Reliability of estimates. Since the estimates are based on a sample, they may differ somewhat from the figures that would have been obtained if a complete census had been taken using the same schedules, instructions, and enumerators. As in any survey work, the results are also subject to errors of response and reporting. These may be relatively large in the case of persons with irregular attachments to the labor market.

The standard error is primarily a measure of sampling variability, that is, the variations that might occur by chance because only a sample of the population is surveyed. As calculated for this report, the standard error also partially measures the effect of response and enumeration errors, but does not reflect any systematic biases in the data. The chances are about 68 out of 100 that an estimate from the sample would differ from a complete census by less than the standard error. The chances are about 95 out of 100 that the difference would be less than twice the standard error and about 99 out of 100 that it would be less than 21⁄2 times as large.

The estimates of standard errors shown in the following tables are approximations for the 330-area sample. Corresponding figures for the 230-area sample may be found in previous reports in this series. (See Current Population Reports, series P-57, No. 166.) Table E shows the average estimates of standard errors for the major employment status categories. The figures presented in table F are to be used for other characteristics and are approximations of the standard errors of all such characteristics. In order to derive standard errors which would be applicable to a wide variety of labor force items and could be prepared at a moderate cost, a number of approximations were required. As a result, table F should be interpreted as providing an indication of the order of magnitude of the standard errors rather than as the precise standard error for any specific item.

TABLE E.-Standard error of major employment status categories

TABLE F.-Standard error of level of monthly estimates

The standard error of the change in an item from one month to the next month is more closely related to the standard error of the monthly level for that item than to the size of the specific month-to-month change itself. Thus, in order to use the approximations to the standard errors of month-to-month changes as presented in table G, it is first necessary to obtain the standard error of the monthly level of the item in table F, and then find the standard error of the month-to-month change in table G corresponding to this standard error of level. It should be noted that table G applies to estimates of change between 2 consecutive months. Changes between the current month and the same month last year, or between two other nonconsecutive months, will generally be subject to somewhat greater sampling variability than is indicated in table G.

Illustration.-Assume that the tables showed the total number of persons working a specific number of hours, as 15 million, an increase of 500,000 over the previous month. Linear interpolation in the first column of table F shows that the standard error of 15 million is about 160,000. Consequently, the chances are about 68 out of 100 that the figure which would have been obtained from a complete count of the number of persons working the given number of hours would have differed by less than 160,000 from the sample estimate. Using the 160,000 as the standard error of the monthly level in table G, it may be seen that the standard error of the 500,000 increase is about 135,000.

TABLE G.-Standard error of estimates of month-to-month change

The statistics by age and sex in table 2 are generally subject to smaller sampling variability than would be indicated by reference to tables F and G. The reductions are particularly large for estimates amounting to a substantial part of the total population in the specific age-sex category (for example, the number of males in the labor force in most age groups). For estimates comprising small proportions of the total population (such as the unemployed or certain categories of the group not in the labor force) the standard errors in tables F and G constitute satisfactory approximations.

The reliability of an eestimated percentage, computed by using sample data for both numerator and denominator, depends upon both the size of the percentage and the size of the total upon which the percentage is based. Estimated percentages are relatively more reliable than the corresponding absolute estimates of the numerator of the percentage, particularly if the percentage is large (50 percent or greater).