# Science & Research

# Volume III - 4.11 Statistics Applied to pH in Canned Foods

| DOCUMENT NO.:
| VERSION NO.:1.4 | ||

| EFFECTIVE DATE: 10/01/2003 | REVISED: 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. Convert each pH value to hydrogen-ion activity (H+), using the equation:

Activity = 10-pH

In Excel, the formula is: =10^(-pH number) - 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. 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.