comparison in the text have passed a hypothesis test at the 0.10 level of significance or better, and most have passed a hypothesis test at the 0.05 level of significance or better. This means that, for most differences cited in the text, the estimated difference between characteristics is greater than twice the standard error of the difference. For the other differences mentioned, the estimated difference between characteristics is between 1.6 and 2.0 times the standard error of the difference. When this is the case, the statement of comparison is qualified, e.g., by the use of the phrase "some evidence."

Comparability of data. Caution should be used when comparing estimates for 1979 and later, which reflect 1980 census-based population controls, to those for 1969 through 1978, which reflect 1970 census-based population controls. This change in population controls had relatively little impact on summary measures such as means, medians, and percent distributions, but did have a significant impact on levels. For example, use of 1980-based population controls resulted in about a 2-percent increase in the civilian noninstitutional population and in the number of families and households. Thus, estimates of levels for 1979 and later will differ from those for earlier years more than what could be attributed to actual changes in the population and these differences could be disproportionately greater for certain subpopulation groups than for the total population.

A number of changes were made in data collection and estimation procedures beginning with the March 1980 CPS. The major changes were the use of a more detailed income questionnaire, the use of the "householder" concept instead of the traditional "head" concept, the introduction of the new farm definition, and use of more detailed income intervals in the upper range of the income distribution. Due to these and other changes caution should be used in comparing estimates for 1979 through 1985 with estimates for earlier years. A description of these changes and the effect they had on the data is given in the section "Modifications to the March 1980 CPS" of an earlier report (Series P-60, No. 130).

Another major change is that income and poverty estimates for 1985 are the first based entirely on households selected from the 1980 census-based sample design. Estimates by type of residence categories such as metropolitan, nonmetropolitan, farm and nonfarm, which were omitted from the 1984 report because of the mixed 1970 and 1980 census sampling frame used for the March 1985 CPS, have been resumed. The residence categories reflect metropolitan areas defined as of June 1984. In addition, the March 1986 CPS income supplement was revised to allow the coding of larger earnings amounts on the questionnaire.

Note when using small estimates. Summary measures

only when the base is 75,000 or greater. Because of the large standard errors involved, there is little chance that summary measures would reveal useful information when computed on a smaller base. Estimated numbers are shown, however, even though the relative standard errors of these numbers are larger than those for corresponding percentages. These smaller estimates are provided primarily to permit such combinations of the categories as serve each data user's needs. Also, care must be taken in the interpretation of small differences. For instance, even a small amount of nonsampling error can cause a borderline difference to appear significant or not, thus, distorting a seemingly valid hypothesis test.

Standard error tables and their use. In order to derive standard errors that would be applicable to a large number of estimates and could be prepared at a moderate cost, a number of approximations were required. Therefore, instead of providing an individual standard error for each estimate, generalized sets of standard errors are provided for various types of characteristics. As a result, the sets of standard errors provided give an indication of the order of magnitude of the standard error of an estimate rather than the precise standard

error.

The figures presented in table B-1 provide approximations to the standard errors of estimates of the number of persons and families by poverty status and race for the years 1980 through 1985 for Total, White and Black. Table B-2 provides approximations to the standard errors of estimates of the number of persons and families by poverty for Hispanics for the years 1973 through 1985. Table B-3 contains approximations to standard errors of estimated percentages of persons below the poverty level. Table B-4 presents the factors (f1) to be used to calculate standard errors for selected characteristics. Table B-5 presents the factors (f2) to be used to estimate standard errors for the years 1959 to 1979.

To calculate standard errors for estimated numbers and percentages of persons and families in poverty it was necessary to use two parameters (denoted as "a" and "b") which are presented in tables B-6 through B-10. These parameters were used to calculate the standard errors in tables B-1, B-2 and B-3 and to calculate the "f," factors in table B-4. Direct computation of the standard errors will give more accurate results than the use of the standard error tables. Methods for direct computations are given in the following sections.

Data based on 1960 census 1-in-1,000 sample. Standard errors for data based on the 1960 census 1-in-1,000 sample are estimated by applying the appropriate factor given in table B-5 to the standard errors shown in tables

This means that a 68-percent confidence interval for the percentage of Black persons below the poverty level in 1985 is from 26.2 to 27.8 percent. A 95-percent confidence interval is from 25.4 to 28.6 percent.

Standard error of a difference. For a difference between two sample estimates, the standard error is approximately equal to

S(x,y)

=

(5)

where S, and S, are the standard errors of the estimates x and y. The estimates can be numbers, percents, ratios, etc. The correlation coefficient r can be determined from table B-11 for year-to-year comparisons for poverty estimates of numbers and proportions; for other comparisons assume that r equals zero. Making this assumption will result in accurate estimates of the same characteristic in two different areas, or for the difference between separate and uncorrelated characteristics in the same area. If, however, there is a high positive (negative) correlation between the two characteristics, the formula will overestimate (underestimate) the true standard error.

Illustration of the computation of the standard error of a difference. Text table A shows that the number of families below the poverty level in 1985 was 7,223,000 and in 1984 was 7,277,000. The apparent difference is 54,000. Using formula (2), the appropriate parameters from table B-8 (a = +0.000084 and b = 2067), the standard errors on 7,223,000 and 7,277,000 are 139,000 and 140,000, respectively.

2Using formula (3), table B-3, and the appropriate f, and f2 from tables B-4 and B-5, the approximate standard error is 0.7.