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.

Copyright 2000. Dr. Roland Jeske