TFQA: Tools for Quantitative Archaeology - Statistical Analysis Software for Archaeology TFQA
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### BRSAMPLE: Brainerd-Robinson Coefficient Differences Due to Sampling Error

BRSAMPLE provides a Monte Carlo estimate of the sampling error of the Brainerd Robinson coefficient 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) 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. The program was developed based on a suggestion from Warren DeBoer of Queens College and is described and used in DeBoer et al. (1996).

Note: This program has been replaced by resampleBRED. It does everything that BRsample does, but adds calculations for Euclidean Distance Coefficients based on Percents.

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 {1000} ?
100%
Brainerd Robinson  Population-Sample Similarity
Sample Size=100  Mean=188.09  Std=  5.31  Trials=1000
Rerun Using Same Population {Y} ?
Rerun Using Different Population {N} ?```

SAMPLE PROGRAM OUTPUT

```Estimate Sampling Error in Brainerd-Robinson Similarity Coefficient
(c) Keith W. Kintigh, Arizona State University, 1992

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 BR Coefficient <= K
estimates the probability of obtaining by chance a similarity of K
or less between the sample and the population, or between two samples.
Thus, a cumulative probability of 0.350 associated with a 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

Brainerd Robinson  Population-Sample Similarity
Sample Size=100  Mean=188.09  Std=  5.31  Trials=1000
Probability Estimates Based on % of Trials - (BR Coeff: Prob, Cum Prob)
199:0.002,1.000 198:0.007,0.998 197:0.020,0.991 196:0.023,0.971 195:0.055,0.948
194:0.043,0.893 193:0.084,0.850 192:0.038,0.766 191:0.090,0.728 190:0.051,0.638
189:0.109,0.587 188:0.049,0.478 187:0.097,0.429 186:0.033,0.332 185:0.095,0.299
184:0.020,0.204 183:0.059,0.184 182:0.008,0.125 181:0.031,0.117 180:0.004,0.086
179:0.036,0.082 178:0.003,0.046 177:0.020,0.043 176:0.002,0.023 175:0.009,0.021
174:0.001,0.012 173:0.005,0.011 172:0.000,0.006 171:0.003,0.006 170:0.000,0.003
169:0.001,0.003 168:0.000,0.002 167:0.000,0.002 166:0.000,0.002 165:0.001,0.002
164:0.000,0.001 163:0.001,0.001

Brainerd Robinson  Population-Sample Similarity
Sample Size=100  Mean=188.09  Std=  5.31  Trials=1000
B-R   Num of  Pct of  Cumulative
Coeff  Trials  Trials    Percent   Histogram (*=4 trials)
200-199      2     0.2 100.0- 99.8 |
198-197     27     2.7  99.8- 97.1 |*******
196-195     78     7.8  97.1- 89.3 |********************
194-193    127    12.7  89.3- 76.6 |********************************
192-191    128    12.8  76.6- 63.8 |********************************
190-189    160    16.0  63.8- 47.8 |****************************************
188-187    146    14.6  47.8- 33.2 |************************************
186-185    128    12.8  33.2- 20.4 |********************************
184-183     79     7.9  20.4- 12.5 |********************
182-181     39     3.9  12.5-  8.6 |**********
180-179     40     4.0   8.6-  4.6 |**********
178-177     23     2.3   4.6-  2.3 |******
176-175     11     1.1   2.3-  1.2 |***
174-173      6     0.6   1.2-  0.6 |**
172-171      3     0.3   0.6-  0.3 |*
170-169      1     0.1   0.3-  0.2 |
168-167      0     0.0   0.2-  0.2 |
166-165      1     0.1   0.2-  0.1 |
164-163      1     0.1   0.1-  0.0 |```

Page Last Updated: 17 October 2020

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