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For a characteristic tabulated by color or tenure, the factor for the characteristic in table D approximates the factor that applies to the data in the cross tabulation. For example, to obtain the standard error of the estimate of the number of owner-occupied units built in the period 1950 to 1954 (table 10), as an approximation, apply the factor in table D for "year structure built" to the estimate in table B.

Table D.--FACTOR TO BE APPLIED TO TABLES B AND C (Refer to table A for sample rate applying to data tables)

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Homeowner and rental vacancy rates, which are given in tables 1, 2, 12, 18, and 22, are subject to relatively small sampling variability in most cases since they are computed by using the 100-percent count of vacant units and the estimates of owner-occupied and renter-occupied units.

Standard error of differences.-The standard errors estimated from tables B and C (using the factors given in table D) are not directly applicable to differences between two sample estimates. These estimates are to be applied differently in the following three situations:

1. For a difference between a sample figure and one based on a complete count (e.g., a difference arising from comparison between condition and plumbing facilities based on a 25-percent sample for one area, and condition and plumbing facilities from the 100-percent tabulations in another area), the standard error of the difference is identical with the standard error of the estimate which is based on a sample.

2. For a difference between two sample figures (e.g., one from 1960 and the other from 1950, or both from the same census year), the standard error is approximately the square root of the sum of the squares of the standard error of each estimate considered separately. This formula will represent the standard error quite accurately for the difference between 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 correlation between the two characteristics, the formula will overestimate the true standard error.

3. For a difference between two sample estimates, one of which represents a subclass of the other, the difference should be considered as the sample estimate and an estimate of the sampling error of the difference obtained directly.

Standard error of medians.-The sampling variability of the medians presented in certain tables (median number of persons, number of rooms, value of property, contract rent, and gross rent) depends on the size of the base and on the distribution on which the median is based. An approximate method for measuring the reliability of an estimated median is to determine an interval about the estimated median, such that there is a stated degree of confidence that the true median lies within the interval. As the first step in estimating the upper and lower limits of the interval about the median (that is, the confidence limits), compute one-half the number reporting (designated N/2) the characteristic on which the median is based. By the methods described above for computing the standard error of an estimated number, compute the standard error of N/2. Subtract this standard error from N/2. Cumulate the frequencies (in the table on which the median is based) up to the interval containing the difference between N/2 and its standard error, and by linear interpolation obtain a value corresponding to this number. In a similar manner, add the standard error to N/2, cumulate the frequencies in the table, and obtain a value corresponding to the sum of N/2 and its standard error. The chances are about 2 out of 3 that the median would lie between these two values. The range for 19 chances out of 20 and for 99 in 100 can be computed in a similar manner by multiplying the standard error by the appropriate factors before subtracting from and adding to one-half the number reporting the characteristic. Interpolation to obtain the values corresponding to these numbers gives the confidence

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SUBJECTS PRESENTED BY TYPE OF AREA AND TABLE NUMBER

(Tables 1 and 8 not listed; see note. For tables 9 to 11, 33, 34, and 36 to 42, the term "All units" means the same as "All occupied units")

XXXV

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Occupied 100 to 400 400 to 2,000 2,000 or more farm such units such units such units

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Population, 1960: All occupied......

Per occupied unit: All occupied....
Owner, renter.....

Population, 1950: All occupied..

Per occupied unit: All occupied. Tenure by color or ethnic group....... Percent owner occupied....

Year moved into unit: Owner, renter......

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NOTE: Tables 1 and 8 present selected summary data for the State (urban, rural nonfarm, occupied rural farm; inside SMSA's, by "inside central cities" and "outside central cities," and outside SMSA's); for each SMSA; and each place of 10,000 inhabitants or more. Table 1 is for all units and table 8 is for units with nonwhite heads. 1 Not included in data on rent and value.

2 Tables 9 to 11 omitted if fewer than 25,000 units with nonwhite heads in the State.

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5 Units with white heads having Spanish surname s in Arizona, California, Colorado, New Mexico, Texas; units with heads of Puerto Rican birth or parentage in other States. 6 Tenure and color not cross tabulated.

7 Published in U.S. Summary, Volume I, for places which had a population of 50,000 or more in 1950, or in an interim census, and a population of 50,000 or more in 1960.

Michigan

LIST OF TABLES

[Page numbers listed here omit the State prefix number which appears as part of the page number for each page.
The prefix for this State is 24]

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11

26. Occupancy and financial characteristics, year built, and heating equipment, for places of 2,500 to 10,000 inhabitants: 1960... 27.-Selected characteristics of housing units, for places of 1,000 to 2,500 inhabitants: 1960....

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6.-Type of fuel and selected equipment, for the State, inside and outside SMSA's, urban and rural: 1960.

7.-Financial characteristics and duration of vacancy, for the State, inside and outside SMSA's, urban and rural nonfarm: 1960.

8. Selected characteristics of housing units with nonwhite household heads, for the State, SMSA's, and places of 10,000 inhabitants or more: 1960.. 9.-Tenure, condition and plumbing facilities, and structural characteristics of housing units with nonwhite household heads, for the State, inside and outside SMSA's, urban and rural: 1960. 10. Occupancy characteristics, units in structure, and year structure built for housing units with nonwhite household heads, for the State, inside and outside SMSA's, urban and rural: 1960. 11. Selected equipment and financial characteristics of housing units with nonwhite household heads, for the State, inside and outside SMSA's, urban and rural: 1960_.

STANDARD METROPOLITAN STATISTical areas, PLACES OF 50,000 INHABITANTS OR MORE, AND URBANIZED AREAS

12.-Tenure, vacancy status, and condition and plumbing facilities, for SMSA's, constituent counties, places of 50,000 inhabitants or more, urban balance, rural total, and urbanized areas: 1960.. 13.-Bathrooms, rooms, and bedrooms, for SMSA's, constituent counties, places of 50,000 inhabitants or more, urban balance, rural total, and urbanized areas: 1960. 14. Structural characteristics and heating equipment, for SMSA's, constituent counties, places of 50,000 inhabitants or more, urban balance, rural total, and urbanized areas: 1960. 15.-Occupancy characteristics, for SMSA's, constituent counties, places of 50,000 inhabitants or more, urban balance, rural total, and urbanized areas: 1960.

16.-Type of fuel and selected equipment, for SMSA's, constituent counties, places of 50,000 inhabitants or more, urban balance, rural total, and urbanized areas: 1960. 17.-Financial characteristics and duration of vacancy, for SMSA's, constituent counties, places of 50,000 inhabitants or more, urban balance, rural total, and urbanized areas: 1960.

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PLACES OF 1,000 TO 50,000 INHABITANTS

18.-Tenure, vacancy status, and condition and plumbing facilities, for places of 25,000 to 50,000 inhabitants: 1960...

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19. Structural characteristics, for places of 25,000 to 50,000 inhabitants: 1960....

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20.-Occupancy characteristics, year built, and heating equipment, for places of 25,000 to 50,000 inhabitants: 1960.. 21.-Financial characteristics, yeår moved into unit, and duration of vacancy, for places of 25,000 to 50,000 inhabitants: 1960....

41. Characteristics of housing units with household heads of Puerto Rican birth or parentage, for SMSA's and places with 2,000 or more such units: 1960..

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APPENDIX

Table

A-1.-Percent of allocation for nonresponse or inconsistency, for the State, by size of place: 1960_.

LIST OF MAPS

The State, showing standard metropolitan statistical areas, counties, and places of 10,000 inhabitants or more.
Urbanized areas..

Page 155

3 157

24-1

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