In constructing the first 1940 index of rural-farm level of living, considerable work was done to experiment with the effect of using varying numbers of items in the index. The results indicated that an index derived from a small number of items by the methods to be described had a very high correlation with an index similarly derived from a considerably larger number of items. Whereas in 1940, the availability of data from the Censuses of Population, Housing and as well as from the Census of Agriculture, permitted considerable leeway for choice, this was not the case in the construction of indexes for farm-operator families based on data from the Census of Agriculture only. As the number of items available from Censuses of Agriculture was small, there could not be the same type of experimentation with larger and smaller numbers. Items Included in The Index Indexes presented in this bulletin are based on four items that were available for farm-operator families for each county in the United States for 5 years in the 25 years covered. They do not cover all the goods, services, and other satisfactions that make up the level of living of families. However, many studies have shown that the various items are closely associated. For example, farmhouses with electricity are more likely to have other household facilities and conveniences than those without electricity. Farms with high gross incomes are obviously likely to have more income available for familyliving expenditures than farms with low gross incomes. And farm families with automobiles are more likely to be able to take advantage of various services located away from the farm, such as health facilities, libraries, and recreation, than those who do not own automobiles. The validity of the indexes based on only four items could not be tested until data from field surveys were available. Appraisal of the validity of the indexes will be made in connection with the AMS survey of family-living expenditures made in 1956. The items on which these farm-operator family level-of-living indexes are based are the following: (1) Percentage of farms with electricity; (2) percentage of farms with telephones; (3) percentage of farms with automobiles; and (4) average value of products sold or traded in the year preceding the census (adjusted for changes in purchasing power of the farmer's dollar). Data on these items from the Censuses of Agriculture were combined into indexes by methods explained below. County indexes were first compiled to show geographic variations of counties at one date. Later, with some modification to the formula, indexes were compiled to be used not only for this purpose, but also for showing changes over time, although they may not serve the latter purpose as adequately as the former. Method of Deriving Weights for the Indexes The next step was to choose methods for putting the items together into one composite index. To derive weights for combining the items, the methods of factor or component analysis were used. The factor-analysis methods of getting weights for an index are appropriate if the following assumptions can be made: (1) That each item is a partial but imperfect measure of the "level of living" to be measured; (2) That the most important factor the items have in common is the "level of living" to be measured; (3) That the characteristic (or dimension) these items in combinations can best measure (or discriminate) is the "level of living" for which there is no one directly-observed measure. (1) To compute the correlation coefficients between each pair of the items chosen; (2) To perform a factor analysis on the group of correlation coefficients; (3) To transform the factor-analysis results into actual weights to use the formula for computing county indexes. 3 A summary of the results of these steps is shown in table C. The actual computing formulas which were applied to each county to obtain an index for each of the 4 years X1, X2, X3 and X4 represent the items electricity, telephone, automobile, and value of products sold or traded, respectively. The formulas for the other years are identical with that for 1945 except for the weight for X4, the average value of products sold. The weight used for 1945, the base year, was adjusted to allow for the different purchasing power of the farmer's dollar in the other years. For example, the index of prices farmers pay increased 37.1 percent between 1939 and 1944. To adjust the 1944 situation, the average value of products sold in 1939 could have been increased by 37.1 percent for each county. For computing purposes, it was simpler to increase by 37.1 percent the weight for the 1939 item used in the 1940 index. Similar adjustments were made for the weights for X in the index formu4 las for other years. Scaling the Index The factor-analysis method of deriving weights for combining items of diverse nature into an index first produces an index with a mean or base of zero, with about half the units having positive values and about half having negative values. This is not a conventional index scale. By the procedure described in the lower part of table C, the weights were coded so as to scale the index to have a mean value of 100 and to have a value of zero when all of the items have a value of zero. Further technical discussion of the reasons for adopting this type of scale is presented in an article in Rural Sociology for June, 1947. It should be noted that the rural-farm, rural-nonfarm, and composite rural indexes for 1940 that were published in 1943 were not scaled in exactly the same way. 3 The actual computation techniques are described step by step in Hagood, Margaret Jarman, and Price, Daniel O., for Sociologists, (Revised Edition), New York, Henry Holt & Co., 1952, pp. 526-530. Statistics Table C.--Stages in development of index formula from intercorrelations of four items related to farm-operator level of living, sample of 196 counties, 1945 1 Percentage of farms with electricity in farm dwelling, 1945. = 2 = 3 = 4 = Mean value of products sold or traded per farm reporting for 1944, (in hundreds of dollars). SPECIAL PROBLEMS IN CONNECTION WITH THE 1950 AND 1954 INDEXES Several problems in connection with the 1950 and 1954 indexes required special at tention. Three Items on Sample Basis In the 1950 and 1954 Censuses of Agriculture, data on electricity, telephones, and automobiles were obtained on a sample basis. Questions on these and certain other items were asked for very large farms and for a 20-percent sample of the remaining 4 Hurley, Ray and Smith, Richard K. "New Approaches and Methods for the 1950 Census of Agriculture." Agr. Econ. Research 3:113-118. farms. For the 1950 indexes a formula was developed to provide an approximate value of the sampling error of the farm-operator level-of-living index arising from the fact that three of the four items in the index were based on a sample. On the basis of the sampling error computed from this formula, 800 farms was set as the lower limit below which, with very few exceptions, indexes of level of living would not be shown. Each county with fewer than 800 farms (with a few exceptions) was combined with one or more counties in such a way that the combination would have at least 800 farms. The criteria for deciding which counties should be used were: (1) That the counties have level-of-living indexes as similar as possible; (2) that the counties be in the same economic area; (3) that the type of farming of the counties be as similar as possible. In applying the third criterion, the judgment of regional specialists in the Bureau of Agricultural Economics was followed. In the case of 14 counties--6 single counties, and 4 combinations of 2 counties each-it was impossible to make a combination with 800 farms without violating one or more of these criteria. For these counties, indexes are shown that are based on the sample from fewer than 800 farms. The counties in which exceptions were made are as follows: The indexes for the counties and county combinations listed above are subject to a greater sampling error than the other indexes. For the 1950 indexes there were 766 counties that were combined, including both counties with fewer than 800 farms and the counties with which they were combined. These counties resulted in 303 combinations of counties. Indexes for these combinations are shown for 1930, 1940, 1945 and 1950 in the publication containing the 1950 indexes. Indexes of farm-operator family level of living for the combinations of counties made in 1950 were also computed for 1954. There were, however, 4 counties with less than 800 farms included in combinations in 1950 which had more than 800 farms in 1954. In addition to the indexes computed for the combinations, separate 1954 indexes were computed for these 4 counties and for the counties with which they were combined. There were in 1954 an additional 97 counties and 34 combinations of counties which had fewer than 800 farms. New combinations were not made for these areas. Indexes for |