Essential Mathematics and Statistics for Science, 2nd Edition
Graham Currell and Antony Dowman, John Wiley & Sons, 2009

Study Guide:     Experiment/Research Design

When planning a new experiment or embarking on a research project, you will need to consider a wide range of issues.
This page prompts you with some relevant questions, and then directs you to section references or video answers in the book (e.g. 9.4.1, Q9.2), to additional digital support on this website (e.g. Excel2007, Common Statistical Tests), or to other useful sources.

Main Issues:

Types of experimentation and research
Type and distribution of data
Linear / non-linear relationships
Handling variations / uncertainties
Design of the experiment and selection of statistical tests/analyses
Presenting data/results

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Types of experimentation and research

As a student, you will (hopefully) encounter a wide range of experimental science over your period of study, starting with simple pre-planned experiments, but then leading to extended 'research' projects or 'case studies'.

When it becomes your responsibility to plan the experimental work and the analysis of results, you must first step back and get an overview of the main elements of the proposed experiment/research:-

Are you going to test a hypothesis? - see Chapter 9
 - a hypothesis test usually involves a Yes/No question - e.g. "Does the speed of reaction increase with temperature?"
- not all research projects involve a hypothesis - e.g. you may already know that "the speed of reaction" does increase with temperature and your project is to measure the rate of this increase.
If you are  testing a hypothesis you will need to understand:
- p-value (9.3, Q9.2), 1 or 2 tailed/sided (9.4.3, Q9.1), types of errors (9.4.4), power of an experiment (9.4.5)

Will you be recording the changes that occur in a system (e.g. concentration) due to changes in some external factor?
 - these might also be measurements that provide the data to test a hypothesis.
In any measurement, you will need to be clear about:
- the type of data variables that you are measuring - see Type and distribution of data
- how you will handle variations in your data - see Handling variations / uncertainties


Type and distribution of data

You need to understand your data so that you can make the correct selection of statistical test(s) to be used.

What type of data will you be measuring? - see Ch 2.Overview

 - discrete/continuous, nominal/ordinal, parametric/non-parametric (9.5.2),
frequency/proportion (Ch 14.Overview)

Do you expect your measured data to follow a specific distribution? - see Ch 8.Overview

 - normal (8.1), binomial (8.4), Poisson (8.4.4). See also 8.4.7, 8.4.8

For data transformation into a normal distribution -  see Data Transformation

Linear / non-linear relationships

Do you expect your data to follow a linear relationship? - see 4.2

 - do you need to calculate the ‘best-fit’ slope and intercept? - see 4.2, Q4.20, Q4.21, 13.2

To calculate Slope and Intercept in Excel - see ‘Regression’ worksheet in ‘X-Y Graphs’ for  Excel2007 or Excel2003

Non-linear data (e.g. exponential decay), can be transformed into a linear relationship for analysis
 - see 4.3, Q4.24, 5.2.6, Q5.27

To use Excel to linearise and analyse exponential data - see ‘Linearisation’ worksheet in ‘Logarithms and Exponentials’ for  Excel2007 or Excel2003


Handling variations / uncertainties

Are the data variations in the measurement process itself or in the systems that you are measuring?
- see 1.2, 8.2.1, 8.2.2, Q8.4

Do you need to calculate -


sample mean, standard deviation (7.2.4, 7.2.5, Q7.7) ?

- standard error/uncertainty, confidence interval (8.2.3, 8.3.2, 8.2.4, Q8.7) ?
- median and interquartile range (7.1.2, Q7.1) ?
- the uncertainty in a linear calibration line (13.3, Q13.4) ?
- the effect of combining uncertainties/errors (8.3.3, Q8.9, Q8.10) ?

To use Excel for basic statistics
- see 'Functions' worksheet in ‘Statistics Intro’ for  Excel2007 or Excel2003

To add error bars in Excel X-Y graphs
- see ‘Error Bars’ worksheet in ‘X-Y Graphs’ for  Excel2007 or Excel2003


Design of the experiment and selection of statistical tests/analyses

The design of the experiment and the selection of the statistical test or analysis are highly interdependent, and should be considered together.

What are the main sources of variation and uncertainty in your measurements,
e.g random and systematic errors?
 - see  15.1.1

 - it is important to be clear about the data being measured (outcomes) and factor levels (inputs) that affect the system being studied -  see 9.1

The major principles of experiment design  - are given in Ch 15.

For the selection of common statistics tests - see 9.5, Table of Common Statistical Tests

In selecting the appropriate statistical test / analysis, it is necessary to ask - see 9.5

 - what is the data type being measured, e.g. parametric, ordinal?
- what assumptions can be made about its distribution, e.g. normal?
- what is the statistic to be calculated or tested, e.g. sample mean, proportion?
- what factors affect the measured data, e.g. two factors plus an interaction?

For the use of software to perform statistical tests - see

 - common statistical tests using Minitab - Video Examples
- data analysis files using Excel for parametric tests (Excel2007, Excel2003),
chi-squared Tests (Excel2007, Excel2003) and ANOVAs (Excel2007, Excel2003)


Presenting data/results

Graphical presentations of replicate data - see 7.1

 - boxplots for raw data - see 7.1.2, Q7.3
- confidence intervals - see 8.2.4, Q7.3
- presenting uncertainty - see 8.3

Graphical presentation of X-Y data using Excel
- see ‘X-Y Graphs’ worksheet in ‘X-Y Graphs’ for  Excel2007 or Excel2003

To draw a ‘best-fit’ trendline of regression in Excel
- see ‘Trendline’ worksheet in ‘X-Y Graphs’ for  Excel2007 or Excel2003

To add error bars in Excel X-Y graphs
- see ‘Error Bars’ worksheet in ‘X-Y Graphs’ for  Excel2007 or Excel2003

For factor plots from ANOVA calculations - see Q11.5


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