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19 h apparent HRT 14 h apparent HRT<br />

n = 21 n = 16<br />

Alkalinity values Alkalinity values<br />

inflow sample time inflow outflow inflow sample time inflow outflow<br />

5/27/03 10:00 254.0032 299.3122 5/27/03 10:00 254.0032<br />

5/27/03 11:00 202.1441 5/27/03 11:00 202.1441<br />

5/27/03 12:00 185.905 280.0952 5/27/03 12:00 185.905<br />

5/27/03 13:00 173.9968 285.2678 5/27/03 13:00 173.9968<br />

5/27/03 14:00 171.2507 278.0478 5/27/03 14:00 171.2507<br />

5/27/03 15:00 169.1991 269.519 5/27/03 15:00 169.1991 299.3122<br />

5/27/03 16:00 162.359 266.4764 5/27/03 16:00 162.359<br />

5/27/03 17:00 254.2003 271.4025 5/27/03 17:00 254.2003 280.0952<br />

5/27/03 18:00 203.4527 5/27/03 18:00 203.4527 285.2678<br />

5/27/03 19:00 187.6578 249.3755 5/27/03 19:00 187.6578 278.0478<br />

5/27/03 20:00 181.7426 268.7387 5/27/03 20:00 181.7426 269.519<br />

5/27/03 21:00 179.8516 261.2244 5/27/03 21:00 179.8516 266.4764<br />

5/27/03 22:00 171.4792 272.247 5/27/03 22:00 171.4792 271.4025<br />

5/27/03 23:00 174.3711 275.0962 5/27/03 23:00 174.3711<br />

5/28/03 0:00 175.9694 276.4672 5/28/03 0:00 175.9694 249.3755<br />

5/28/03 1:00 173.6886 262.5183 5/28/03 1:00 173.6886 268.7387<br />

5/28/03 2:00 163.8433 275.574 5/28/03 2:00 163.8433 261.2244<br />

5/28/03 3:00 146.4356 265.2663 5/28/03 3:00 146.4356 272.247<br />

5/28/03 4:00 149.2014 276.5242 5/28/03 4:00 149.2014 275.0962<br />

5/28/03 5:00 164.3512 299.0592 5/28/03 5:00 164.3512 276.4672<br />

5/28/03 6:00 286.8892 5/28/03 6:00 262.5183<br />

5/28/03 7:00 208.4026 338.1573 5/28/03 7:00 208.4026 275.574<br />

5/28/03 8:00 293.6795 300.4317 5/28/03 8:00 293.6795 265.2663<br />

5/28/03 9:00 282.7434 286.2702 5/28/03 9:00 282.7434 276.5242<br />

299.0592<br />

286.8892<br />

338.1573<br />

300.4317<br />

286.2702<br />

Figure A4. 2: Construction <strong>of</strong> data tables for correlation <strong>analysis</strong> for 19 h and 14 h apparent<br />

hydraulic retention time. Dot-dash lines indicate the data sets to be compared.<br />

The correlation co-efficient r for each combination set was calculated according to Eq. A4- 2 (Davies<br />

and Goldsmith, 1977):<br />

r =<br />

∑<br />

n<br />

∑<br />

i<br />

n<br />

i<br />

n<br />

( x − x)<br />

( y − y)<br />

∑<br />

n<br />

2<br />

( x − x)<br />

( y − y)<br />

i<br />

i<br />

i<br />

∑<br />

i<br />

i<br />

i<br />

2<br />

203<br />

Eq. A4- 2<br />

Where xi and yi are values from the two data sets (x and y) to be compared and x and y are<br />

the average values <strong>of</strong> each <strong>of</strong> the data sets.<br />

The significance <strong>of</strong> the correlation coefficients describes the probability that two data sets are<br />

correlated and was calculated from a Student’s t-distribution: the t-statistic is determined from<br />

Eq. A4- 3, and the probability P was determined from the associated t-distribution with the appropriate<br />

number <strong>of</strong> degrees <strong>of</strong> freedom using Excel’s TDIST function for a 2-tailed application.<br />

t =<br />

2<br />

r φ<br />

2<br />

1 + r<br />

where φ is the degree <strong>of</strong> freedom and equals n-2.<br />

Eq. A4- 3

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