# Differences

This page will support you in satisfying Writing Learning Outcome:

ANALYSIS - Analyze lab data using comparative methods.

## Learning Objectives

You should be able to:

Quantify differences using absolute and relative means

Explain potential sources of differences depending on the goals of secondary sources

## Why do we calculate differences?

Differences are at the heart of engineering experimentation. We often want to compare the results of an experiment to an expected value, which could be

a published design value like a material strength or resistor rating,

the result of a previous measurement

the result of some sort of benchmark test

a value calculated using a mathematical model or based on a scientific theory or law

The source of the difference we calculate will depend on the nature of both the expected value and the way we conducted the experiment.

## How do we calculate differences?

A difference is simply one number minus another. We usually compare a measured value and an expected value. The expected value is the basis for the difference, so we would subtract it from the measured value.

### Absolute Difference

For example, if the design yield strength of A36 steel is reported to be 36 ksi, but we measure the yield strength to be 53 ksi, the difference is 53 - 36 or 17 ksi. The fact that this difference is positive tells us that the measured value is greater than the expected value.

Difference = Measured Value - Expected Value

### Relative (Percent) Difference

Very often, it is useful to express differences in relative terms, usually relative to the expected value because it is the basis for the difference. So, we divide the difference by the expected value:

Percent Difference = [ (Measured Value - Expected Value) / Expected Value ] x 100% = [ Difference / Expected Value ] x 100%

In the yield strength example, the percent difference would be

[ (53 - 36) / 36 ] x 100% = [17 / 36 ] x 100% = 47%

We can use the relative difference to support a claim that the difference is significant. In this case, a 47% difference is large and we should attempt to explain such a large difference.

## How do we explain differences?

The explanation of differences is the primary objective of a lab report and is often offered in the discussion section. In some cases, the source of a difference is error and we can posit the reasons for that error. The analysis - error page goes into greater depth on this. However, in some cases, the reason for a difference is based on the nature of the expected value. In the case of the yield strength example, it is sensible that measured values of yield strength would be greater than a design yield strength, because the design yield strength is intended for design. It is not an average value. Otherwise, half of all designs using it would fail. So, it is intentionally a conservatively low value and we should expect measured yield strengths to be higher. Examining the nature of expected values is therefor very important if we are going to explain a difference. We delve into this further in the analysis - simple statistics page.

## Common Mistakes

Using a measured value as the basis for a difference or percent difference calculation

Assuming an expected value is an average value, rather than a value intended for design

## References

Vardeman & Jobe (2023) Basic Engineering Data Collection and Analysis (a free open educational resource)