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U.S. Department of Health and Human Services

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Volume III - 4.11 Statistics Applied to pH in Canned Foods

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Other Laboratory Operations

Food and Drug Administration

DOCUMENT NO.:

III-04

VERSION NO.:1.4

Section 4 - Basic Statistics and Presentation

EFFECTIVE DATE: 10/01/2003REVISED: 01-31-13

pH is a logarithmic measure for the acidity of an aqueous solution. Since pH represents the negative logarithm of a number, it is not mathematically correct to calculate simple averages or other summary statistics. Instead, the values should be converted to hydrogen ion concentrations, averaged, and re-converted to pH values.
The following guidance is provided

  1. 1. Convert each pH value to hydrogen-ion activity (H+), using the equation:

    Activity = 10-pH
    In Excel, the formula is: =10^(-pH number)
  2. 2. Calculate the mean of the activity values by adding the values and dividing the sum by the total number of values. Calculate the standard deviation also from the activity values.
  3. 3. Convert the calculated mean activity back to pH units, using the equation: pH = (-)(log10)(mean H+ activity). Also convert the standard deviation to pH units. In Excel, the formula is: = -LOG10(number)

When the pH values correspond closely, there is not a significant difference between the mathematical mean and the logarithmic mean. As the pH values spread further apart from each other, the difference between the two means become more significant.