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TECHNICAL NOTE DATA QUALITY
5 There are about two chances in three that the value that would have been produced if all dwellings had been included in the survey will fall in the range 3,792,600 to 3,840,600, and about 19 chances in 20 that the value will fall within the range 3,768,600 to 3,864,600. This example is illustrated in the diagram below:
6 In general, the size of the SE increases as the size of the estimate increases. Conversely, the RSE decreases as the size of the estimate increases. Very small estimates are thus subject to such high RSEs that their value for most practical purposes is unreliable. In the tables in this publication, only estimates with RSEs of 25% or less are considered reliable for most purposes. Estimates with RSEs greater than 25% but less than or equal to 50% are preceded by an asterisk (e.g. *3.4) to indicate they are subject to high SEs and should be used with caution. Estimates with RSEs of greater than 50%, preceded by a double asterisk (e.g. **0.3), are considered too unreliable for general use and should only be used to aggregate with other estimates to provide derived estimates with RSEs of less than 25%. Table T2 presents the levels at which estimates have RSEs of 25% and 50%.
MEANS AND MEDIANS
7 The RSEs of estimates of mean and median duration of time spent looking for work are obtained by first finding the RSE of the estimate of the total number of persons contributing to the estimate (see table T1) and then multiplying the resulting number by the following factors:
8 The following is an example of the calculation of SEs where the use of a factor is required. Table 7 shows that the estimated number of males aged 15 years and over who looked for work at some time during the year was 906,800 with a median duration of time spent looking for work of 12 weeks. The SE of 906,800 can be calculated from table T1 (by interpolation) as 11,100. To convert this to an RSE we express the SE as a percentage of the estimate, or 11,100/906,800 = 1.2%.
9 The RSE of the estimate of median duration of time spent looking for work for males aged 15 years and over is calculated by multiplying this number (1.2%) by the appropriate factor shown in paragraph 7 (in this case 1.04): 1.2 x 1.04 = 1.2%. The approximate SE of this estimate of median duration of time spent looking for work for males aged 15 years and over is therefore 1.2% of 12 weeks, i.e. about 0.1 weeks. Therefore, there are two chances in three that the median duration of time spent looking for work for males aged 15 years and over that would have been obtained if all dwellings had been included in the survey would have been within the range 11.9 weeks to 12.1 weeks, and about 19 chances in 20 that it would have been within the range 11.8 weeks to 12.2 weeks.
10 Mean and median estimates produced from population estimates smaller than the values in T2 have RSEs larger than 25% and should be used with caution. Table T2 also indicates the size of population estimates that would produce means and medians with RSEs greater than 50%, which are considered too unreliable for general use.
PROPORTIONS AND PERCENTAGES
11 Proportions and percentages formed from the ratio of two estimates are also subject to sampling errors. The size of the error depends on the accuracy of both the numerator and the denominator. A formula to approximate the RSE of a proportion is given below. This formula is only valid when x is a subset of y:
12 Considering the example above, of the 3,816,600 persons aged 15 years and over in the labour force for part of the year, 499,000, or 13.1%, looked for work at some time during the year. The SE of 499,000, may be calculated by interpolation as 8,300. To convert this to an RSE we express the SE as a percentage of the estimate, or 8,300/499,000 = 1.7%. The SE for 3,816,600 was calculated previously as 24,000, which converted to an RSE is 24,000/3,816,600 = 0.6%. Applying the above formula, the RSE of the proportion is:
13 The SE for the proportion, 13.1%, of persons aged 15 years and over who looked for work at some time during the year is 0.2 percentage points, calculated as (13.1/100)x1.6. There are about two chances in three that the proportion of persons aged 15 years and over who looked for work at some time during the year is between 12.9% and 13.3%, and 19 chances in 20 that the proportion is within the range 12.7% to 13.5%.
14 Published estimates may also be used to calculate the difference between two survey estimates (of numbers or percentages). Such an estimate is subject to sampling error. The sampling error of the difference between two estimates depends on their SEs and the relationship (correlation) between them. An approximate SE of the difference between two estimates (x-y) may be calculated by the following formula:
15 While this formula will only be exact for differences between separate and uncorrelated characteristics or subpopulations, it is expected to provide a good approximation for all differences likely to be of interest in this publication.
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