ANALYSIS OF EXPERIMENTAL DATA

2.1 INTRODUCTION 

In an experiment, one major task is to conduct measurements for collecting data. A large number of measurement data can be the direct outcome of experimental work. In general, the more data the better. Statistics is a popular valuable tool for experimentalists to conduct data analysis and eventually draw conclusions from data processing. The mean of a data sample is usually used as the final result for a measurement. The standard deviation of the sample measures the confidence of the final result and is usually used as additional information. In addition, each measurement needs to be independent so that the data set is equally weighed. Statistics may be used in experimental design and plan. Indeed, before conducting an experiment, several aspects need to be considered in preparation, including the selection of apparatus, relevant mathematical correlations, and uncertainty estimate of the final results. Selecting the proper apparatus is essential to any experimental work. For example, temperature measurement requires thermometers. There are several types of thermometers with various ranges and resolutions. A high-resolution apparatus is usually expensive and requires training before use. However, low-resolution apparatuses usually lead to a large standard deviation or uncertainty in the final result. In engineering applications, uncertainty needs to be within tolerance to avoid component mismatch or design failures. Understanding how the apparatus’ resolution is related to the measurement error or uncertainty and how the error or uncertainty propagates to the final value is thus fundamentally important for experimental design, which will be introduced in this chapter.