Quantitative Investigations in the Biosciences using MINITAB

John Eddison

• Publisher: Routledge
• Year: 2017
• ISBN:
  9781351420556
• Edition: 1
• Topic: Mathematics
• Subtopic: Probability & Statistics
• Index: Mathematics

Until recently, acquiring a background in the basic methodological principles that apply to most types of investigations meant struggling to obtain results through laborious calculations. The advent of statistical software packages has removed much of the tedium and many of the errors of manual calculations and allowed a marked increase in the depth and sophistication of analyses. Although most statistics classes now incorporate some instruction in using a statistics package, most introductory texts do not.Quantitative Investigations in the Biosciences using MINITAB fills this void by providing an introduction to investigative methods that, in addition to outlining statistical principles and describing methods of calculations, also presents essential commands and interprets output from the statistics package MINITAB.The author introduces the three basic elements of investigations-design, analysis, and reporting-using an extremely accessible approach that keeps mathematical detail to a minimum. He groups statistical tests according to the type of problem they are used to examine, such as comparisons, sequential relationships, and associations.Quantitative Investigations in the Biosciences using MINITAB draws techniques and examples from a variety of subjects, ranging from physiology and biochemistry through to ecology, behavioral sciences, medicine, agriculture and horticulture, and complements the mathematical results with formal conclusions for all of the worked examples. It thus provides an ideal handbook for anyone in virtually any field who wants to apply statistical techniques to their investigations.

CHAPTER 1

Introduction

1.1 Introduction

In all areas of the sciences, questions are posed and answers are pursued. While some popular fiction would have us believe in inspired and charismatic scientists making discoveries that can change mankind virtually overnight, real examples of inspirational or accidental discoveries (e.g., Röntgen’s discovery of the effects of X-rays on photographic plates) are extremely rare. In fact, the converse is nearer to the truth, most answers being obtained through methodical, lengthy, and, sometimes, exciting endeavour. In short, science does not differ from any other occupation in that it involves its fair share of hard work.

Given that most investigators obtain their results through systematic enquiries, the question arises as to the nature of the system or systems that these ‘normal’ scientists employ. Is there one basic method or are there many? For example, are there any areas of common ground in the way physicists, physiologists, and ecologists approach investigations in their respective spheres of science? And, if there are any general principles of scientific method, what are they? These and similar questions have occupied scientific philosophers for many years (e.g., Popper, 1959; Kuhn, 1970; Hull, 1974). Fortunately, accounts of the work performed by practical scientists, combined with the thoughts and writings of scientific philosophers, have provided us with a methodological framework within which we can conduct rigorous biological investigations. The purpose of this chapter is twofold. The first aim is to introduce these basic principles of investigative methods with their various processes and components, illustrating their application in the biosciences. The second objective of this chapter is to demonstrate the importance within this methodological framework of quantifying our observations.

1.2 The process of conducting an investigation

The big question

Whatever the nature of an enquiry, whether it be general, specific, in the form of an experiment conducted rigorously under laboratory conditions, or general observations in an inhospitable wilderness, the investigator must be aware of the purpose of his or her work. This objective has sometimes been described as the “big question.” Without some known direction or defined aims for the information-gathering process (whether it be experimental or observational), the quality or appropriateness of the data obtained may be inadequate, or possibly even so poor that they are useless. There is also the important, but often ignored, consideration of the motivation of the investigator, which can be influenced considerably by the presence or absence of clearly-defined goals. For example, the prospect of leaving a warm building to spend a day observing animals in the wild with the certainty of returning later thoroughly soaked by rain and quite chilled may instill a certain reluctance in the investigator. While a clear knowledge of the ultimate goal will not make the rain any drier nor the wind any warmer, it may help to increase the observer’s motivation and maintain attention so that data quality is more assured.

The formalisation of key questions is not only confined to studies where the investigator has an element of choice in the subject of the project. In applied investigations, objectives are often determined by a sponsor, but the initial remit may be couched in terms that are not precise enough to be translated directly into an experimental design.

The first principle of any investigation, therefore, is to be able to formalise the aims and objectives in a clear, concise, and unambiguous manner. This may seem to be common sense; it is! However, there is a great temptation to spend insufficient time on this aspect of the project and to proceed with some sort of physical activity. So, remember that thought prior to action will generally not only minimise the energy required to find the answers, but will also reduce the potential for fundamental errors that, in turn, may decrease the value of the project. It is worth adding at this point that all investigations comprise many stages, many of which precede data collection, the latter generally comprising the main physical activity. The requirement for intellectual activity is not confined solely to the development of ultimate goals, and a considerable amount of thought is required before and after any physical action.

The form that questions may take is almost endless. They may be extremely general, such as: What factors influence the vegetational composition of an area of moorland? Or, what changes, if any, take place in blood chemistry when an individual is stressed? Alternatively, the questions could be quite specific. For example, what is the sequence of behaviours that culminates in mating between mallards (Anas platyrhynchos L.)? Or, what is the relationship between grain yield of maize and the concentration of nitrogen in the fertiliser?

All of the above questions are perfectly adequate starting points for an investigation, but they all require further clarification, generating further questions that have to be answered before proceeding on to the next stage.

As an example of the need for clarification, consider the first question concerning vegetational distribution. At what level are we to conduct this investigation? What factors are we going to consider? Are we to confine ourselves to physical factors such as soil characteristics (e.g., pH, soil water content), topography, and climatic conditions? Or might we include an examination of grazing pressure, the effect of soil invertebrates, or trampling by human visitors? To what ultimate ends are the results to be applied (sometimes determined by the financial sponsor of the work)? Do we intend to confine our conclusions to the specific section of the moorland that we have studied? To the entire location? Or to all areas that bear some resemblance to our study area? Clearly, answers to these simple questions will have direct implications on the nature of the data that we will need to collect and also to the manpower, expertise, and equipment required to carry out this project.

The fact that wide-ranging questions need to be made more specific before a project can be started, is no surprise. However, even the more specific questions may need to be reconsidered and clarified to some degree.

Consider the example of mallard pre-copulatory behaviour, or any other sequence of behaviours for that matter. Tinbergen (1963) described four key questions that have to be answered about the level at which we can examine the behaviour patterns.

1. What are the mechanisms (external and internal) that have stimulated the individual to perform the behaviour? What cues initiate the behavioural sequence?
2. How did the behaviour develop in the individual? That is to say, what environmental and genetic factors combined for this behaviour to develop within the individual?
3. What use or survival value does this behaviour serve the individual?
4. How did this behaviour evolve within the species?

These four questions or problems were developed in the context of behavioural research and they illustrate very clearly the need to define the objectives of an investigation at the very outset, showing that a particular phenomenon may be examined at different levels and the central questions of the investigation vary according to the level of interest. Of course, this principle is parallelled in all scientific disciplines.

The level of the problem will be an important factor in determining the detail of the data that will have to be gathered in order to answer the key questions. The mallard example illustrates this point well. If we were interested in the evolutionary development of the displays of this duck, we would not need to obtain a detailed knowledge of the neural anatomy of the visual system even though vision would be an important sensory system in the courtship displays.

Without well-defined aims, the investigator will not be able to determine what data to gather, and this may lead to investigations being conducted that either may not be able to provide the answers that are sought, or that might provide perfectly correct answers to quite different questions. In answering questions, all scientific investigators try to be as objective and as unambiguous as possible. In order to achieve these aims, it is necessary to couch both the problem and the solution in quantitative terms. This necessarily requires the scientist to become conversant with the different types of problems and quantitative measurements that can be applied to his or her field of study. Therefore, there is a need to define, in quantitative terms, the particular problem under examination because it is only with such a specification that we can ensure that a study is performed successfully. Moreover, if it were possible to produce a simple categorisation of basic problem types, this would be a very useful tool that could be employed at the start of any investigation.

Problem types

At first sight, classifying the great diversity of biological problems into a small number of categories may seem to be an overwhelming task. How could we devise general headings across such different topics as molecular biology, physiology, biomechanics, and ecology? In fact, a basic classification of problem types can be constructed that cover many scientific disciplines (not just biology) and this is just one example of all branches of science being unified. Later in this chapter, the principles of hypothesis testing, which also apply throughout science will be introduced.

Throughout the biological and medical sciences, researchers need to perform comparisons. For example, are the hairs of reindeer thicker than those of tropical deer? Are the red blood cell counts of Peruvian inhabiting the high Andes different from those living at lower altitudes? Is the level of Cortisol produced by the adrenal glands of sows in one husbandry system different from that of similar sows kept in an alternative housing regime? Furthermore, the comparisons do not have to be restricted to two groups. We might wish to compare three or more similar groups simultaneously, such as the effect of several different pest control measures on the yield of crops infested by aphid (the groups might include several concentrations of a pesticide as well as an organic method of aphid control), or the effectiveness of several drugs or treatment regimes in combatting a specific disease. Alternatively we may have a single set of measurements that we wish to compare against an independent prediction. For example, we might wish to establish whether the mean dissolved oxygen content of a series of water samples falls within a specified acceptable range. In all of these comparisons, whatever variables are compared, the principles of the questions posed are the same. Is X bigger than Y? Or is there any difference between a, b, and c?

Many investigations require the simultaneous measurement of two variables on a series of individuals (or subjects). For example, we may wish to examine the effect of the concentration (or dose) of a drug on the blood pressure (response) of human patients, or perhaps the relationship between bone length and age in a species of mammal. Both of these examples incorporate the notion of cause and effect: drug concentration exerting an effect on blood pressure, and body size as measured by bone length being dependent upon age (at least in early life). Allied to this sort of problem are those that also examine the simultaneous variation in two or more variables on a series of subjects but do not contain any reference to a cause and effect relationship Examples of such relationships include the height and weight of humans, and the bill length and depth of fulmars (Fulmarus glacialis L.). The latter relationship is used to differentiate between the sexes of this Northern Hemisphere seabird using a technique called discriminant analysis. These types of problems, with or without any implicit notion of cause and effect, can be summarised by the following question: Is a high value of X associated with values of Y that are high, low, or is there no consistent pattern to the relationship between X and Y? These problems examine relationships over a sequence or range of values, and, for want of a better term, I shall refer to them as problems of sequential relationships.

Table 1.1 Presence/absence of two species: measured as frequency of occurrence in a quadrat survey.

		Species A
		Present	Absent	Total
	Present	16	40	56
Species B	Absent	35	15	50
	Total	51	55	106

Both groups of problems described so far are based upon numerical measurements of various kinds. Qualitative data, on the other hand, are often concerned in problems of association. For example, animal and plant ecologists are often interested in the coexistence or mu...