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Table 4. Principal Means of Transportation, by Distance to Work, for the San Diego SMSA (Workers 14 years old and over. SMSA as of the 1970 census. For explanation of symbols, see text)

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Table 5. Principal Means of Transportation, by Travel Time to Work, for the San Diego SMSA (Workers 14 years old and over. SMSA as of the 1970 census. For explanation of symbols, see text)

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SAMPLE DESIGN

mation procedure modified for the DOT Supplement as described below.

The DOT Travel-to-Work Supplement and The Annual Housing Survey

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The DOT Travel-to-Work Supplement data are based on interviews completed during the period April 1975 through March 1976 in 21 SMSA's as part of the enumeration for the Year || Annual Housing Survey (AHS) sponsored by the Department of Housing and Urban Development. Under the sponsorship of the Department of Transportation (DOT), the 1975 AHS-SMSA questionnaire included a supplementary group of questions pertaining to travel-to-work. In the four largest SMSA's, the survey sample consisted of about 15,000 housing units, and for the remaining 17 SMSA's, the survey was based on a sample of about 5,000 housing units.

In this SMSA, 4,556 housing units were eligible for interview in AHS. Of these sample units, 212 interviews were not obtained because, for occupied sample units, the occupants were not at home after repeated visits or were unavailable for some other reason; or, for vacant units, no informed respondent could be found after repeated visits. In addition to units eligible for interview, 352 units were visited but found not to be eligible for interview because they were condemned, unfit, demolished, converted to group quarters use, etc. Within the interviewed households of this SMSA there were 8,542 persons 14 years and older. Of these, 68 persons did not respond to the DOT Travel-toWork Supplement.

Within each sector (central city and balance) of each SMSA, a noninterview factor was computed separately for 56 noninterview cells.

A ratio estimation procedure was then employed for all sample housing units from the permit-issuing universe. This factor was computed separately for all sample housing units within the 54 noninterview cells pertaining to the permitissuing universe. The ratio estimate factor for each cell was equal to the following:

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1970 census count of housing units from permit-issuing

universe in a cell AHS sample estimate of 1970 housing units from the cell

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Selection of the AHS-SMSA sample. The sample for the SMSA's which are 100 percent permit-issuing was selected from two sample frames-units enumerated in the 1970 Census of Population and Housing in areas under the jurisdiction of permit-issuing offices (the permit-issuing universe) and units constructed in permit-issuing areas since the 1970 census (the new construction universe). In addition, the sample for those SMSA's which are not 100 percent permit-issuing included a sample selected from a third frame-those units located in areas not under the jurisdiction of permit-issuing offices (the nonpermit universe). This SMSA is 100 percent permit-issuing. A more detailed description of the selection of the sample can be found in the AHS Series H-170 reports for 1975.

DOT Supplement Adjustments. For the DOT Supplement, the weight resulting from the AHS-SMSA estimation procedure described above was adjusted to account for persons in households that were interviewed for AHS-SMSA who did not respond to the travel-to-work section of the questionnaire. This noninterview adjustment factor was calculated separately for each sector of each SMSA. Within each sector of each SMSA, a noninterview factor was computed separately for sex, age, and marital status categories.

The final adjustment for persons interviewed for the DOT Supplement was an additional ratio estimation procedure. This procedure was designed to adjust the AHS-SMSA sample estimate of persons 14 years and older in each SMSA to an independently derived current estimate of that same popula. tion group. In SMSA's where there was differential undercoverage of persons within the sectors, the sample estimate of persons 14+ in the SMSA was adjusted to an independently derived estimate of persons 14+ in the SMSA. For SMSA's where there was evidence of differential

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Reinterview program. No reinterview program was undertaken for the DOT Travel-to-Work Supplement. However, for the 1975 AHS-SMSA sample a study was conducted to obtain a measurement of some of the components of the nonsampling error associated with the AHS estimates. Results of this study may be a useful indicator of the accuracy to be expected in the travel-to-work data which was collected as a supplement to the AHS-SMSA data. A detailed descrip. tion can be found in the AHS Series H-170 reports for 1975.

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The numerator of this ratio was based on the Census Bureau's estimates of population 14+ as of October 1, 1975. The denominator of this ratio was obtained from the weighted estimate of persons interviewed for the DOT Supplement, using the existing weight after the DOT Supplement noninterview adjustment had been applied. For this SMSA, a person ratio estimate factor was calculated for each sector.

The weight that resulted from the application of this final adjustment was the tabulation weight utilized to produce final tabulations.

The effect of this person ratio estimation, as well as the overall estimation procedure, was to reduce the sampling error for most statistics below what would have been obtained by simply weighting the results of the sample by the inverse of the probability of selection. Since the population 14 years and older of the sample differed somewhat by chance from the actual population in each city, SMSA balance, or SMSA as a whole, it can be expected that the sample estimates will be improved when the sample population is brought into agreement with known independent estimates of the actual population. RELIABILITY OF THE DATA

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Coverage errors. With respect to errors of coverage and estimation for missing data, it is believed that the AHS new construction sample had deficiencies with regard to the representation of both conventional new construction and new mobile homes (and trailers) in permit-issuing areas. Although it is not known exactly, an estimated 8,900 conventional new construction units and 13,400 new mobile homes in permit-issuing areas in this SMSA were missed by the 1975 AHS-SMSA survey. It is felt that deficiencies also exist in non-permit-issuing areas. The 1975 AHS sample has been estimated to miss as much as 2 percent of all housing units in these areas.

Therefore, all persons 14 years or older who live in the above "missing" housing units or who live in enumerated housing units but were not detected by the enumerators had no chance for enumeration in the DOT Travel-to-Work Supplement. The person ratio estimation corrects for these deficiencies with respect to the count of persons 14+ in each SMSA. However, biases associated with estimates of travelto-work characteristics of these people may still remain.

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There are two types of possible errors associated with data from sample surveys: sampling and nonsampling errors. The following is a description of the sampling and nonsampling errors associated with the DOT Travel-to-Work Supplement.

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Rounding errors. With respect to errors associated with processing, the rounding of estimates introduces another source of error in the data, the severity of which depends on the statistic being measured. The effect of rounding is significant relative to the sampling error only for small percentages and medians derived from relatively large bases (e.g., median number of workers per household or median distance traveled to work).

This means that confidence intervals formed from the standard errors given may be distorted, and this should be taken into account when considering the results of the survey.

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Nonsampling Errors In general, nonsampling errors can be attributed to many sources: inability to obtain information about all cases, definitional difficulties, differences in the interpretation of questions, inability or unwillingness to provide correct information on the part of respondents, mistakes in recording or coding the data, and other errors of collection, response, processing, coverage, and estimation for missing

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The DOT Travel-to-Work Supplement. One possible source of bias in the DOT Travel-to-Work Supplement data is proxy interviewing. That is, responses for a particular worker may have been given by someone else who is not as knowledgeable as the worker himself. For example, the person available for the interview may not know how long it takes the reference person (worker) to travel to work or whether or not the principal means of transportation to work is satisfactory to the worker. Although it is known that biases due to proxy interviewing, as well as other nonsampling errors, could exist in the DOT Travel-to-Work Supplement, their magnitude is unknown.

Sampling errors. The particular sample used for this survey is one of a large number of possible samples of the same size that could have been selected using the same sample design. Even if the same schedules, instructions, and enumerators were used, estimates from each of the different samples would differ from each other. The variability between estimates from all possible samples is defined as the sampling error. One common measure of this sampling error is the standard error which measures the precision with which an estimate from a sample approximates the average result of all possible samples.

In addition, the standard error as calculated for this survey also partially measures the variation in the estimates due to some nonsampling errors, but it does not measure, as such, any systematic biases in the data. Therefore, the accuracy of the estimates depends on both the sampling and

estimates of standard errors are considered to be over. estimates of the true standard errors.

Illustration of the Use of the Standard Error Tables

nonsampling error measured by the standard error, biases, and some additional nonsampling errors not measured by the standard error.

The sample estimate and its estimated standard error enable the user to construct interval estimates in which the interval includes the average result of all possible samples with a known probability. For example, if all possible samples were selected, each of these surveyed under essentially the same general conditions, and an estimate and its estimated standard error were calculated from each sample, then:

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1. Approximately 68 percent of the intervals from one

standard error below the estimate to one standard error above the estimate would include the average result of all possible samples.

2. Approximately 90 percent of the intervals from 1.6

standard errors below the estimate to 1.6 standard errors above the estimate would include the average result of all possible samples.

Table 3 of the report indicates that there were 214,000 female workers in this SMSA in 1975-76. Interpolation in table A-1 of the appendix shows that the standard error of an estimate of this size is approximately 4,890. Consequently, the 68-percent confidence interval, as shown by these data, is from 209,110 to 218,890. Therefore, a conclusion that the average estimate, derived from all possible samples, of female workers lies within a range computed in this way would be correct for roughly 68 percent of all possible samples. Similarly, we could conclude that the average estimate, derived from all possible samples, lies within the interval from 206,180 to 221,820 workers with 90-percent confidence and within the interval from 204,220 to 223,780 with 95-percent confidence.

Table 3 also shows that of the 214,000 female workers, 5.1 percent commuted by means of public transportation. Interpolation in table A-2 of the appendix shows that the standard error of this percent is approximately 0.6 percentage points. Consequently, the 68-percent confidence interval, as shown by these data, is from 4.5 to 5.7 percent; the 90-percent confidence interval is from 4.1 to 6.1 percent; and the 95-percent confidence interval is from 3.9 to 6.3 percent.

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3. Approximately 95 percent of the intervals from two

standard errors below the estimate to two standard errors above the estimate would include the average result of all

possible samples. For very small estimates the lower limit of the confidence interval may be negative. In this case, a better approximation to the true interval estimate can be achieved by restricting the interval estimate to positive values, that is, by changing the lower limit of the interval estimate to zero.

The average result of all possible samples either is or is not contained in any particular computed interval. However, for a particular sample, one can say with specified confidence that the average result of all possible samples is included in the constructed interval.

All the statements of comparison appearing in the text are significant at a 1.6 standard error level or better, and most are significant at a level of more than 2.0 standard errors. This means that for most differences cited in the text, the estimated difference is greater than twice the standard error of the difference. Statements of comparison qualified in some way (e.g., by use of the phrase, ''some evidence'') have a level of significance between 1.6 and 2.0 standard errors.

The figures presented in the tables below are approximations to the standard errors of various estimates for this SMSA. In order to derive standard errors that would be applicable to a wide variety of items and also could be prepared at a moderate cost, a number of approximations were required. As a result, the tables of standard errors provide an indication of the order of magnitude of the standard errors rather than precise standard errors for any specific item.

Tables A-1 and A-2 present the standard errors applicable to estimates of travel-to-work characteristics of persons 14 years and older who were employed at the time of the 1975-76 AHS-SMSA survey. Standard errors for estimates not shown in the tables can be obtained by linear interpolation. Included in these tables are estimates of standard errors for estimates of zero and zero percent. These

Standard errors of differences. The standard errors shown are not directly applicable to differences between two sample estimates. The standard error of a difference between estimates is approximately equal to the square root of the sum of the squares of the standard error of each estimate considered separately. This formula is quite accurate for the difference between estimates of the same characteristic in two different areas or the difference between separate and uncorrelated characteristics in the same area. However, if there is a high positive correlation between the two characteristics, the formula will overestimate the true standard error; whereas if there is a high negative correlation, the formula will underestimate the true standard error.

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Consequently, the 68-percent confidence interval for the 2.5 percent difference is from 1.8 to 3.2 percent. Therefore, a conclusion that the average estimate of this difference, derived from all possible samples, lies within a range computed in this way would be correct for roughly 68 percent of all possible samples. Similarly, the 90-percent confidence interval is from 1.4 to 3.6 percent, and the 95-percent confidence interval is from 1.1 to 3.9 percent. Thus, we can conclude with 95-percent confidence that the percentage of female workers who used public transportation in 1975 is greater than the percentage of male workers who used transit, since the 95-percent confidence interval does not include zero or negative values.

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Thus, the 95-percent confidence interval on the estimated median is from 17.8 to 18.7 minutes.

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Standard error of an arithmetic mean. The standard error of an arithmetic mean can be approximated by the following formula:

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where y is the size of the base, and b is a parameter which equals 140.5 for this SMSA, 146.2 for the central city, and 136.0 for the balance.

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Standard error of a median. The sampling variability of an estimated median depends upon the form of the distribution as well as the size of its base. An approximate method for measuring the reliability of a median is to determine an interval about the estimated median, such that there is a stated degree of confidence that the median based on a complete census lies within the interval. The following procedure can be used to estimate the 68-percent confidence limits on sample data: 1. Determine, using the appropriate standard error table, the

standard error of the estimate of 50 percent from the distribution.

The variance, S?, is given by

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where c is the number of groups; i indicates a specific group, thus taking on values 1 through c; Pi is the estimated proportion with the characteristic in group i; 2-1 and 2; are the lower and upper interval boundaries, respectively, for

2.1 + 2; group i; and x;

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2 representative value for the characteristic for persons in group i. Group c is open-ended, i.e., no upper interval boundary exists. For this group an approximate average value is

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Illustration of the Computation of a Confidence Interval for a Median

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Illustration of the Computation of the Standard Error of an Arithmetic Mean

Table 5 of the report shows that the mean travel time for persons driving alone in 1975-76 was 17.7 minutes. The values of P; and 7; for each group are shown below:

1. Using table A-2 of the appendix, the standard error of 50

percent on a base of 363,000 is found to be about 1.0

percent. 2. A 95-percent confidence interval on a 50 percent item is

obtained by adding to and subtracting from 50 percent twice the standard error found in step 1. This yields

percent limits 48.0 and 52.0. 3. The median interval is 15 to 24 minutes (14.5 to 24.5). It

can be seen that 34.5 percent of the persons fall in the intervals below the median interval, while 41.5 percent fall in the median interval itself. Thus, the lower limit on the estimate is found to be about

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10 to 14 min.
15 to 24 min.
25 to 29 min.
30 to 34 min.
35 to 49 min.
50 to 59 min.
60 min, or more

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4.5 12.0 19.5 27.0 32.0 42.0 54.5 90.0

14.5+ (24.5 – 14.5)

48.0-34.5

41.5

= 17.8

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