Part VI: Appendices

Appendix A1: Number of Killings and Disappearances by Year, 1959-1995

Appendix A2: Number of Killings and Disappearances by Source, by Month and Year, July 1979 to December 1983

Appendix A3: Percent of All Killings that are Rural and Percent of All Killings in Groups of Size 10+, by Year

Appendix A4: Top Five Years for Killings, by Rural and Urban Areas

Appendix A5: Monthly Seasonal Variation Analysis

Visual inspection of the seasonal monthly patterns of killings and disappearances in urban (Figure 12.1) and rural (Figure 12.2) areas shows a declining level of violations throughout the year in both areas, with a pronounced rise in numbers of violations from December to January (month 12 to month 13 on the horizontal axis).

The purpose of this analysis is to determine the probability that this pattern could have occurred by chance, if the numbers of violations were obtained from random samples. To make this comparison, we will first remove some of the extreme variability in the monthly values and then set up a time series model from which we can test the hypothesis of non-randomness in the monthly pattern.

We remove a known source of high variability in the means shown in Figures 12.1 and 12.2. The 37 annual killings and disappearances have the means, standard deviations, and ranges shown in Figure A5.1 below.

Figure A5.1. Mean, standard deviation, and range of the annual number of killings and disappearances in rural and urban areas, 1959 to 1995 by year (n=37)

This high level of variability is due to the extremely high numbers of violations reported during the years 1980-1985. Extremely high values, even if few in number, have a high influence on a parametric measure such as the mean. For that reason, we measure the monthly fluctuations in these violations by finding the ratios f of the monthly value to the annual total, following the conventional time series analysis approach.1

The monthly data are arrayed in a two-way table of 444 values:

yij, where i = 1959, …, 1995, and j = 1, …, 12.

The monthly ratios are:

fij = yij/y.j, for j=1959 to 1995

where yij is the monthly value, and "." indicates a summation over the variable replaced by ".".

The values plotted in Figure A5.2 are the means:

mj = f.j/37 , for j = 1, …, 12.

Figure A5.2. Means of ratio of monthly number of killings and disappearances to the total annual number occurring in rural and urban areas, 1959 to 1995 by year (n=37)

Figure A5.2 shows the revised plot of the monthly seasonal pattern, expressed in the mj, the mean of the ratios of monthly value to the annual total.

The essential element of these urban and rural series—the apparent decline through the year—is similar in Figures 12.1, 12.2, and A5.2.

We also separately analyze the time series for the period of the most extreme violations, 1980-1985. Figure A5.3 shows the time series plots for this period.

Figure A5.3. Means of ratio of monthly number of killings and disappearances to the total annual number occurring in rural and urban areas, 1980 to 1985 by year (n=6)

If the values yij were random selections, the m.j would be a time series of m=12 independent values of a random variable. Under these conditions, there would be zero autocorrelation. Because of the small number (m-12) of points in this series, the usual tests for autocorrelation (Durbin-Watson, or autocorrelation function) will have little statistical power. Controlling a, the probability of Type I error at the usual levels would lead to an extremely low power (1-b, the probability of Type II error).

For that reason, we choose as our test statistic the duration of completed like-sign runs of the time-ordered residuals above and below the mean of the ratios (Bowerman 1987, p. 470; Cowden 1957):

The primary statistic is the d, the duration of completed runs of like sign. The observed frequencies of runs of given duration are compared to the expected frequencies and tested by with the c2-test.

To determine d, each value mj is compared to 0.0833 (1/12), since by definition, m•º 1. The expected numbers of completed runs xd of like sign with a given duration d is (Wallis 1941):

xd = (n-d-1)/2d+1, d = 1, …, 11

We apply the method described above to the full series for urban and rural killings and disappearances (1959-1995) and then for the shortened urban and rural series covering the period of extreme numbers of violations (1980-1985). For the latter series, i = 1980, …, 1985, and mj = fij/6.

Urban, 1959-1995

For the urban series, the signs of the deviations, retaining the original order is:

+ + - + + + - - - - - -

The number of completed runs of size d = 1 to 6 is:

The value of c2 is 25.37, the degrees of freedom are n = 5, and the probability of the occurrence of this value if H0 is true is p = 0.00012.

Rural, 1959-1995

For the rural series, the signs of the deviations, retaining the original order is:

+ - + + + + - - - - - -

The number of completed runs of size d = 1 to 6 is:

The value of c2 is 29.05, the degrees of freedom are n = 5, and the probability of the occurrence of this value if H0 is true is p = 0.000023.

Urban, 1980-1985

For the urban series, the signs of the deviations, retaining the original order is:

+ + - - + + + - + - - -

The number of completed runs of size d = 1 to 3 is:

The value of c2 is 5.28, the degrees of freedom are n = 5, and the probability of the occurrence of this value if H0 is true is p = 0.07.

Rural, 1980-1985

For the rural series, the signs of the deviations, retaining the original order is:

+ + + + - - + + - - - -

The number of completed runs of size d = 1 to 4 is:

The value of c2 is 18.2, the degrees of freedom are n = 5, and the probability of the occurrence of this value if H0 is true is p = 0.0004.

The summary of results follows in Figure 5.4.

Figure A5.4. Summary of tests of hypothesis of homogeneity of series with respect to completed runs of like size.

** denotes a high level of statistical signficance

The results of these hypothesis tests lead us to this conclusion. If the monthly numbers of violations were the result of random selection, the downward trend of Figures 12.1, 12.2, and A5.2 would be extremely unlikely to have occurred by chance in rural areas for 1959-1995 and 1980-1985, and for urban areas during the period 1959-1995.

Appendix A6: Number of Killings and Percent Overkill by Group Size and Department

Appendix A7: Identifying Perpetrators by Geographic Area and Source Type

Why do violations that happen in urban areas so rarely have identified perpetrators? This appendix considers this question in terms of the differences in the sources of the data for urban and rural areas.

Table A7.1. Percent of rural and urban killings and disappearances with and without identified perpetrators

From A7.1, note that about two-thirds of all rural killings have at least one identified perpetrator, whereas urban killings have no identified perpetrator for over 80% of killings and disappearances. The lack of data on perpetrators in urban areas results from the data source: most of the data on urban killings in the CIIDH database comes from the press (see Table A7.2), and the press rarely reports who the perpetrators are alleged to have been (see Table A7.3). In Table A7.2, note that data on killings in the rural areas comes mostly from documentary sources (61%), whereas data on urban killings comes mostly from press sources (77%).

Table A7.2. Percent of rural and urban killings and disappearances by source type

The closer the data are to the primary source, the more likely it is that the perpetrators of killings will be identified. However, it is also true that relative to rural killings, urban killings are more likely to be committed by paramilitary units, and are consequently more difficult to identify. As discussed in the text, rural killings were most frequently committed by army units operating openly.

Table A7.3. Percent of killings and disappearances by source type, with and without identified perpetrators