TFQA: Tools for Quantitative Archaeology - Statistical Analysis Software for Archaeology TFQA
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### resampleBRED: Estimate Sampling Error for Brainerd-Robinson & Euclidean Distance Coefficients

resampleBRED provides a Monte Carlo estimate of the sampling error of the Brainerd Robinson coefficient and Euclidean Distance Coefficient (based on percents) of a sample drawn from a known population or of two samples drawn from the same population. Input consists of the population proportions (or counts) and the sample size or sample sizes to be drawn. Output consists of a table of probabilities of getting the same or lower BR coefficient (as or less similar) and the same or greater Euclidean Distance Coefficient between a sample of the specified size drawn from the population and the population itself or between two different samples drawn from the population. A histogram is also provided. This program replaces the BRSample program (it includes all of the functionality of that program and adds computations for Euclidean Distance computations. The program was initially developed for Brainderd-Robinson Coefficients based on a suggestion from Warren DeBoer of Queens College and is described and used in DeBoer et al. (1996).

SAMPLE PROGRAM RUN

```File or Device for Output (CON for Screen) {CON} ?
Random Generator Seed (0 to set from clock) {0} ?
Read Population Data from [K]eyboard or a [F]ile {K} ?
Number of Types in the Population ? 4
Population Proportion (or % or Count) ? 12
Population Proportion (or % or Count) ? 31
Population Proportion (or % or Count) ? 64
Population Proportion (or % or Count) ? 133
Input Total =  240.00

[P]opulation-Sample or [S]ample-Sample Similarity {P} ?
Sample Size {100} ?
Number of Monte Carlo Trials {10000} ?
100%
Population-Sample Similarity  Sample Size=20  Trials=10000  BR Mean=173.47  BR Std= 12.00  ED Mean= 15.24  ED Std= 12.00
Rerun Using Same Population {Y} ?
Rerun Using Different Population {N} ?```

SAMPLE PROGRAM OUTPUT

```Estimate Sampling Error for Brainder-Robinson
and Euclidean Distance Coefficients
(c) Keith W. Kintigh, Arizona State University, 2007

Monte-Carlo samples with specified sample sizes are drawn with
replacement from a single population with given type proportions.
The proportion of Monte Carlo trials with a similarity coefficient
<= K or a distance coefficient >= K estimates the probability of
obtaining by chance a value as or more extreme than K between the
sample and the population, or between two samples.

Thus, a cumulative probability of 0.350 associated with a similarity
coefficient of 150 indicates that 35% of the time a similarity of 150
or less would be obtained by chance, suggesting no significant difference.

Population Percents (4 Types): Type-Pct
1 -   5.00   2 -  12.92   3 -  26.67   4 -  55.42

Population-Sample Similarity  Sample Size=100  Trials=10000
BR Mean=188.04  BR Std=  5.66  ED Mean=  7.05  ED Std=  5.66

B-R Probability Estimates Based on % of Trials - (B-R Coeff, Prob, Cum Prob)
199:0.005,1.000 198:0.007,0.996 197:0.024,0.989 196:0.023,0.965 195:0.059,0.942
194:0.039,0.884 193:0.081,0.844 192:0.049,0.763 191:0.103,0.714 190:0.049,0.611
189:0.103,0.562 188:0.033,0.459 187:0.098,0.426 186:0.024,0.328 185:0.072,0.304
184:0.018,0.232 183:0.061,0.214 182:0.011,0.153 181:0.047,0.142 180:0.005,0.095
179:0.033,0.090 178:0.003,0.057 177:0.021,0.054 176:0.001,0.033 175:0.013,0.032
174:0.001,0.019 173:0.008,0.018 172:0.000,0.010 171:0.004,0.010 170:0.000,0.006
169:0.003,0.006 168:0.000,0.003 167:0.002,0.003 166:0.000,0.001 165:0.001,0.001
164:0.000,0.000 163:0.000,0.000 162:0.000,0.000 161:0.000,0.000

E-D Probability Estimates Based on % of Trials - (E-D Coeff, Prob, Cum Prob)
1:0.013,0.000   2:0.039,0.013   3:0.082,0.052   4:0.106,0.134   5:0.129,0.240
6:0.126,0.369   7:0.111,0.496   8:0.102,0.607   9:0.072,0.709  10:0.063,0.781
11:0.049,0.844  12:0.036,0.893  13:0.024,0.929  14:0.018,0.953  15:0.011,0.971
16:0.007,0.981  17:0.004,0.988  18:0.003,0.992  19:0.002,0.995  20:0.001,0.997
21:0.001,0.999  22:0.000,0.999  23:0.000,0.999  24:0.000,1.000  25:0.000,1.000

B-R   Num of  Pct of  Cumulative
Coeff  Trials  Trials    Percent   Histogram (*=60 trials)
200-198    114     1.1 100.0- 98.9 |**
197-195   1051    10.5  98.9- 88.3 |******************
194-192   1694    16.9  88.3- 71.4 |****************************
191-189   2549    25.5  71.4- 45.9 |******************************************
188-186   1555    15.6  45.9- 30.4 |**************************
185-183   1503    15.0  30.4- 15.3 |*************************
182-180    639     6.4  15.3-  9.0 |***********
179-177    568     5.7   9.0-  3.3 |*********
176-174    149     1.5   3.3-  1.8 |**
173-171    119     1.2   1.8-  0.6 |**
170-168     30     0.3   0.6-  0.3 |
167-165     27     0.3   0.3-  0.0 |
164-162      0     0.0   0.0-  0.0 |
161-159      2     0.0   0.0-  0.0 |

E-D   Num of  Pct of  Cumulative
Coeff  Trials  Trials    Percent   Histogram (*=56 trials)
0-  1    131     1.3   2.6-  1.3 |**
2-  3   1209    12.1  25.5- 13.4 |**********************
4-  5   2353    23.5  60.5- 36.9 |******************************************
6-  7   2373    23.7  84.4- 60.7 |******************************************
8-  9   1743    17.4  95.5- 78.1 |*******************************
10- 11   1121    11.2 100.5- 89.3 |********************
12- 13    600     6.0 101.3- 95.3 |***********
14- 15    282     2.8 100.9- 98.1 |*****
16- 17    109     1.1 100.3- 99.2 |**
18- 19     51     0.5 100.2- 99.7 |*
20- 21     22     0.2 100.2- 99.9 |
22- 23      4     0.0 100.0-100.0 |
24- 25      2     0.0 100.0-100.0 |
```

Page Last Updated: 21June 2022

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