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Statistical Analysis of pH Values Obtained from Wildlands

Since pH is a measure of the hydrogen ion concentration of water and influences chemical reactions of all types in soils, waters, and animal and plant tissues, it is useful to analyze it.

Often analyses are done with pH values, treating them as conventional cardinal values, "indices" to acidity. It may be reasonable, though, to do analyses on the hydrogen ion values, not their transformation. For example, since one unit above a pH value is not equal to one unit below the same pH value, some analyses may be inappropriate. When analyses are done on actual hydrogen ion concentration (or reported pH transformed) then many conventional statistical analyses can be appropriately used.

The stream or pond pH values for three sites might be reported as 5.2, 5.4, and 5.9.

The proper average or mean value is not 5.5 but 5.41. The average is obtained by computing 1/x where x is the pH value and the negative hydrogen ion concentration expressed as an exponent, base 10.

Thus, in the above example,
c = 1/105.2
c = 1/EXP (x / 0.43429448)
c = 1/EXP (5.2 / 0.43429448)
c = 1/158489.2
c = 1/158489.2 = 6.3096 x 10-6

Repeating this procedure,
when pH = 5.2 then c = 6.31 x 10-6
when 5.4 then c = 3.98 x 10-6
when 5.9 then c = 1.26 x 10-6

The average concentration is thus
c = 3.85 x 10-6
and average pH is 5.41.

The standard deviation of the above 3 numbers (c) is 2.53 x 10-6.

Estimating the limits on an estimate of the mean, one standard deviation on each side, results in
upper limit 3.85 x 10-6 - 2.53 x 10-6 = 3.32 x 10-6
thus a pH of 5.88

lower limit 3.85 x 10-6 + 2.53 x 10-6 = 3.38 x 10-6
thus a pH of 5.20.

The pH values are thus between 5.20 and 5.88 about two-thirds of the time. The mean of 5.41 may be useful. When pH values range widely (e.g., 5, 6, and 7 as in mine land soil) the distribution is very asymmetrical and using the standard deviation may be inappropriate.

The BASIC program PONDff1.BAS (DOS) may be useful to some readers.

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