Index > Appendixes >

E.3 Interpreting survey results

Contents:
E.3.1 Probability of detecting an area with an elevated contamination;
E.3.2 Stem and leaf display:
E.3.3 Quantile plots

E.3.1 Probability of detecting an area with an elevated contamination

Table E.7 Risk that an elevated area with length l/g and shape s will not be detected and the area (%) of the elevated area relative to a triangular sample grid area of 0.866 G2

Shape Parameter, S
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
L/G Risk Area Risk Area Risk Area Risk Area Risk Area Risk Area Risk Area Risk Area Risk Area Risk Area
0.01 1 <1% 1 <1% 1 <1% 1 <1% 1 <1% 1 <1% 1 <1% 1 <1% 1 <1% 1 <1%
0.02 1 <1% 1 <1% 1 <1% 1 <1% 1 <1% 1 <1% 1 <1% 1 <1% 1 <1% 1 <1%
0.03 1 <1% 1 <1% 1 <1% 1 <1% 1 <1% 1 <1% 1 <1% 1 <1% 1 <1% 1 <1%
0.04 1 <1% 1 <1% 1 <1% 1 <1% 1 <1% 1 <1% 1 <1% 1 <1% 0.99 1% 0.99 1%
0.05 1 <1% 1 <1% 1 <1% 1 <1% 1 <1% 0.99 1% 0.99 1% 0.99 1% 0.99 1% 0.99 1%
0.06 1 <1% 1 <1% 1 <1% 0.99 1% 0.99 1% 0.99 1% 0.99 1% 0.99 1% 0.99 1% 0.99 1%
0.07 1 <1% 1 <1% 0.99 1% 0.99 1% 0.99 1% 0.99 1% 0.99 1% 0.99 1% 0.98 2% 0.98 2%
0.08 1 <1% 1 <1% 0.99 1% 0.99 1% 0.99 1% 0.99 1% 0.98 2% 0.98 2% 0.98 2% 0.98 2%
0.09 1 <1% 0.99 1% 0.99 1% 0.99 1% 0.99 1% 0.98 2% 0.98 2% 0.98 2% 0.97 3% 0.97 3%
0.10 1 <1% 0.99 1% 0.99 1% 0.99 1% 0.98 2% 0.98 2% 0.97 3% 0.97 3% 0.97 3% 0.96 4%
0.11 0.99 1% 0.99 1% 0.99 1% 0.98 2% 0.98 2% 0.97 3% 0.97 3% 0.96 4% 0.96 4% 0.96 4%
0.12 0.99 1% 0.99 1% 0.98 2% 0.98 2% 0.97 3% 0.97 3% 0.96 4% 0.96 4% 0.95 5% 0.95 5%
0.13 0.99 1% 0.99 1% 0.98 2% 0.98 2% 0.97 3% 0.96 4% 0.96 4% 0.95 5% 0.94 6% 0.94 6%
0.14 0.99 1% 0.99 1% 0.98 2% 0.97 3% 0.96 4% 0.96 4% 0.95 5% 0.94 6% 0.94 6% 0.93 7%
0.15 0.99 1% 0.98 2% 0.98 2% 0.97 3% 0.96 4% 0.95 5% 0.94 6% 0.93 7% 0.93 7% 0.92 8%
0.16 0.99 1% 0.98 2% 0.97 3% 0.96 4% 0.95 5% 0.94 6% 0.94 6% 0.93 7% 0.92 8% 0.91 9%
0.17 0.99 1% 0.98 2% 0.97 3% 0.96 4% 0.95 5% 0.94 6% 0.93 7% 0.92 8% 0.91 9% 0.9 10%
0.18 0.99 1% 0.98 2% 0.96 4% 0.95 5% 0.94 6% 0.93 7% 0.92 8% 0.91 9% 0.89 11% 0.88 12%
0.19 0.99 1% 0.97 3% 0.96 4% 0.95 5% 0.93 7% 0.92 8% 0.91 9% 0.9 10% 0.88 12% 0.87 13%
0.20 0.99 1% 0.97 3% 0.96 4% 0.94 6% 0.92 8% 0.91 9% 0.9 10% 0.88 12% 0.87 13% 0.85 15%
0.21 0.98 2% 0.97 3% 0.95 5% 0.94 6% 0.92 8% 0.9 10% 0.89 11% 0.87 13% 0.86 14% 0.84 16%
0.22 0.98 2% 0.96 4% 0.95 5% 0.93 7% 0.91 9% 0.89 11% 0.88 12% 0.86 14% 0.84 16% 0.82 18%
0.23 0.98 2% 0.96 4% 0.94 6% 0.92 8% 0.9 10% 0.88 12% 0.87 13% 0.85 15% 0.83 17% 0.81 19%
0.24 0.98 2% 0.96 4% 0.94 6% 0.92 8% 0.9 10% 0.87 13% 0.85 15% 0.83 17% 0.81 19% 0.79 21%
0.25 0.98 2% 0.95 5% 0.93 7% 0.91 9% 0.89 11% 0.86 14% 0.84 16% 0.82 18% 0.8 20% 0.77 23%
0.26 0.98 25 0.95 5% 0.93 7% 0.9 10% 0.88 12% 0.85 15% 0.83 17% 0.8 20% 0.78 22% 0.75 25%
0.27 0.97 3% 0.95 5% 0.92 8% 0.89 11% 0.87 13% 0.84 16% 0.81 19% 0.79 21% 0.76 24% 0.74 26%
0.28 0.97 35 0.94 6% 0.91 9% 0.89 11% 0.86 14% 0.83 17% 0.8 20% 0.77 23% 0.74 26% 0.72 28%
0.29 0.97 3% 0.94 6% 0.91 9% 0.88 12% 0.85 15% 0.82 18% 0.79 21% 0.76 24% 0.73 27% 0.69 31%
0.30 0.97 3% 0.93 7% 0.9 10% 0.87 13% 0.84 16% 0.8 20% 0.77 23% 0.74 26% 0.71 29% 0.67 33%
0.31 0.97 3% 0.93 7% 0.9 10% 0.86 14% 0.83 17% 0.79 21% 0.76 24% 0.72 28% 0.69 31% 0.65 35%
0.32 0.96 4% 0.93 7% 0.89 11% 0.85 15% 0.81 19% 0.78 22% 0.74 26% 0.7 30% 0.67 33% 0.63 37%
0.33 0.96 45 0.92 8% 0.88 12% 0.84 16% 0.8 20% 0.76 24% 0.72 28% 0.68 32% 0.64 36% 0.61 40%
0.34 0.96 45 0.92 8% 0.87 13% 0.83 17% 0.79 21% 0.75 25% 0.71 29% 0.66 34% 0.62 38% 0.58 42%
0.35 0.96 4% 0.91 9% 0.87 13% 0.82 18% 0.78 22% 0.73 27% 0.69 31% 0.64 36% 0.6 40% 0.56 44%
0.36 0.95 5% 0.91 9% 0.86 14% 0.81 19% 0.76 24% 0.72 28% 0.67 33% 0.62 38% 0.58 42% 0.53 47%
0.37 0.95 5% 0.9 10% 0.85 15% 0.8 20% 0.75 25% 0.7 30% 0.65 35% 0.6 40% 0.55 45% 0.5 50%
0.38 0.95 5% 0.9 10% 0.84 16% 0.79 21% 0.74 26% 0.69 31% 0.63 37% 0.58 42% 0.53 47% 0.48 52%
0.39 0.94 6% 0.89 11% 0.83 17% 0.78 22% 0.72 28% 0.67 33% 0.61 39% 0.56 44% 0.5 50% 0.45 55%
0.40 0.94 6% 0.88 12% 0.83 17% 0.77 23% 0.71 29% 0.65 35% 0.59 41% 0.54 46% 0.48 52% 0.42 58%
0.41 0.94 6% 0.88 12% 0.82 18% 0.76 24% 0.7 30% 0.63 37% 0.57 43% 0.51 49% 0.45 55% 0.39 61%
0.42 0.94 6% 0.87 13% 0.81 19% 0.74 26% 0.68 32% 0.62 38% 0.55 45% 0.49 51% 0.42 58% 0.36 64%
0.43 0.93 7% 0.87 13% 0.8 20% 0.73 27% 0.66 34% 0.6 40% 0.53 47% 0.46 54% 0.4 60% 0.33 67%
0.44 0.93 7% 0.86 14% 0.79 21% 0.72 28% 0.65 35% 0.58 42% 0.51 49% 0.44 56% 0.37 63% 0.3 70%
0.45 0.93 7% 0.85 15% 0.78 22% 0.71 29% 0.63 37% 0.56 44% 0.49 51% 0.41 59% 0.34 66% 0.27 73%
0.46 0.92 8% 0.85 15% 0.77 23% 0.69 31% 0.62 38% 0.54 46% 0.46 54% 0.39 61% 0.31 69% 0.23 77%
0.47 0.92 8% 0.84 16% 0.76 24% 0.68 32% 0.6 40% 0.52 48% 0.44 56% 0.36 64% 0.28 72% 0.2 80%
0.48 0.92 8% 0.83 17% 0.75 25% 0.67 33% 0.58 42% 0.5 50% 0.41 59% 0.33 67% 0.25 75% 0.16 84%
0.49 0.91 9% 0.83 17% 0.74 26% 0.65 35% 0.56 44% 0.48 52% 0.39 61% 0.3 70% 0.22 78% 0.13 87%
0.50 0.91 9% 0.82 18% 0.73 27% 0.64 36% 0.55 45% 0.46 54% 0.37 63% 0.27 73% 0.18 82% 0.09 91%
0.51 0.91 9% 0.81 19% 0.72 28% 0.62 38% 0.53 47% 0.43 57% 0.34 66% 0.25 75% 0.15 85% 0.07 94%
0.52 0.9 10% 0.8 20% 0.71 29% 0.61 39% 0.51 49% 0.41 59% 0.32 69% 0.22 78% 0.13 88% 0.05 98%
0.53 0.9 10% 0.8 20% 0.7 31% 0.59 41% 0.49 51% 0.39 61% 0.29 71% 0.19 82% 0.1 92% 0.03 102%
0.54 0.89 11% 0.79 21% 0.68 32% 0.58 42% 0.47 53% 0.37 63% 0.27 74% 0.17 85% 0.08 95% 0.02 106%
0.55 0.89 11% 0.78 22% 0.67 33% 0.56 44% 0.46 55% 0.35 66% 0.24 77% 0.14 88% 0.06 99% 0.01 110%
0.56 0.89 11% 0.77 23% 0.66 34% 0.55 46% 0.44 57% 0.33 68% 0.22 80% 0.12 91% 0.04 102% 0 114%
0.57 0.88 12% 0.77 23% 0.65 35% 0.54 47% 0.42 59% 0.31 71% 0.2 83% 0.1 94% 0.02 106% 0 118%
0.58 0.88 12% 0.76 24% 0.64 37% 0.52 49% 0.4 61% 0.29 73% 0.18 85% 0.08 98% 0.01 110% 0 122%
0.59 0.87 13% 0.75 25% 0.63 38% 0.51 51% 0.39 63% 0.27 76% 0.16 88% 0.06 101% 0 114% 0 126%
0.60 0.87 13% 0.74 26% 0.62 39% 0.49 52% 0.37 65% 0.25 78% 0.14 91% 0.04 104% 0 118% 0 131%
0.61 0.87 13% 0.73 27% 0.6 40% 0.48 54% 0.35 67% 0.23 81% 0.12 94% 0.03 108% 0 121% 0 135%
0.62 0.86 14% 0.73 28% 0.59 42% 0.46 56% 0.34 70% 0.21 84% 0.1 98% 0.02 112% 0 126% 0 139%
0.63 0.86 14% 0.72 29% 0.58 43% 0.45 58% 0.32 72% 0.2 86% 0.09 101% 0.01 115% 0 130% 0 144%
0.64 0.85 15% 0.71 30% 0.57 45% 0.43 59% 0.3 74% 0.18 89% 0.07 104% 0 119% 0 134% 0 149%
0.65 0.85 15% 0.7 31% 0.56 46% 0.42 61% 0.29 77% 0.16 92% 0.06 107% 0 123% 0 138% 0 153%
0.66 0.84 16% 0.69 32% 0.55 47% 0.4 63% 0.27 79% 0.15 95% 0.05 111% 0 126% 0 142% 0 158%
0.67 0.84 16% 0.68 33% 0.53 49% 0.39 65% 0.25 81% 0.13 98% 0.03 114% 0 130% 0 147% 0 163%
0.68 0.84 17% 0.68 34% 0.52 50% 0.38 67% 0.24 84% 0.12 101% 0.02 117% 0 134% 0 151% 0 168%
0.69 0.83 17% 0.67 35% 0.51 52% 0.36 69% 0.22 86% 0.1 104% 0.01 121% 0 138% 0 155% 0 173%
0.70 0.83 18% 0.66 36% 0.5 53% 0.35 71% 0.21 89% 0.09 107% 0.01 124% 0 142% 0 160% 0 178%
0.71 0.82 18% 0.65 37% 0.49 55% 0.33 73% 0.2 91% 0.08 110% 0 128% 0 146% 0 165% 0 183%
0.72 0.82 19% 0.64 38% 0.48 56% 0.32 75% 0.18 94% 0.07 113% 0 132% 0 150% 0 169% 0 188%
0.73 0.81 19% 0.63 39% 0.46 58% 0.31 77% 0.17 97% 0.05 116% 0 135% 0 155% 0 174% 0 193%
0.74 0.81 20% 0.62 40% 0.45 60% 0.29 79% 0.15 99% 0.04 119% 0 139% 0 159% 0 179% 0 199%
0.75 0.8 20% 0.61 41% 0.44 61% 0.28 82% 0.14 102% 0.04 122% 0 143% 0 163% 0 184% 0 204%
0.76 0.8 21% 0.61 42% 0.43 63% 0.27 84% 0.13 105% 0.03 126% 0 147% 0 168% 0 189% 0 210%
0.77 0.79 22% 0.6 43% 0.42 65% 0.25 86% 0.12 108% 0.02 129% 0 151% 0 172% 0 194% 0 215%
0.78 0.79 22% 0.59 44% 0.4 66% 0.24 88% 0.1 110% 0.01 132% 0 154% 0 177% 0 199% 0 221%
0.79 0.78 23% 0.58 45% 0.39 68% 0.23 91% 0.09 113% 0.01 136% 0 158% 0 181% 0 204% 0 226%
0.80 0.78 23% 0.57 46% 0.38 70% 0.22 93% 0.08 116% 0 139% 0 163% 0 186% 0 209% 0 232%
0.81 0.77 24% 0.56 48% 0.37 71% 0.2 95% 0.07 119% 0 143% 0 167% 0 190% 0 214% 0 238%
0.82 0.77 24% 0.55 49% 0.36 73% 0.19 98% 0.06 122% 0 146% 0 171% 0 195% 0 220% 0 244%
0.83 0.76 25% 0.54 50% 0.35 75% 0.18 100% 0.05 125% 0 150% 0 175% 0 200% 0 225% 0 250%
0.84 0.76 26% 0.53 51% 0.33 77% 0.17 102% 0.05 128% 0 154% 0 179% 0 205% 0 230% 0 256%
0.85 0.75 26% 0.52 52% 0.32 79% 0.16 105% 0.04 131% 0 157% 0 183% 0 210% 0 236% 0 262%
0.86 0.74 27% 0.51 54% 0.31 80% 0.14 107% 0.03 134% 0 161% 0 188% 0 215% 0 241% 0 268%
0.87 0.74 27% 0.5 55% 0.3 82% 0.13 110% 0.02 137% 0 165% 0 192% 0 220% 0 247% 0 275%
0.88 0.73 28% 0.5 56% 0.29 84% 0.12 112% 0.02 140% 0 169% 0 197% 0 225% 0 253% 0 281%
0.89 0.73 29% 0.49 57% 0.28 86% 0.11 115% 0.01 144% 0 172% 0 201% 0 230% 0 259% 0 287%
0.90 0.72 29% 0.48 59% 0.27 88% 0.1 118% 0.01 147% 0 176% 0 206% 0 235% 0 264% 0 294%
0.91 0.72 30% 0.47 60% 0.26 90% 0.1 120% 0.01 150% 0 180% 0 210% 0 240% 0 270% 0 300%
0.92 0.71 31% 0.46 61% 0.25 92% 0.09 123% 0 154% 0 184% 0 215% 0 246% 0 276% 0 307%
0.93 0.71 31% 0.45 63% 0.24 94% 0.08 126% 0 157% 0 188% 0 220% 0 251% 0 282% 0 314%
0.94 0.7 32% 0.44 64% 0.23 96% 0.07 128% 0 160% 0 192% 0 224% 0 256% 0 288% 0 321%
0.95 0.69 33% 0.43 65% 0.22 98% 0.07 131% 0 164% 0 196% 0 229% 0 262% 0 295% 0 327%
0.96 0.69 33% 0.42 67% 0.21 100% 0.06 134% 0 167% 0 201% 0 234% 0 267% 0 301% 0 334%
0.97 0.68 34% 0.41 68% 0.2 102% 0.05 137% 0 171% 0 205% 0 239% 0 273% 0 307% 0 341%
0.98 0.68 35% 0.4 70% 0.19 105% 0.05 139% 0 174% 0 209% 0 244% 0 279% 0 314% 0 348%
0.99 0.67 36% 0.4 71% 0.18 107% 0.04 142% 0 178% 0 213% 0 249% 0 284% 0 320% 0 356%
1.00 0.67 36% 0.39 73% 0.17 109% 0.04 145% 0 181% 0 218% 0 254% 0 290% 0 326% 0 363%

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E.3.2 Stem and leaf display

The construction of a stem and leaf display is a simple way to generate a crude histogram of the data quickly. The ‘stems’ of such a display are the most significant digits of the data. Consider the sample data of Section 3.10.8.3:

  • 90.7, 83.5, 86.4, 88.5, 84.4, 74.2, 84.1, 87.6, 78.2, 77.6,
  • 86.4, 76.3, 86.5, 77.4, 90.3, 90.1, 79.1, 92.4, 75.5, 80.5.

Here the data span three decades, so one might consider using the stems 70, 80 and 90. However, three is too few stems to be informative, just as three intervals would be too few for constructing a histogram. Therefore, for this example, each decade is divided into two parts. This results in the six stems 70, 75, 80, 85, 90, 95. The leaves are the least significant digits, so 90.7 has the stem 90 and the leaf 0.7. 77.4 has the stem 75 and the leaf 7.4. Note that even though the stem is 75, the leaf is not 2.4. The leaf is kept as 7.4 so that the data can be read directly from the display without any calculations.

Stem Leaves
70 4.2
75 8.2, 7.6, 6.3, 7.4, 9.1, 5.5
80 3.5, 4.4, 4.1, 0.5
85 6.4, 8.5, 7.6, 6.4, 6.5
90 0.7, 0.3, 0.1, 2.4
95
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Stem Sorted Leaves
70 4.2
75 5.5, 6.3, 7.4, 7.6, 8.2, 9.1
80 0.5, 3.5, 4.1, 4.4
85 6.4, 6.4, 6.5, 7.6, 8.5
90 0.1, 0.3, 0.7, 2.4
95

Figure E.3 Example of a stem and leaf display.

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As shown in the top part of Figure E.3, simply arrange the leaves of the data into rows, one stem per row. The result is a quick histogram of the data. In order to ensure this, the same number of digits should be used for each leaf, so that each occupies the same amount of horizontal space.

If the stems are arranged in increasing order, as shown in the bottom half of Figure E.3, it is easy to pick out the minimum (74.2), the maximum (92.4), and the median (between 84.1 and 84.4).

A stem and leaf display (or histogram) with two peaks may indicate that residual radioactivity is distributed over only a portion of the survey unit. Further information on the construction and interpretation of data plots is given in [EPA-1996d].

E.3.3 Quantile plots

A quantile plot is constructed by first ranking the data from smallest to largest. Sorting the data is easy once the stem and leaf display has been constructed. Then, each data value is simply plotted against the percentage of the samples with that value or less. This percentage is computed from:

Percent = 100 (rank – 0.5) / (number of data points) …………………………………………… (E-8)

The results for the example data of Appendix E.3.2 are shown in Table E.8. The quantile plot for this example is shown in Figure E.4.

The slope of the curve in the quantile plot is an indication of the amount of data in a given range of values. A small amount of data in a range will result in a large slope. A large amount of data in a range of values will result in a more horizontal slope. A sharp rise near the bottom or the top is an indication of asymmetry. Sudden changes in slope or notably flat or notably steep areas may indicate peculiarities in the survey unit data needing further investigation.

Table E.8 Data for quantile plot

Data: 74.2 75.5 76.3 77.4 77.6 78.2 79.1 80.5 83.5 84.1
Rank: 1 2 3 4 5 6 7 8 9 10
Percent: 2.5 7.5 12.5 17.5 22.5 27.5 32.5 37.5 42.5 47.5
.
Data: 84.4 86.4 86.4 86.5 87.6 88.5 90.1 90.3 90.7 92.4
Rank: 11 12.5 12.5 14 15 16 17 18 19 20
Percent: 52.5 60.0 60.0 67.5 72.5 77.5 82.5 87.5 92.5 97.5

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A useful aid to interpreting the Quantile plot is the addition of boxes containing the middle 50% and middle 75% of the data. These are shown as the dashed lines in Figure E.4. The 50% box has its upper right corner at the 75th percentile and its lower left corner at the 25th percentile. These points are also called the Quartiles. These are ~78 and ~88, respectively, as indicated by the dashed lines. They bracket the middle half of the data values. The 75% box has its upper right corner at the 87.5th percentile and its lower left corner at the 12.5th percentile. A sharp increase within the 50% box can indicate two or more modes in the data. Outside the 75% box, sharp increases can indicate outliers. The median (50th percentile) is indicated by the heavy solid line at the value ~84, and can be used as an aid to judging the symmetry of the data distribution.
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Figure D.4 Example of a quantile plot.
Figure E.4 Example of a quantile plot.

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There are no especially unusual features in the example quantile plot shown in Figure E.4, other than the possibility of slight asymmetry around the median.

Another quantile plot, for the example data of Section 3.10.3.4, is shown in Figure E.5.
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Figure D.5 Quantile plot for example Class 2 exterior survey unit.
Figure E.5 Quantile plot for example Class 2 exterior survey unit.

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A quantile-quantile plot is extremely useful for comparing two sets of data. Suppose the following 17 concentration values were obtained in a reference area corresponding to the example survey unit data of Appendix E.3.2:

  • 92.1, 83.2, 81.7, 81.8, 88.5, 82.4, 81.5, 69.7, 82.4, 89.7,
  • 81.4, 79.4, 82.0, 79.9, 81.1, 59.4, 75.3.

A quantile-quantile plot can be constructed to compare the distribution of the survey unit data, Yj, j=1,…n, with the distribution of the reference area data Xi , i=1,… m. (If the reference area data set were the larger, the roles of X and Y would be reversed.) The data from each set are ranked separately from smallest to largest. This has already been done for the survey unit data in Table E.8. For the reference area data, the results in Table E.9 are obtained.

Table E.9 Ranked reference area concentrations.

Data: 59.4 69.7 75.3 79.4 79.9 81.1 81.4 81.5 81.7 81.8
Rank: 1 2 3 4 5 6 7 8 9 10
Data: 82.0 82.4 82.4 83.2 88.5 89.7 92.1
Rank: 11 12.5 12.5 14 15 16 17

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The median for the reference area data is 81.7, the sample mean is 80.7, and the sample standard deviation is 7.5.
For the larger data set, the data must be interpolated to match the number of points in the smaller data set. This is done by computing

v1 = 0.5 (n/m) + 0.5 and vi+1 = vi +(n/m) for i = 1, … m-1 ………………………………….. (E-9)

where m is the number of points in the smaller data set and n is the number of points in the larger data set. For each of the ranks, i, in the smaller data set, a corresponding value in the larger data set is found by first decomposing vi into its integer part, j, and its fractional part, g.

Then the interpolated values are computed from the relationship:

Zi = (1-g) Yj + g Yj + 1 ………………………………………………………………………… (E-10)

The results of these calculations are shown in Table E.10.

Table E.10 Interpolated ranks for survey unit concentrations

Rank 1 2 3 4 5 6 7 8 9 10
vi 1.09 2.26 3.44 4.62 5.79 6.97 8.15 9.33 10.50 11.68
Zi 74.3 75.7 76.8 77.5 78.1 79.1 80.9 83.7 84.3 85.8
Xi 59.4 69.7 75.3 79.4 79.7 81.1 81.4 81.5 81.7 81.8
11\<.
|<. Rank
11 12.5 12.5 14 15 16 17
vi 12.85 14.03 15.21 16.38 17.56 18.74 19.91
Zi 86.4 86.5 87.8 89.1 90.2 90.6 92.3
Xi 82.0 82.4 82.4 83.2 88.5 89.7 92.1

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Finally, Zi is plotted against Xi to obtain the quantile-quantile plot. This example is shown in Figure E.6.

The quantile-quantile plot is valuable because it provides a direct visual comparison of the two data sets. If the two data distributions differ only in location (e.g., mean) or scale (e.g., standard deviation), the points will lie on a straight line. If the two data distributions being compared are identical, all of the plotted points will lie on the line Y=X. Any deviations from this would point to possible differences in these distributions. The middle data point plots the median of Y against the median of X. That this point lies above the line Y=X, in the example of Figure E.6, shows that the median of Y is larger than the median of X. Indeed, the cluster of points above the line Y = X in the region of the plot where the data points are dense, is an indication that the central portion of the survey unit distribution is shifted toward higher values than the reference area distribution. This could imply that there is residual radioactivity in the survey unit. This should be tested using the nonparametric statistical tests described in Section 3.10.
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Figure D.6 Example quantile-quantile plot.
Figure E.6 Example quantile-quantile plot.

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Further information on the interpretation of Quantile and Quantile-Quantile plots are given in EPA QA/G-9 [EPA-1996d].