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16 Whether using proportionate or disproportionate sam- degree of precision and reflects the spread of observed val- pling, weights are developed for each group (strata) in the ues that would be seen if the survey were repeated numerous sample once the surveying is completed. Weights are most times. The confidence level (95%) is how often the observed often based on ridership. The weight for each stratum is cal- transfer rate would be within 3 percentage points of the true culated based on the ratio of total ridership for the strata and transfer rate if the survey were repeated numerous times. the number of surveys collected from that group. Total ridership may be for a given route, route and time-of-day The sample size that is needed for a given survey depends combination, or station. As an example in a rail survey, on the population size and level of precision desired. If the WMATA weighted surveys to daily ridership by mezzanine. researcher wants to be within 3 percentage points, for exam- ple, a sample size of 1,066 is required for a large population, For weighting by boardings, transit agencies measure but approximately one-half that number for a population of total boardings in a variety of ways. SANDAG, for example, about 1,000. Table 8 provides sample sizes needed for three used automatic passenger counters to determine the number levels of precision (10%, 5%, and 3%) at a 95% confidence of passengers boarding for each route and time-of-day com- level for various population sizes. bination. Ridership can also be based on entries as recorded by bus fare boxes or turnstiles. Another method is for survey In transit surveys, it is often desired to achieve a given level workers to count the total number of passengers entering, of precision for each of a number of major routes or for each whether or not they accepted a survey form. (See chapter five of several time periods. In this situation, the sample size needs for further discussion of the fieldwork protocols for these to be computed for each subgroup; for example, each route or counts.) day part. A Transit Authority of River City (TARC) survey, for example, developed the sample plan based on achieving a Although most responding transit agencies weighted sampling error of 8 percentage points for routes with 1,000 or surveys by ridership, more complex methods are sometimes more average weekday boardings and 12 percentage points for used, particularly for O&D surveys. A good example is routes with fewer weekday boardings. In addition, the bottom PATH, which used an advanced statistical technique called 10 routes in terms of ridership were sampled as one unit with iterative biproportional fitting to weight response by station a sampling error of 5 percentage points. entry and exit and time of day. For surveys with stratified sampling, as in the TARC survey, calculating the sampling error for the entire survey must take MINIMIZING SAMPLING AND NONRESPONSE account of the stratified sample design. One cannot simply use ERROR IN SURVEY the overall number of responses to calculate the sampling error. Stratification may change the efficiency of the sample-- The precision of a survey is determined by the amount of in some cases improving efficiency (as when the strata are error created in the process of taking a sample and conduct- relatively homogeneous) or reducing efficiency (when the vari- ing data collection. Sampling error, which arises from ance of each strata are about the same). The specific situation surveying a sample of the study population rather than the will affect the sampling error of the total sample. entire population, is often the focus of discussion of survey error issues. There are other sources of error, however, including nonresponse error, coverage error (discussed Nonresponse Error earlier), and measurement error (discussed in chapter four). Another major source of error is nonresponse error, which results from failure to obtain completed surveys from some Sampling Error Virtually all on-board and intercept transit surveys involve TABLE 8 taking a sample of the study population and are thus subject SAMPLE SIZES NEEDED FOR VARIOUS POPULATION SIZES to sampling error. Because surveys rely on a sample of the AT VARIOUS LEVELS OF PRECISION population, survey results are likely to be somewhat differ- Sampling Error for 95% Confidence Level ent than if the entire population was interviewed. Population 10% 5% 3% 200 65 132 169 The sampling error is an expression of the difference 400 78 196 291 between the true (but unknown) value and observed values 1,000 88 278 517 if, hypothetically, the survey were repeated numerous times. To use an example, suppose that an on-board bus survey 6,000 95 361 906 found that 20% of riders transferred to another bus on the 20,000 96 377 1,013 trip. The sampling error might be stated as plus or minus 1,000,000 96 384 1,066 3 percentage points with a 95% confidence level. The con- Note: Sample size needed for each sampling error; responses with frequency fidence interval (plus or minus 3 percentage points) is the of 50%.

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17 portion of the population selected in the sample. It is inevitable However, one can attempt to evaluate and possibly compen- that some riders refuse to take a survey, never return a survey sate for nonresponse. The likely impact from nonresponse can that they took, or refuse to be interviewed. These respondents be evaluated by comparing characteristics of respondents with might have responded in the same way as respondents who did those of the entire population or those within the sampling complete the survey, or they might not have. In contrast frame. The comparison is sometimes made for rider charac- to sampling error that can be computed, there is no standard- teristics such as gender, race, and place of residence, or for trip ized way to compute the error that arises from nonresponse. characteristics such as on and off locations.