# Error Analysis

All scientific reports must contain a section for error analysis. The purpose of this section is to explain how and why the results deviate from the expectations.

Error analysis should include a calculation of how much the results vary from expectations. This can be done by calculating the percent error observed in the experiment.

Percent Error = 100 x (Observed- Expected)/Expected

Observed = Average of experimental values observed

Expected = The value that was expected based on hypothesis

The error analysis should then mention sources of error that explain why your results and your expectations differ. Sources of error must be specific. "Manual error" or "human error" are not acceptable sources of error as they do not specify exactly what is causing the variations. Instead, one must discuss the systematic errors in the procedure (see below) to explain such sources of error in a more rigorous way. Once you have identified the sources of error, you must explain how they affected your results. Did they make your experimental values increase or decrease. Why?

One can classify these source of error into one of two types: 1) systematic error, and 2) random error.

## Systematic Error

Systematic errors result from flaws in the procedure. Consider the Battery testing experiment where the lifetime of a battery is determined by measuring the amount of time it takes for the battery to die. A flaw in the procedure would be testing the batteries on different electronic devices in repeated trials. Because different devices take in different amounts of electricity, the measured time it would take for a battery to die would be different in each trial, resulting in error.

Because systematic errors result from flaws inherent in the procedure, they can be eliminated by recognizing such flaws and correcting them in the future.

## Random Error

Random errors result from our limitations in making measurements necessary for our experiment. All measuring instruments are limited by how precise they are. The precision of an instrument refers to the smallest difference between two quantities that the instrument can recognize. For example, the smallest markings on a normal metric ruler are separated by 1mm. This means that the length of an object can be measured accurately only to within 1mm. The true length of the object might vary by almost as much as 1mm. As a result, it is not possible to determine with certainty the exact length of the object.

Another source of random error relates to how easily the measurement can be made. Suppose you are trying to determine the pH of a solution using pH paper. The pH of the solution can be determined by looking at the color of the paper after it has been dipped in the solution. However, determining the color on the pH paper is a qualitative measure. Unlike a ruler or a graduated cylinder, which have markings corresponding to a quantitative measurement, pH paper requires that the experimenter determine the color of the paper to make the measurement. Because people's perceptions of qualitative things like color vary, the measurement of the pH would also vary between people.

Random error can never be eliminated because instruments can never make measurements with absolute certainty. However, it can be reduced by making measurements with instruments that have better precision and instruments that make the measuring process less qualitative.