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Pencil, paper and a scientific calculator are often adequate when analysing small amounts of data. However, spreadsheets are favoured especially when large amounts of data are involved. This chapter explores some of the basic features of spreadsheets and show how they may be applied to the analysis and presentation of experimental data. The Excel spreadsheet program by Microsoft is highlighted due to its availability, power, and longevity. Specific features of Excel are discussed such as the LINEST function for fitting equations, and the Analysis ToolPak which contains a number of useful analysis tools.
Errors in data are a part of life for experimenters in science and engineering. This chapter considers the types of errors, including random and systematic error that can occur during an experiment and methods by which uncertainties arising from such errors can be combined. Many worked examples are included in this chapter, as well as exercises for the student to complete
This chapter is an overview of experimentation and explains why experiments are important. The role of the laboratory notebook for keeping a faithful record of work is emphasised. Guidelines are given for keeping a laboratory notebook. Examples pages from the author's own notebook are included.
This chapter introduces the technique of fitting equations to data using least squares. Both unweighted fitting and weighted fitting are considered. Worked examples are included in the chapter. The technique described can be extended to situations where equations have more than two parameters. Discussion is confined to cases where there is a linear relationship between x and y and the errors in measured quantities are limited to the y quantity.
Graphs are a powerful and concise way to communicate information. Representing data from an experiment in the form of an x-y graph allows relationships to be examined, scatter in data to be assessed and allows for the rapid identification of special or unusual features. A well laid out graph containing all the components discussed in this chapter can act as a 'one stop' summary of a whole experiment. Someone studying an account of an experiment will often examine the graph(s) included in the account first to gain an overall picture of the outcome of an experiment. The importance of graphs, therefore, cannot be overstated as they so often play a central role in the communication of the key findings of an experiment. This chapter contains many examples of graphs and includes exercises and end of chapter problems which reinforce the graph-plotting principles.
This chapter considers the application of computers to data gathering. Computers play a key role in data gathering as well as the analysis and presentation of data derived from experiments. An appreciation of the power and limitations of computers used in this context requires some familiarity with the performance and characteristics of transducers, signal conditioning circuits, and DAQ software. Several options for data gathering are explored, including plug and play systems, the Arduino microcontroller, and smartphones that utilise their on-board sensors.
This chapter considers report writing, posters and oral presentation as means of communicating findings from experiments in science and engineering. Detailed advice is given on report writing supported by specific examples of, for example, how to write an abstract. A full report is included for the student to critique. Example posters are also included. Advice on how to approach oral presentations is included.
Data provide the foundation upon which understanding in science and engineering is built. A basic requirement is that data are expressed in units that are recognised and accepted internationally. This chapter considers the most commonly adopted system of units: The International System of Units. The chapter also considers how to express data, for example using scientific notation. The importance of presenting data clearly in tables is emphasised.
In some situations, it is possible to estimate the size of values likely to emerge from an experiment, prompting our attention to be alerted when the values obtained differ considerably from our estimation. Exploring the reasons for a discrepancy can lead to improved insight of the experiment or perhaps hint that a mistake has occurred, for example when converting units.
No matter how much care is taken during an experiment, or how sophisticated the equipment used, values obtained through measurement are influenced by errors. Errors can be thought of as acting to conceal the true value of the quantity sought through experiment. Random errors cause values obtained through measurement to occur above and below the true value. This chapter considers statistically-based methods for dealing with variability in experimental data such as that caused by random errors. As statistics can be described as the science of assembling, organising and interpreting numerical data, it is an ideal tool for assisting in the analysis of experimental data.