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were then converted into percentages of total sales for all independent food retailers in the city. The sample distribution by areas and for the city was calculated by applying these percentages to the total number of independent stores previously determined as the sample for the city.
The sample of stores in each area of a city was selected from the total number of stores by random sampling within type and volume class, modified by a simple device designed to reduce travel time and collection costs to a minimum without affecting the representativeness of the sample. This was accomplished by dividing the total sample for an area into groups of three stores, each store in a group located as near to the other two, geographically, as was possible within the sample pattern. After dividing the total sample for an area by 3 to determine the number of groups of three stores or less into which the sample for the area was to be concentrated, one store in each group was selected at random from the list of stores sorted by type and volume class and termed the "primary unit." To facilitate the grouping of stores in threes, the primary units were selected from the least prevalent type and volume class to be represented in the sample for the area, with the two remaining stores of the types and classes specified within each group, selected as close geographically as possible to the primary unit. For example, if the calculated sample for one area in a city was as follows—
Total independent stores..
Grocery and combination....
Class I (annual sales: Less than $50,000). Class II (annual sales: $50,000-$250,000) Class IV (annual sales: $250,000 or more) Meat markets___
Class I (annual sales: Less than $50,000).
three groups were set up-two groups of 3 stores each and one group of 2 stores. Selecting the least prevalent type and class, a supermarket (class IV combination store) and two class I meat markets were used as primary units. These primary units were drawn at random from the lists of those types and classes of stores in the area. After the managers of these stores agreed to furnish prices regularly to the Bureau, additional units within the sample pattern were selected as near to the primary unit as possible and, if feasible, along the best transportation route to the next primary unit. Thus, a class I grocery or combination store was selected near the supermarket designated as a primary unit; and a class II and class I grocery or combination near each of the class I meat markets designated as primary units. Insofar as was consistent with the sampling pattern,
stores that had been reporting prices regularly to the Bureau for a number of years were retained.
The revised independent store sample in each city brings up to date the representation of each type and class of store in proportion to its relative importance in total food sales of independent stores in the city. Some of the types, such as fresh fruit and vegetable stores, had not been represented adequately in the former samples for a few cities. The size of the independent store sample was increased for 50 of the 56 cities and decreased for 6 cities. The changes in the sample vary from only minor adjustments in some cities to major changes in others. For example, in Boston the new sample constitutes a major revision as shown by the following:
In Washington, D. C., the sample of independent stores was reduced from 40 to 35 stores, with only minor changes in type and volume class.
A minimum number of foods on which prices were to be reported by each store was specified, based on the type of foods sold, with the result that the number of quotations for each food in a city was usually increased by a much greater ratio than the number of stores in the sample was enlarged. For example in one city a 10-percent increase in the number of stores was accompanied by a 45-percent increase in the total number of prices reported.
The method of obtaining chain store representation was not changed; that is, every important food chain that was willing to report prices regularly was included in the city sample. At the time the independent store sample was reviewed the list of chain stores was also checked and some additions were made to the chain sample for certain cities. One schedule of prices is collected from each chain organization reporting for a city (two schedules if the firm operates both supermarkets and service stores and there are any price differentials between the two types). Collection of prices from a number of outlets of the same chain proportional to its importance in the total chain sales in the city would result in a large sample and greatly increased collection costs. Such procedure is not necessary to secure reliable average
prices, since outlets of the same chain organization generally sell foods at approximately the same prices throughout the city.
Changes in Data Processing
The Bureau also made changes in some phases of the summarization of prices collected in addition to revisions of store samples. These changes were first used in February 1946 with a recomputation of January summaries for comparability. Average prices were affected in varying degrees, but there was no immediate effect on indexes used for measuring trends.
The most important change in summarization was made in the method of reflecting State and local sales taxes which are applicable to foods sold at retail in 16 of the 56 cities regularly surveyed by the Bureau. Prior to February 1946, sales taxes were included in average prices published by the Bureau as well as in the indexes of prices. Beginning in February all indexes of retail food prices reflected the tax levies and changes in sales tax rates as in the past. Average prices for the individual foods in each city, however, were computed without adding the amount of sales tax.
The primary reason for changing the method of handling sales taxes was that these taxes are usually collected on the total purchase made by an individual at any one time rather than on each individual item. Also, the average consumer does not think of the price quotation for a single article as including tax. Therefore, from a practical standpoint it appeared best to publish average prices and ranges of prices without taxes, and to continue to reflect tax changes in the total food costs used for the computation of the indexes.
COMBINATION OF CHAIN AND INDEPENDENT STORE QUOTATIONS
In computing average prices for each food in a given city, recognition must be given to the relative importance of sales of an individual food store to total volume of sales for all food stores in the city. Obviously, prices from a supermarket with an annual sales volume of $600,000 should be given more weight in an average than a grocery with annual sales of $25,000. Thus, it is necessary to use a system of weights which will maintain the proper ratio between prices from each type of independent store and each chain organization and at the same time maintain the ratio between total sales volume of all independents and total sales volume of all chains.
Prior to February 1946 the Bureau accomplished this by developing weights for each food for each store. Prices from each independent
4 See An Appraisal of the U. S. Bureau of Labor Statistics' Cost of Living Index: Appendix, Prepared for a Special Committee of the American Statistical Association, in Journal of the American Statistical Association, March 1944, Vol. 39 (p. 70).
store were given a weight of 1 and were thus weighted implicitly, since the number of stores in the sample in each sales volume group was roughly proportional to the total number in that group, as reported by the Bureau of the Census.
The total weight for all chain store quotations was calculated so that it would bear the same ratio to the total of independent quotations that the total food sales by chains in that city bore to the total sales by independents, as determined from the latest available data from the Bureau of the Census, merchants associations, and any other reliable sources. The weighting factors for each of the reporting chains were based on the sales volume of each chain, and adjusted to the total chain weight required for the city. The following example illustrates the procedure used prior to February 1946. In city A, chain stores made 40 percent and independent stores made 60 percent of the food sales. The sample for city A consisted of 18 independent stores and 4 chain organizations, the 4 chains having annual sales of 10, 6, 4, and 4 million dollars, respectively. An average price was obtained as follows:
1. Each independent store was given a weight of 1, making a total independent weight of 18.
2. The total of all chain store weights was computed by multiplying 18 by 4%, the ratio of chain store sales to independent store sales, resulting in a total chain weight of 12.
3. The total chain weight was then distributed among the four chains in proportion to their individual sales volumes.
Total, 4 chains.............
4. Each price quotation was weighted by the factor assigned to the store or
5. The sum of the weighted prices was divided by the sum of the weighting factors to produce the average price for the food item for the city.
This method of weighting maintains the relative importance of each quotation in the average as long as all stores in the sample report prices for a specified food. However, during periods of short supplies it was not possible to obtain the same number of quotations at every collection date and, as the ratio between the number of chain and independent quotations varied, the chain-independent ratio was distorted in varying degrees. For example, in the illustration above: So long as 18 independents and 4 chains reported prices for bacon, the ratio was maintained. However, if only 12 independents quoted prices for bacon while all 4 chains continued to report, the ratio of
chain-independent reports for bacon automatically became 12 to 12 or 50-50, instead of 40 to 60 percent, as previously determined to be the correct ratio.
In February 1946, the procedure was changed. A separate average was computed for independent stores and for chain stores and the two averages combined by use of the chain-independent ratio to arrive at an average price for the city. Thus, the relative importance of sales by each type of organization is maintained, regardless of variations in the number of quotations reported. Each independent store quotation was given a weight of 1 as before, since the number of independents in the sample for a given sales volume group is proportional to the total sales of independents of that group in the city and therefore the independent quotations are weighted implicitly. Weighting factors for chains were determined as before, except that the factors used were the percentages of total sales. An average price for a specified food is now computed by the following steps:
1. An average price for independent stores is computed by dividing the sum of the independent quotations by the number of independent quotations. 2. An average price for chain stores is computed by multiplying each quotation by a weighting factor assigned to that chain, summing the weighted quotations, and dividing by the sum of the weights.
3. An average price for the city is computed by combining the independent and chain averages (steps 1 and 2), weighting each by the percentage of total food sales in the city made by that type of store, and dividing the sum by 100.
Prior to February 1946, a price was used only if it was for the identical size, grade, and brand of the article quoted the preceding month by the same store, with the exception of meats, fresh fruits and vegetables, and certain canned goods. If no price was quoted for a given article, either for the current or the preceding month, an adjustment was made in the food cost aggregates for comparability before computing the indexes. This procedure was time-consuming and often resulted in a reduction in the number of quotations used to compute average prices and indexes. Under new procedures, all price quotations for articles which meet the specifications are used, thus greatly reducing the costs of processing.
AVERAGE PRICES FOR 56 CITIES COMBINED
No changes were made in the method of combining averages for the various cities into averages for 56 cities combined. The average price in each city is weighted by a factor representing the population of the metropolitan area of the city and of other cities in the same region. and size class.