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Illustration of the use of tables of standard errors. -Table 1 of this report shows that in 1968 there were 4 million male members 14 years old and over in the farm population. Table D shows the standard error on an estimate of this size to be approximately 72,000. The chances are 68 out of 100 that the estimate would have shown a figure differing from a complete census by less than 72,000. The chances are 95 out of 100 that the estimate would have shown a figure differing from a complete census by less than 144,000 (twice the standard error).

Table 3 shows that of these 4 million, 3,221,000, or 80.5 percent, were in the labor force. Table E shows the standard error of 80.5 percent on a base of 4 million to be approximately 0.6 percent. Consequently, chances are 68 out of 100 that the estimated 80.5 percent would be within 0.6 percent of a complete figure, and chances are 95 out of 100 that the estimate would be within 1.2 percent of a census figure, i.e., this 95 percent confidence interval would be between 79.3 and 81.7 percent.

The above standard errors are appropriate for April-centered 1967 and 1968 figures.

To obtain standard errors for data collected for the single month, April 1960, multiply the above numbers by 2.2.

The standard error of the difference between 1967 and 1968 estimates of U.S. farm population is about 150,000. The standard error of the difference between the 1966 and 1967 estimates of the U.S. farm population is about 200,000. The standard error for differences in two consecutive annual estimates for earlier years (back to 1960) is about 175,000. This figure of 175,000 is a lower standard error for these differences than has been cited in earlier reports.

COMPARABILITY WITH 1960 CENSUS DATA

The total farm population on April 1, 1960, according to the 1960 Census of Population, was 13,474,771.

The corresponding figure from the April 1960 Current Population Survey was 15,669,000 and the Aprilcentered annual average was 15,635,000. These discrepancies between the census and the Current Population Survey figures are a function of several factors.

Although there is no conclusive evidence on the relative validity of the farm-nonfarm classification in the Current Population Survey as compared with the census, investigations in other subject-matter fields have demonstrated that the more experienced and better trained Current Population Survey interviewers generally were more successful in obtaining correct responses in marginal cases. For example, the census enumerators may have been less successful in identifying households living on places from which the value of farm products sold amounted to only a little more than the minimum qualifying value.

The Current Population Survey figures are subject to sampling variability, as pointed out above. The census figures are also subject to a small sampling variability.

As pointed out in the section on "Definitions and explanations," there are a number of differences in procedures and definitions which may account for some of the differences in the numbers. In general, they would tend to raise the Current Population Survey estimates in comparison with the census.

The former procedure of retaining the original farm-nonfarm classification from the first to the last time when the household was in the CPS panel (a period of 16 months), mentioned above in the section on "Farm population, 1960 definition" accounts for part of the excess of the CPS farm population count over the corresponding count in the 1960 census. The maximum period for which the CPS classification could have been out of date in April 1960, however, was only 3 months, since the new definition was first used in January 1960.