a metre. However, it must be remembered that the grid co-ordinates relate to the "centres" of the areas concerned, and a journey may start or finish some distance from the "centre" of the recorded area, so the estimated distances are not as precise as might be thought from the number of digits that are produced.)

A5.4 In cases where the interviewer could not obtain sufficient details of the origin and/or destination to enable the contractors to assign a postcode (or other type of area), the Scottish Executive had imputed the distance travelled. The imputation process uses information about the recorded time taken for the trip and an imputed speed for the trip. The imputed speed is based upon information about the speeds of other trips made by the same mode of transport for the same purpose by people who live in the same type of area (in terms of the "urban"/"rural" category), distinguishing between journeys which start in what may be described as "peak" periods (for this purpose, taken as 7.00 a.m. to 9.30 a.m. and 4.30 p.m. to 6.30 p.m.) and at other times of the day. Both the average speed and the distribution of speeds for each mode / purpose / area / time category were used to impute the speed for each journey for which this was required. The imputed speed was then multiplied by the recorded journey time to calculate the imputed distance. Overall, the distance was imputed for about 13.6% of all journey stages. It was not possible to calculate or even impute a distance for about 0.8% of journey stages, because there was insufficient or inadequate information about the location of the origin or destination, or about the start or end time of the journey stage.

A5.5 The distance of a multi-stage journey was calculated by adding up the distances of each of its component stages. For series of calls journeys, as information is only collected about the first and last calls, there are no estimates of distance for all the intermediate stages, and therefore the total distance is underestimated. In addition, as most journeys are not made in a straight line, the "crow flies" distance will underestimate the actual distance travelled.

A6 The SHS urban /rural classification

A6.1 The urban / rural classification shown in the tables was developed for use in analysing the results of the SHS. It is based on settlement sizes, and (for the less-populated areas) the estimated time that would be taken to drive to a settlement with a population of over 10,000. The classification is based on postcodes. First, each postcode in Scotland was classed as either "urban" or "non-urban" on the basis of its "density" (measured in terms of the numbers of [a] residential and [b] non-residential addresses per hectare). Then, clumps of adjacent "urban" postcodes, which together contained more than a certain total number of addresses, were grouped together to form "settlements". (Any apparently "non-urban" postcodes which were entirely surrounded by "urban" postcodes, or by a combination of "urban" postcodes and coastline, were reclassified as "urban", and included in the relevant settlements.)

A6.2 Six categories were then defined:

• Large urban areas - settlements with populations of over 125,000. These are around - but are not the same as - Aberdeen, Dundee, Edinburgh and Glasgow. Because of the way in which settlements are defined, this category may (a) include some areas outwith the boundaries of these four cities, in cases where the settlements extend into neighbouring local authorities, and (b) exclude some "non-urban" areas within the boundaries of these four cities.
• Other urban areas - other settlements of over 10,000 population
• "Accessible" small towns - settlements of between 3,000 and 10,000 people, which are within 30 minutes drive of a settlement of over 10,000 people
• "Remote" small towns - settlements of between 3,000 and 10,000 people, which are not within 30 minutes drive of a settlement of over 10,000 people
• "Accessible" rural areas - settlements of less than 3,000 people, which are within 30 minutes drive of a settlement of over 10,000 people
• "Remote" rural areas - settlements of less than 3,000 people, which are not within 30 minutes drive of a settlement of over 10,000 people

A7 Possible sampling variability, and "95% confidence limits" for SHS estimates

A7.1 Although the SHS's sample is chosen at random, the people who take part in the survey will not necessarily be a representative cross-section. For example, purely by chance, the sample could include disproportionate numbers of certain types of people, in which case the survey's results would be affected. In general, the smaller the sample from which an estimate is produced, the greater the likelihood that the estimate could be misleading. As an example, Table 3 provides information about journeys by purpose reported by adults who have a full driving licence in a household which has access to 1 or more motor vehicles. In some cases, the figure for some of the modes of transport is based on data for only a couple of hundred journeys, each of whom therefore represents about 0.35% of the total. So, which particular households were selected for inclusion in the sample could make a significant difference to the results, and they are therefore subject to considerable potential sampling variability. For example, the estimate of the percentage of journeys by bicycle for shopping would have been two or three percentage points higher had the SHS sample included, purely by chance, just 10 more adults who made shopping trips by bicycle. Results produced from a small sample could therefore be greatly affected by sampling variability. The larger the sample, the less likely it is that the results will be affected greatly by sampling variability.

A7.2 The likely extent of sampling variability can be quantified, by calculating the "standard error" associated with the estimate of a quantity produced from a random sample. Statistical sampling theory states that, on average:

• only about one sample in three would produce an estimate that differed from the (unknown) true value of that quantity by more than one standard error;
• only about one sample in twenty would produce an estimate that differed from the true value by more than two standard errors;
• only about one sample in 400 would produce an estimate that differed from the true value by more than three standard errors.

By convention, the "95% confidence interval" for a quantity is defined as the estimate plus or minus about twice the standard error (from sampling theory, the interval is plus or minus 1.96 times the standard error), because there is only a 5% chance (on average) that a sample would produce an estimate that differs from the true value of that quantity by more than this amount.

A7.3 There is no simple "rule of thumb" for the size of standard errors: the standard error of the estimate of a percentage depends upon several things:

• the value of the percentage itself;
• the size of the sample (or sub-sample) from which it was calculated (i.e. the number of sample cases corresponding to 100%);
• the sampling fraction (i.e. the fraction of the relevant population that is included in the sample); and
• the "design effect" associated with the way in which the sample was selected (for example, a "clustered" random sample would be expected to have larger standard errors - but lower fieldwork costs - than a simple random sample of the same size).

A7.4 Table 16 shows the "95% confidence limits" for estimates of a range of percentages calculated from sub-samples of a range of sizes (NB: the confidence limits for estimates of x% and for (100-x)% are the same). The table was produced in the same way as the tables of "95% confidence limits" in the "Annual Report" volumes of Scotland's People (see section B4), but has a more detailed breakdown of the smaller sample sizes.

A7.5 The interpretation of an entry in Table 16 is best explained by an example:

• the value in the cell at the intersection of the "45% or 55%" column and the "800" row is 3.8;
• this means that the "95% confidence limits" for an estimate of 55% which is produced from a sub-sample of 800 are +/- 3.8%-points;
• so the "95% confidence interval" for the estimate is 55% +/- 3.8%-points (i.e. from about 51.2% to around 58.8%, assuming that the value of the estimate is 55.0%);
• or, on average, only 1 in 20 sub-samples of size 800 would produce an estimate that differs from the (unknown) true value of this quantity (if it is around 55%) by more than 3.8%-points.

A7.6 As an example of the use of this table, it will be seen from figure at the end of the first row in the "by social class" part of Table 2 that there were 2,366 journeys reported by adults in the "professional occupations" social class in the survey in 1999/2000. The first figure in that row of Table 2 shows that an estimated 13% of journeys by "professional" adults were made by foot. Because that estimate was produced from data for only 2,366 journeys, sampling variability could (by chance) produce an error of a couple of percentage points. The entry in the cell at the intersection of the "15%" column and the "2,500" row in Table 16 shows that the "95% confidence limits" for the estimate will be roughly +/- 1.5%-points. This means that there is a 1-in-20 chance that the estimate differs from the true value by more than 1.5%-points. It follows that there is roughly a 1-in-3 chance that the estimate differs from the true value by more than 0.75%-points. Clearly, estimates based on smaller samples have wider confidence limits. (It should be emphasised that these are indicative confidence limits: there are reasons for believing that estimates based on a particular number of journeys may be subject to greater sampling errors than estimates based on the same number of households and Table 16 was calculated on the latter basis.)

A7.7 Because the survey's estimates may be affected by sampling errors, apparent differences of a few percentage points between the figures for two sub-groups of the population may not be "significant": it could be that the true values for the two sub-groups are similar, but the random selection of households for the survey has, by chance, produced a sample which gives a high estimate for one sub-group and a low estimate for the other. A difference between two sub-groups is "significant" at the conventional "5%" level if it is so large that fewer than one random sample in twenty would be expected to produce a difference of that size (or greater) purely by chance, if the two sub-groups' true values were the same. One way of assessing significance at the 5% level involves comparing the difference with the 95% confidence limits for the two estimates. Suppose that these are +/- 3.0%-points and +/- 4.0%-points, respectively. Clearly:

• a difference which is less than the magnitude of the greater of the limits (which, in this case, is 4.0%-points) is not significant; and
• a difference which is greater than the sum of the magnitudes of the limits (in this case 3.0%-points + 4.0%-points = 7.0%-points) is significant.

Statistical sampling theory suggests that a difference whose magnitude is between these values is significant if it is greater than the square root of the sum of the squares of the magnitudes of the limits for the two estimates - in this case, the square root of (3.0² + 4.0²) - i.e. the square root of (9 + 16) - i.e. the square root of 25, which is 5.0. So, in this case, a 5.0%-point difference would be considered significant. Similar calculations will indicate whether or not other pairs of estimates differ significantly.

A7.8 The above information relates only to sampling variability. The survey's results could also be affected by non-contact / non-response bias: the characteristics of the people who should have been in the survey but who could not be contacted, or who refused to take part, could differ markedly from those of the people who were interviewed. If that is the case, the SHS's results will not be representative of the whole population. Without knowing the true values (for the population as a whole) of some quantities, one cannot be sure about the extent of any such biases in the SHS. However, comparison of SHS results with information from other sources suggests that they are broadly representative of the overall Scottish population, and therefore that any non-contact or non-response biases are not large overall. However, such biases could, of course, be more significant for some sub-groups of the population or in certain Council areas, particularly those which have the highest non-response rates. In addition, because it is a survey of private households, the SHS does not cover some sections of the population - for example, it does not collect information about many students in halls of residence (see paragraph B2.3). The "Technical Report" volumes of Scotland's People (see section B4) provide more information on these matters.

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