Scenario Calculation for Spoerer's Projection

The following scenario calculation for Mr. Spoerer's projection will reveal that his analysis leads to distorted results and false conclusions.

For the moment being, let us assume that his data concerning the forced labor workers from Eastern Europe (given in Table A 2.1 in Mr. Spoerer's work) are accurate. Let us further assume that, after multiplying these data by a factor of 1000, they reflect the distribution of Ukrainian forced labor workers in 1945. This distribution can then be described as in Table 1.

Table 1: The distribution of Ukrainian forced labor workers in 1945, according to Mr. Spoerer's data.

 Year Male Female Both before 1908 137,000 63,000 200,000 1908 - 1912 59,000 38,000 97,000 1913 - 1917 48,000 75,000 123,000 1918 - 1922 62,000 226,000 288,000 1923 - 1927 207,000 523,000 730,000 1928 - 1932 47,000 61,000 108,000 Total 560,000 986,000 1,546,000

The contingency between the variables gender and age can be captured by several measures. We chose to calculate the so-called Phi-Coefficient:

Let us now suppose that Mr. Spoerer's probabilities of survival are accurate. This implies that the probabilities of being alive in 1997, conditional on the fact that the respective age class has survived 1945, can be calculated as in Table 2.

Table 2: Probabilities of survival (in percent) in 1997 for selected age classes of the Ukrainian population that have survived 1945 (according to Mr. Spoerer).

 Year Male Population Female Population before 1908 0.1 % 1.9 % 1908 - 1912 0.7 % 9.0 % 1913 - 1917 7.5 % 23.0 % 1918 - 1922 18.6 % 41.8 % 1923 - 1927 31.6 % 59.4 % 1928 - 1932 43.5 % 71.9 %

Assembling the information contained in Table 1 and 2, we are now able to calculate the expected population of the Ukrainian population in 1997, based on age classes.

Table 3: Expected Ukrainian population in 1997 (in age classes).

 Year Male Female Both before 1908 137 1,197 1,334 1908 - 1912 413 3,420 3,833 1913 - 1917 3,600 17,250 20,850 1918 - 1922 11,532 94,468 106,000 1923 - 1927 65,412 310,662 376,074 1928 - 1932 20,445 43,859 64,304 Total 101,539 470,856 572,395

Based on the population given in Table 3 the following Phi-Coefficient can be derived:

Obviously, this value differs considerably from the corresponding value in 1945. From a statistical point of view, this difference was expected. The reason is the higher life expectancy of women. This leads to a different distribution of the population with respect to gender in 1997 as compared to 1945.

We now ask what happens to the non-gender specified age distribution from Table 3, if one employs Mr. Spoerer's technique. This can be inferred from Table 4.

Table 4: Continuation of the scenario calculation using Mr. Spoerer's technique

 Year Survivors in 1997 in scenario calculation (cf. Tab. 3) So-called "weighted probability of survival" (in %) So-called "share 1997" (in %) So-called "survivors 1997" according to Spoerer's technique Corresponding projections for 1945 Total male female male female male female male female before 1908 1,334 0.1 1.9 4.8 95.2 64 1,270 64,000 66,842 130,842 1908 - 1912 3,833 0.7 9.2 7.3 92.7 280 3,553 40,000 39,478 79,478 1913 - 1917 20,850 7.3 23.5 23.8 76.2 4,962 15,888 66,160 69,078 135,238 1918 - 1922 106,000 18.1 42.8 29.8 70.2 31,588 74,412 169,827 178,019 347,846 1923 - 1927 376,074 30.9 60.7 33.7 66.3 126,737 249,337 401,066 419,759 820,825 1928 - 1932 64,304 42.5 73.5 36.7 63.3 23,600 40,704 54,253 56,612 110,865 Total 572,395 187,231 385,164 795,306 829,788 1,625,094

Summary:

By using this technique, any conclusions can be drawn. Therefore, the results of Spoerer's analysis have to be rejected. The major effects ensuing from Spoerer's faulty analysis include (i) a mis-specification of some classes by more than 100 percent, (ii) a difference between the resulting marginal distributions and the one that can be found in the original data set, and (iii) a change in the size of the data set.

The statistical fallacies Mr. Spoerer succumbed to can be expressed as follows:

1. Based on two marginal distributions, it is impossible to draw any conclusions regarding their common distribution when the variables under consideration are dependend. If the marginal distributions are classified with K, respectively L classes, the additional information of (K-1)(L-1) entries of the common distribution is indispensable in order to specify the common distribution accurately.
2. The structure of dependence between the variables gender and age in 1945 deviates from the one existing in 1997. This is due to a different life expectancy between the two genders. Even if some properties of the structure of dependence were known, Spoerer's technique would be infeasible.