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Standard Error of a Median. The sampling variability of an estimated median depends on the form of the distribution and the size of the base. One can approximate the reliability of an estimated median by determining a confidence interval about it. (See the section on sampling variability for a general discussion of confidence intervals.)

Estimate the 68-percent confidence limits of a median based on sample data using the following procedure. 1. Determine, using formula (4), the standard error of the estimate of 50 percent from the distribution.

2. Add to and subtract from 50 percent the standard error determined in step 1.

3. Using the distribution of the characteristic, determine upper and lower limits of the 68-percent confidence interval by calculating values corresponding to the two points established in step 2.

Use Pareto interpolation for any point in an income interval greater than $2,500 in width, and linear interpolation otherwise. The formulas for interpolation are:

р

A1,A2

= for distribution of percentages: the value 1.0. = the values obtained in step 2.

= the lower and upper bounds, respectively, of the interval containing XpN

N1,N2 for distribution of numbers: the estimated number of units (persons, households, etc.) with values of the characteristic greater than or equal to A, and A2, respectively.

= for distribution of percentages: the estimated percentage of units (persons, households, etc.) having values of the characteristic greater than or equal to A, and A2, respectively.

exp is the exponential function.

Ln is the natural logarithm function.

A mathematically equivalent result is obtained by using common logarithms (base 10) and antilogarithms.

4. Divide the difference between the two points determined in step 3 by two to obtain the standard error of the median.

The new, more detailed income intervals used in this report have $2,500 increments up to $40,000 for households and families and up to $20,000 for persons, and Pareto interpolation is needed only when a median income falls in an interval of width larger than $2,500 (beginning with March 1980 CPS). Therefore, this type of interpolation will seldom be needed (i.e., only in cases where the estimated median income exceeds $40,000 for households and families and $20,000 for persons). For this reason, illustration of the use of Pareto interpolation in computing a confidence interval for a median has been omitted. An illustration of this procedure can be found in the source and reliability section of Current Population Reports, Series P-60, No. 123.

Use of the above procedure could result in standard errors which differ from those given in the detailed tables. The reasons for this discrepancy are the use of a more detailed distribution than that given in the tables in determining the published standard errors, and the rounding of the numbers to thousands in the published tables. Linear interpolation was almost always used to compute the published medians and standard errors. Occasionally, a median may lie in an open-ended interval. To calculate its standard error the user must call Housing and Household Economic Statistics Division of the Census Bureau to obtain the methodology.

Illustration. Table 1 shows that the median age of the Mexican population in 1990 in the United States was 24.1. Table 1 also shows that the base of the distribution from which this median was determined was 13,305,000. 1. Using formula (4) and b = 2,622 from table B-5, the standard error of 50 percent on a base of 13,305,000 is about 0.7 percentage points.

2. Adding to and subtracting from 50 percent the standard error found in step 1 to obtain a 68-percent confidence interval on the estimated median yields limits of 49.3 percent and 50.7 percent.

3. From table 1, 58.1 percent (7,730,000) of the Mexican population was 20 years of age or older and 48.3 percent (6,426,000) was 25 years of age or older. Thus, the entire 68-percent confidence interval falls in the age interval 20 to 25. The upper and lower limits of the confidence interval for the median age of the Mexican population can be calculated using linear interpolation. Using formula (12), the lower limit on the estimate is about

Facsimile I. Form CPS-260-Control Card

At the time of the first CPS interview, the interviewer prepares a list of all persons who are staying in the selected sample unit. The roster is constructed using the field Control Card, Form CPS-260. The roster and questions on the control card are used to identify the living space constituting the sample unit.

A control card is prepared for each housing unit. It provides for recording the personal characteristics of each person who is determined to be a member of a sample household, i.e., a person for whom the sampleunit is the usual place of residence. This record of members, which is brought up to date at each subse

quent interview to take account of new or departed residents, changes in age, marital status, etc., and constitutes the complete sample of persons from which subsamples, having specified characteristics, are selected for specific studies.

Facsimile II. Origin or Descent Flashcard

Hispanic persons were identified by a question that askedfor self-identification of the person's origin or descent. Respondents were asked to select their origin (and the origin of other household members from the flashcard. Hispanic persons were those who indicated that their origin was Mexican-American, Chicano, Mexican, Puerto Rican, Cuban, Central or South American (Spanish countires), or other Spanish origin.