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# Regular Examination of the Statistical Accuracy of the Tankan

February 22, 2016
Research and Statistics Department
Bank of Japan

The Bank of Japan examines the statistical accuracy of the Tankan (Short-Term Economic Survey of Enterprises in Japan) once a year, to prevent a decline in the statistical accuracy due to a decrease in the number of sample enterprises caused by bankruptcies, mergers, and other factors. We add new sample enterprises to the Tankan when the examination shows that statistical accuracy has declined. The result of the recent examination showed that the statistical accuracy of the latest survey (December 2015) met the standard. As a result, the total number of the sample enterprises for the March 2016 survey will be 11,127 (including 197 financial institutions).

(see "Sample Design and Sample Maintenance of TANKAN," June 7, 2004, for details of the statistical accuracy of the Tankan)

Details of the examination are as follows.

## 1. Sample Distribution

Population enterprises are classified into 391 strata by industry, scale based on capital size, and number of regular employees for the population estimation.

For each stratum, we examined whether the distribution of the sample enterprises properly reflected that of the population enterprises. The result showed that there was no stratum in which the distribution of the sample had deviated from that of the population.1

1. The "test of the goodness of fit" using chi-square distribution is used in the regular examination. This method tests the null hypothesis, H0: "The distribution of the sample and that of the population have the same shape." When the hypothesis is statistically rejected, it is judged that a deviation exists between the distribution of the sample enterprises and that of the population enterprises.

## 2. Standard Error Ratios

For all of the six main categories (manufacturing and nonmanufacturing for large, medium-sized, and small enterprises, see below), the standard error ratios2 of the total (measured by sales data) remained within the target range (3 percent for manufacturing and 5 percent for nonmanufacturing).

### Standard Error Ratios (Measured by Sales Data)

%
Large Enterprises Medium-Sized Enterprises Small Enterprises
Manufacturing Actual 1.0 2.7 2.5
Target 3.0 3.0 3.0
Nonmanufacturing Actual 3.0 4.6 4.0
Target 5.0 5.0 5.0
1. 2Standard error ratio is a coefficient of variation for a sample estimate. Sample estimates, such as those in the Tankan, inevitably entail certain estimation errors, and this should be taken into consideration when the data are used.

## Inquiries

### Business Survey, Research and Statistics Department

E-mail : post.rsd5@boj.or.jp