includes piped and pipeless warm air furnaces, as well as floor and wall furnaces. "Noncentral heating, with flue" includes fireplaces and flue-connected heating stoves. A flue is a pipe or enclosed passage, either connected to a chimney or leading directly to the outside of the structure, which carries the smoke or fumes to the outside. All other types of heating equipment, such as electric heaters and portable kerosene heaters, are classified as "Noncentral heating, without flue." Stoves and ranges used primarily for cooking were enumerated as heating equipment when they were also the major source of heating.

The 1950 data on heating equipment may be compared with the 1940 data when certain combinations are made. The 1950 category "Warm air furnace" is comparable with the combination of the 1940 groups "Piped warm air system" and "Pipeless warm air furnace." The 1950 classification combining "Noncentral heating, with flue" and "Noncentral heating, without flue" is roughly comparable with the category "Without central heating" in 1940. Television. Data on television represent the number of dwelling units which have a television set, even though the set was temporarily out of order or being repaired at the time of enumeration.

FINANCIAL CHARACTERISTICS

Contract monthly rent.-Contract monthly rent is the rent at the time of enumeration contracted for by the renter, regardless of whether it includes furniture, heating fuel, electricity, cooking fuel, water, or other services sometimes supplied. The rental amount was reported to the nearest dollar.

The contract monthly rent data for renter-occupied nonfarm units are considered comparable for the 1950 and the 1940 Censuses, although in 1950 no dollar estimates were made for rentfree units, whereas in 1940 estimates made for rent-free units were included in the distribution of renter units. In 1940, estimates of monthly rent were obtained for owner-occupied and for farm units; in 1950, such data were not collected.

The 1950 rent data indicate rent levels in 1950 and do not reflect changes since 1940 in rents for identical units. In addition to units coming on the market through new construction and conversion, there was a considerable withdrawal of existing rental units through purchase for owner occupancy. Further, there was some shifting of rental units between farm and nonfarm residence. Therefore, the 1950 data apply to a largely different group of rental units.

Changes reflected by the 1940 and 1950 Census data are not comparable with changes in rents obtained by the Bureau of Labor Statistics for its Consumers' Price Index. The data compiled by the Bureau of Labor Statistics represent changes in rent charged for essentially identical units with identical services and facilities.

Gross monthly rent.-The computed rental termed "gross rent" eliminates rent differentials which result from varying practices with respect to the inclusion of heat, utilities, and furniture as part of the contract rent. Gross monthly rent is contract monthly rent plus the reported average monthly cost of utilities (water, electricity, gas) and fuels such as wood, coal, and oil, if these items were paid for by the renter in addition to contract monthly rent. If furniture was included in the contract rent, the reported estimated rent of the dwelling unit without furniture was used in the computation rather than the contract rent.

Gross rent as percentage of income.-Gross rent as percentage of income is the percent of the income which is paid for gross rent. The yearly gross rent (gross monthly rent multiplied by 12) is expressed as a percentage of the total income in 1949 of the primary family or the primary individual. The percentage was computed separately for each unit. The category "Not available" includes all dwelling units for which gross rent as a percentage of income was not computed because rent or income or both were not reported, because the unit was reported as being occupied rent-free, or because extremes of either rent or income

would have resulted in relatively meaningless ratios. In processing, rents of $999 or more and incomes of less than $100 or $10,000 or more were considered as extremes.

Value of 1-dwelling-unit structures.-Value represents the amount which the owner-occupant estimates that the property, including the structure and its land, would sell for under ordinary conditions and not at forced sale. Value data are limited to nonfarm units in 1-dwelling-unit structures without business and with only one dwelling unit included in the property. Values for other owner-occupied dwelling units are not provided because they would reflect varying amounts for business uses or for more than one dwelling unit in the property. Value was tabulated to the nearest hundred dollars.

In 1940, the value data were presented for owner-occupied units in both multi-dwelling-unit structures and 1-dwelling-unit structures. If the owner occupied one of the dwelling units in a structure containing two dwelling units or more, or if a part of the structure was used for business purposes, the value reported in 1940 represented an estimate for that portion occupied by the owner and his household. Thus, the data on value of owneroccupied units are not strictly comparable for the two censuses because of differences in the types of units for which value was reported. However, 1940 value statistics for 1-dwelling-unit structures without business, which are roughly comparable with the 1950 data, are presented in Volume III of the 1940 Housing reports for the United States, States, and cities of 100,000 inhabitants or more.

Value-income ratio.-The value-income ratio is the quotient of the value of the owner-occupied dwelling unit divided by the total income in 1949 of the primary family or the primary individual. The ratio was computed separately for each unit. The category "Not available" includes all dwelling units for which the value-income ratios were not computed because either value or income, or both, were not reported or because extremes of either value or income would have resulted in relatively meaningless ratios. In processing, values less than $100 or $99,900 or more and incomes less than $100 or $10,000 or more were considered as extremes.

HOUSEHOLD CHARACTERISTICS

Household. A household consists of all persons who occupy a dwelling unit. Included are the related family members and also the unrelated persons, if any, such as lodgers or employees, who share the dwelling unit. A person living alone in a dwelling unit, or a group of unrelated persons sharing a dwelling unit as partners, is considered a household. The data on households in this volume are expressed in terms of occupied dwelling units.

Each household consists of a primary family, or a primary individual, and nonrelatives, if any.

Despite minor differences between the criteria used in 1950 and 1940 to identify a household, the number of occupied dwelling units (households) as shown in this volume may be regarded as comparable with the number of "private households" shown in the Population reports published by the Bureau of the Census on the basis of the 1940 Census.

Primary family.-A primary family consists of the household head and all persons in the household related to him by blood, marriage, or adoption.

Primary individual.-A household head living alone or with nonrelatives only is a primary individual. He is not regarded as a family. In 1940, the term "family" included both "primary family" and "primary individual.”

Head of household.-One person in each household is designated as "head." He is usually the person regarded as the head by the members of the household. Married women are not classified as heads if their husbands were living with them at the time of the census.

Sex and age of head.-The category "Male head, wife present, no nonrelatives" is identical with "Husband-wife families, no nonrelatives" in the tabulations by type of household. A household was classified in these categories if both the husband and wife were reported as members of the household even though one or

the other may have been temporarily absent on business or vacation, visiting, in a hospital, etc., at the time of the enumeration. From the viewpoint of housing analysis, this group is the most important since about 75 percent of all nonfarm occupied dwelling units contain this type of family. The category "Other male head" includes those dwelling units occupied by households with male heads, wife present, with nonrelatives living with them; male heads who are married, but with wife absent because of separation, divorce, or other reason where husband and wife maintain separate residences for several months or more; and male heads who are widowed or single. "Female head" comprises all female heads of households regardless of their marital status. The age classification is based on the age of the head as of his last birthday.

Type of household.-Each household in the group "Husbandwife families, no nonrelatives" consists of the head, his wife, and other persons, if any, who are related to him. In the Housing reports, this group is considered the normal family group. "Other family groups, no nonrelatives" consist of the head without a spouse, and one or more persons related to the head. A person who occupies a dwelling unit alone constitutes a "1-person household." All households containing one or more nonrelatives are included in the group "Households with nonrelatives."

A nonrelative is a lodger, partner, foster child, ward, resident employee, or other household member who is not related to the head.

Income in 1949.-Income is the sum of the money received by the primary family or primary individual, less losses, from the following sources: wages or salary; net income (or loss) from the operation of a farm, ranch, business, or profession; net income (or loss) from rents or receipts from roomers or boarders; royalties; interest, dividends, and periodic income from estates and trust funds; pensions; veterans' payments, armed-forces allotments for dependents, and other governmental payments or assistance; and other income such as contributions for support from persons who are not members of the household, alimony, and periodic receipts from insurance policies or annuities. The figures in this volume represent the amount of income received before deductions for personal income taxes, social security, bond purchases, union dues, etc.

Receipts from the following sources were not included as income: money received from the sale of property, unless the recipient was engaged in the business of selling such property; the value of income "in kind," such as food produced and consumed in the home, or free living quarters; withdrawals of bank deposits; money borrowed; tax refunds; gifts; and lump-sum inheritances or insurance payments.

CONSISTENCY

Since the unit of tabulation in this volume is an occupied dwelling unit, statistics on income relate to the income of the primary family, or primary individual, occupying the dwelling unit; that is, the sum of the income of the head of the primary family and the incomes of all persons in the household related to the head, or simply the income of the primary individual where no related persons occupy the unit. Incomes of persons living in the unit but not related to the head of the household are not included in this sum.

The figures in all field surveys of income are subject to errors of response and nonreporting. In most cases, the schedule entries for income are based not on records but on memory, usually that of the housewife. The memory factor in data derived from field surveys of income probably produces under-estimates, because the tendency is to forget minor or irregular sources of income. Other errors of reporting are due to misrepresentation or misunderstanding of the income questions.

Another possible source of understatement in the figures on family income was the assumption that there was no other income in the family when only the head's income was reported. It is estimated that this editing assumption was made for about 5 percent of the families. This procedure was adopted in order to make maximum use of the information obtained. In the large majority of the fully reported cases, the head's income constituted all or most of the total family income.

In the 1950 Census, family income is the sum of the incomes of all family members 14 years of age and over. For each member, information was requested on the following income categories: (a) The amount of money wages or salary received in 1949; (b) the amount of net money income received from self-employment in 1949; and (c) the amount of other money income received in 1949; e. g., interest, dividends, veterans' allowances, pensions, or net income from rents. The family income data in this volume are more inclusive than the data from the 1940 Census and therefore are not comparable. In 1940, information was collected on the amount of money wages or salary income of each private family. If more than $50, the receipt, but not the amount, of income from other sources was reported.

The income data in this volume also differ from income data for families and unrelated individuals in the 1950 Population reports. "Families" and "unrelated individuals" as used in the Population reports refer to both primary and secondary families and primary and secondary individuals.

Because of the methods by which the data were compiled, corresponding statistics for some of the items (those based on a 4-percent sample) may not agree from one table to another. The differences generally will be small and should not affect the validity of the cross-classifications.

There are variations also between the figures in this report and those for corresponding subjects in Volume I (H-A bulletins) of the Housing reports. The two sets of data were prepared from separate tabulations and processing differences were not adjusted. Furthermore, the figures in this report were obtained from representative samples of dwelling units and therefore differences from complete counts may be expected because of sampling variability. In Volume I, figures for all subjects except "Year built" and "Equipment and fuels" were obtained from complete counts of dwelling units. To obtain comparable data for standard metropolitan areas from Volume I, data for rural-farm units in the constituent counties (towns in New England) must be subtracted from the area totals.

Figures in this report may not be identical with those for corresponding items in the Population reports. Comparability is limited because of differences in the unit of reporting, the method of tabulating, and sampling.

SAMPLE DESIGN

For most of the statistics a sample of approximately 20 percent of the dwelling units was used. These statistics were obtained by tabulating data for all dwelling units for which the head of the household was enumerated on a sample line of the population schedule. A separate line was provided on the population schedule for each person enumerated, with every fifth line designated as a sample line. Information on year built, television, and heating equipment was requested for about one-fifth of the dwelling units. Consequently, statistics for each of these items are available for only about one-fifth of the 20-percent sample of occupied dwelling units, or about 4 percent of the total occupied units.1

Estimates based on the 20-percent sample were obtained by multiplying by five the number of dwelling units in the sample with the specified characteristic. Estimates based on the 4percent samples were obtained by inflating the sample results by the factors necessary to make the total in each column agree, within rounding error, with the results of the 20 percent sample. Although the procedure established for the selection of the samples did not automatically insure an exact 20-percent or 4percent sample of dwelling units due to the presence of blank or 1 A more complete description of the sample designs is contained in the text for the United States.

voided lines, special entries, etc., it was unbiased, and for large areas the deviation from 20 or 4 percent was expected to be quite small. However, in most areas there was a slight under-sample of households which arose when the enumerator failed to follow his sampling instructions exactly. Another slight bias resulted from the fact that a small proportion of tabulation cards were excluded from processing due to the omission of tenure identification.

These processing and enumeration errors have had the effect of consistently reducing the size of the sample below the 20- and 4-percent level. However, they have relatively little effect on the distributions, although they result in the number of dwelling units in most categories being slightly understated.

SAMPLING VARIABILITY

Since the data are based on samples, they are subject to sampling variability, which can be determined from the standard errors shown in tables A and B. These tables do not reflect the effects of the biases mentioned above. Table A presents the approximate standard errors of sample estimates of selected sizes. Table B shows the approximate standard errors of percentages when computed by using data from this report for both numerator and denominator. For values not shown, linear interpolation will usually provide reasonably accurate results. 2

The standard error is a measure of sampling variability. The chances are about 2 out of 3 that the difference due to sampling variability between an estimate and the figure that would have been obtained from a complete count of the dwelling units is less than the standard error. The amount by which the standard error must be multiplied to obtain other odds deemed more appropriate can be found in most statistical textbooks. For example, the chances are about 19 out of 20 that the difference is less than twice the standard error, and 99 out of 100 that it is less than 21⁄2 times the standard error.

Con

Illustration: Let us assume that for a standard metropolitan area with 100,000 dwelling units, table 5 shows that there were an estimated 5,000 owner-occupied dwelling units with 4 rooms containing 3 persons (50 percent of the 10,000 owner-occupied dwelling units with 4 rooms). Table A shows that for items based on the 20-percent sample the standard error for an estimate of 5,000 in areas with 100,000 dwelling units is about 140. sequently, the chances are about 2 out of 3 that the figure which would have been obtained from a complete count of the owneroccupied dwelling units with 4 rooms and 3 persons differs by less than 140 from the sample estimate. It also follows that there is only about 1 chance in 100 that a complete census result would differ by as much as 350, that is, by about 21⁄2 times the number given in the table. Table B shows that for items based on the 20-percent sample, the standard error of the 50 percent on

2 For estimates based on the 4-percent sample in which the estimate is more than 50 percent of the total of the column, a closer approximation of the standard error may be 24 20 obtained by using x where x is the size of the estimate and y is the total number X y of dwelling units in the column. For example, the approximation provided by the above formula of the standard error of an estimate of 6,000 (x) in a column whose tota number of dwelling units is 8,000 (y) is 230.

a base of 10,000 is 1.0 percent. In table 5, for a "year-built" estimate of the owner-occupied dwelling units with 4 rooms, the column for 10,000 in the 4-percent sample section of table A would be used.

The standard errors shown in tables A and B are not directly applicable to differences between two sample estimates. The standard error of a difference will be approximately the square root of the sum of the squares of each standard error considered separately. This formula will represent the actual 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, although it is only a rough approximation in most other cases.

Some of the tables present estimates of the median number of persons as well as the corresponding distributions. The sampling variability of estimates of medians depends on the distributions upon which the medians are based.3

The smaller figures and small differences between figures should be used with particular care because they are subject to larger relative error arising from processing and enumeration bias and larger relative sampling variability. These smaller figures have been included in the tables to permit analysis of broader groups with smaller relative bias and sampling variability.

RATIO ESTIMATES

It is possible to make an improved estimate of an absolute number (improved in the sense that the standard error is smaller) whenever the class in question forms a part of a larger group for which both a sample estimate and a complete count are available. This alternative estimate is particularly useful when the characteristic being estimated is a substantial part of the larger group; when the proportion is small, the improvement will be relatively minor. The improved estimate (usually referred to as a ratio estimate) may be obtained by multiplying the estimate shown in this report, by the ratio of the complete count of the larger group to the sample estimate of this larger group. Complete counts for many of the items can be derived from Volume I of the Housing reports by excluding data for rural-farm units from the totals for the standard metropolitan area. Ratio estimates may be applied to statistics based either on the 20-percent or on the 4-percent samples. The effect of using ratio estimates of this type is, in general, to reduce the relative sampling variability from that indicated for an estimate of a given size in table A to that shown for the corresponding percentage in table B, or less. Estimates of these types are not published in this report.

3 The standard error of a median based on the 20-percent sample may be estimated as follows: If the estimated total number reporting the characteristic is N, compute the number N/2-√N. Cumulate the frequencies in the table until the class interval which contains this number is located. By linear interpolation, obtain the value below which N/2-N cases lie. In a similar manner, obtain the value below which N/2+VN cases lie. If information on the characteristic had been obtained from a complete count of dwelling units, the chances are about 2 out of 3 that the median would lie between these two values. The chances are about 19 out of 20 that the meN dian would be in the interval computed similarly but using±2√N and about 99 out N

of 100 that it would be in the interval obtained by using ±2.5√N.