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 |
So-called "weighted probability of survival" |
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:

- 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. - 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.

Copyright 2000. Dr. Roland Jeske |