# Analysis

ANALYSIS - Analyze lab data using appropriate methods (statistical, comparative, uncertainty, etc.).

## Engineers Analyze Data to Learn!

All engineering laboratory work is conducted for one reason and one reason only: to learn something. The process of analyzing laboratory data is the process by which engineers make sense of measured data. It is how engineers learn something totally new, never before known by anyone – or at least not known to the same degree. As a student of engineering, you should have the same experience – you should learn something about how the world works when you analyze experimental data.

## Learning Objectives

You should be able to analyze lab data using appropriate methods (statistical, comparative, uncertainty, etc.).

The links at bottom of the page explain specific skills in greater detail.

## What is Meant by Data Variability (Error) and What Causes It?

When engineers perform a laboratory test, they are in essence asking the natural world to give them an answer to their engineering question. Engineers would like to have precise and consistent answers to questions; however, all engineering data has variability. In other words, when we repeat an experiment, we hope to get precisely the same results but usually do not. Variability, or error, in data is caused by variations in the test conditions, test specimens, measurement devices, multiple operators, etc. For example, the ambient temperature in the room may change enough during testing to affect the data. Some definitions of commonly used terms will help you write about differences you identify in your data.

## What is the Role of Statistics in Analyzing Data?

Variability that is inherent in all engineering data can result in a lack of clarity for engineers attempting to reach a conclusion – it may not be obvious what the natural world is telling us. Statistical analysis allows engineers to make sense of variability.

## Definitions

There are many terms used to describe features of measured values. If you are writing about values that you measure, it is important that you understand the definitions and differences.

Difference - a measured value minus a known or published value: measured-known

Percent Difference - the difference of a measured value and known value divided by the known value: [(measured-known)/known][100%]

Accuracy - the degree to which the result of a measurement, calculation, or specification conforms to the correct value or a standard.

Precision - refinement in a measurement, calculation, or specification, especially as represented by the number of digits given.

Error - a measure of the estimated difference between the observed or calculated value of a quantity and its true value. Can have components that are systematic (repeatable) and random. You can learn more here

Uncertainty - the fact of not being known precisely or clearly determined. Also known as random error, it can be quantified using statistical measures like standard deviation or variance.

Bias - a repeatable or systematic error that can have a rational explanation.

Trend - the mathematical relationship between two variables (e.g. linear, quadratic, logarithmic, etc.).

## Analysis Skills

The following links go into greater detail:

Working with simple statistics like average and standard deviation.

Plotting and describing the relationships between independent and dependent variables (trendlines).

Comparing values and quantifying errors and differences.

Determining how the precision of independent measurements influences the accuracy of a calculated result (aka propagation of error).

Each of these topics is treated here in order of increasing difficulty because these are key features of data analysis in engineering laboratory reports. You may rely on one or all of them for a given lab.

## References

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

Stephanie Glen. "Probability and Statistics Topics Index" From StatisticsHowTo.com: Elementary Statistics for the rest of us! https://www.statisticshowto.com/probability-and-statistics/ (a free open educational resource)