Statistics in Psychology

Explanations without Equations

Stephen Jones

• Publisher: Bloomsbury Academic
• Year: 2010
• Print ISBN:
  9780230247499
• Edition: 1
• eBook ISBN:
  9781350312517
• Topic: Psychology
• Subtopic: Research & Methodology in Psychology
• Index: Psychology

How do you choose the appropriate statistical method for any given research task? What are the features that discern one statistical method from another, and for which research projects are they appropriate to use? Written specifically with the undergraduate psychology student in mind and for those who desire an explanation for the use of statistics in psychological research without the mathematics, this refreshing and much-needed introduction is invaluable for any psychology students who 'don't get numbers'. Breaking away from the traditional, numerical approaches, Jones delivers an engaging and insightful read into the rationale behind the use of statistics, drawing upon non-numerical examples and scenarios from both psychological literature and everyday life to explain key statistical concepts. Learn about the methods for testing populations and samples, standard errors, inferential and descriptive statistics as well as variables and participants. This is an ideal companion to core textbooks and will serve a clearer understanding of statistical methods in psychology. By reading this book students can hope to gain a better sense of what makes empirically valid research and learn to critically evaluate facts and figure in any presented research. The foundations of psychology's claims are the empiricism of well-conducted and reliable data.

CHAPTER 1Variables and participants

Almost all research in Psychology – and thus the collection and analysis of psychological data – is based on the concept of variables. A variable in the simplest sense is something that can change; in other words, something that varies! It is a factor, characteristic or feature which can vary over time, or between situations or between people. In psychological research, the term variable usually refers to a feature upon which people can be assessed either in terms of some form of category (such as whether a person is married or single, or is employed or unemployed) or some form of value (e.g. that person’s height, weight, exam results, or the time he or she takes to respond to a stimulus in a reaction time experiment).

As is the case with each of the above examples, all variables need to have more than one potential value in order for them to vary. Marital status, for example, needs to consist of the above two categories – or potentially even more, such as divorced or widowed – while a person’s percentage score on an exam could take any one of a hundred different values. A characteristic or factor which does not have more than one possible value cannot really be treated as a variable and must be considered to be a constant.

Variables are generally classified in the following manner:

•Independent: The variable which is intentionally changed or manipulated by a researcher in order to determine the effects (if any) which this may have on the dependent variable.

•Dependent: The variable which is measured by a researcher, and which may (or may not) change as a result of the manipulation of the independent variable.

•Control: The variable which is held constant, so that the researcher can have a greater degree of certainty that changes in the dependent variable are indeed due to changes brought about in the independent variable, rather than changes in any other factors which may influence the result.

•Confounding: Any variable which is not being manipulated or controlled, but which may have an impact on the measurement of the dependent variable. Such a variable is largely beyond the influence of the researcher.

For example, if we were to conduct a study investigating how exposure to aggressive images can influence young people’s attitude toward the punishment of violent crime, we could construct scales to measure such attitudes and administer these to research participants before and after we had shown them a series of such aggressive images. We would then compare the before and after ratings to determine if there were any significant differences between the two.

Although very simple, this example is useful as an illustration of the aforementioned four types of variables. The dependent variable being measured here is the participant attitude toward punishment, as represented by the attitude scales being administered, while the independent variable being manipulated by the researcher takes the form of the actual exposure to the images. The main control variable being held constant in this scenario is that of age (as the study is concerned with the attitudes of young people), although in reality many other factors would be controlled for also. Finally, the confounding variables here could take many forms – just one example would be the uncontrolled exposure to aggressive images outside the study (e.g. the extent to which participants are exposed to such images on an everyday basis from sources such as newspapers and TV).

This classification of variables is essential for conducting research, as we need to have a clear understanding of just what it is that we are measuring, manipulating or holding constant – particularly with more complex research investigations. Further classification of how each of these variables can be measured, that is, their ‘level’ of measurement, is just as important for the purposes of effective data analysis. This will be outlined in the section below.

1.1Variables and their measurement

1.1.1Concepts

There are two ways in which variables are normally classified. The first refers to the level of measurement, which determines the degree of information available within the variable and the kinds of arithmetic operations that can be performed upon it. The level of measurement of variables in psychology is usually via the ‘nominal’, ‘ordinal’ and ‘scale’ categorization. The second approach to classifying variables refers to the relationship between different scores on that variable, that is, whether the variable is ‘discrete’ or ‘continuous’.

Although these two aspects of variables are relatively straightforward, it is vitally important that they are fully understood from the outset as they form the basis of much of the rest of this book. In order to correctly interpret the results of any statistical test or procedure, such as those discussed in later chapters, we need to be sure that the correct test or procedure is used – the choice of this test being directly based on the nature of the variable being studied. Some procedures which are suited for use with continuous data need not be suitable for data defined as discrete. Similarly, some procedures used with data of a scale level of measurement should not be used with data which are classed as a nominal variable. To do so would simply result in the wrong results and with incorrect conclusions being drawn.

Nominal, ordinal and scale

There are generally considered to be three levels of measurement used in psychological research, known as ‘nominal’, ‘ordinal’ and ‘scale’. With nominal measures, we are able to categorize participants according to their differences, but we cannot say to what extent or to what degree they differ. Similarly, we cannot rank them or place them in any form of order. The term nominal is derived from the word ‘name’, and this is essentially all we can do with this form of variable – that is, name the variable and then count how often we can apply that ‘name’ to participants. Ordinal measures provide additional information to that of nominal, as they permit the ordering of individual scores. We are able to not only differentiate cases from one another, but to also place these in an increasing or decreasing order. Scale data adds to that of ordinal data, as it incorporates additional information regarding the degree of difference between individual items within a set or group. In the case of scale data, we can place each score precisely along a given scale, and determine exactly the size of the intervals between those scores. It is due to this equidistant nature of the scale of measurement that we can also add, subtract, average and generally manipulate the data in ways which are simply not possible with the aforementioned nominal and ordinal levels of measurement.

Discrete and continuous

In addition to the levels of measurement approach to categorization, variables can also be classified by referring to the relationship between the data or scores which are collected. This relationship takes one of two essential forms – that which is based on either a ‘discrete’ or ‘continuous’ scale. A discrete scale is one in which individual scores are independent of one another, and which involve only ‘whole’ numbers. Scores on a continuous scale, however, can be situated anywhere along a continuum, and can take the form of not only whole numbers, but also of fractions.

The discrete and continuous aspects of variables and their measurement are usually considered alongside the aspects of nominal, ordinal and scale rather than separately. By considering both of these aspects together, we are better able to fully appreciate the nature of the variable under investigation, and to then select the most appropriate method by which it should be analysed. It may be useful to consider the following rules of thumb concerning the relationship between the two aspects – (1) nominal data will always be discrete, (2) ordinal data will always be discrete, (3) scale data may be either discrete or continuous.

It may be worth adding here that measurements taken of a continuous variable are considered as approximations, at least in the way that they are reported – in other words they are ‘rounded up’ to the required number of decimal places. For example, a reaction time of 352.5505 ms may be rounded to 352.551, or 352.55, or 352.6, or 353, depending on the degree of accuracy required. A discrete variable, on the other hand, is more definite and does not normally require this rounding up procedure. For example, the recall of ten items in a memory test is just that – ten items – and needs no further approximation or adjustment.

1.1.2Everyday examples

One of the most frequently used classifications in psychological research, and also a categorization of people that we tend to use on an everyday basis, is that of the sex of the participants in a given study. This is usually denoted as M or F for obvious reasons. This is the classic textbook example of a nominal level of measurement, along with other – often sociodemographic – factors such as married or single, and employed or unemployed. Such variables are considered to be nominal as they are mutually exclusive (one cannot be simultaneously married and also single), and as they offer no indication of order (one cannot say that married is ‘higher’ than single, or that indoors is ‘lower’ than outdoors).

One of the most important features to remember when dealing with nominal data is that it is just that – nominal (i.e. not numerical). This can sometimes be overlooked when numbers rather than letters are used to indicate categories. Although men and women are often classed or coded in research as ‘Category M and Category F’, this could just as easily be coded as ‘Category 1 and Category 2’. In such cases, even though numerical codes are used, we are still restricted to simply counting the number of cases in Category 1 and Category 2. We cannot, for example, add one to the other and create Category 3! Similarly, it is still just as meaningless to regard one category as higher or lower than another. Taking a sporting example, we can see that the use of shirt numbers is used to distinguish the eleven members of a football team, but based on this alone it is meaningless to say that player number eight is higher or better than player number five.

Just as with the nominal data variable of ‘sex’, there are a number of classic textbook examples of the ordinal level of measurement. Perhaps the most frequent of these is the ‘running in a race’ analogy – or more precisely, the ‘first past the post’ analogy. If we were to stand near the finishing line of a race at its closing moments we may see the winner, the runner up, the runner in third place and so on, but the exact differences in finishing times between these three would be unknown without the use of a stopwatch. Indeed, whatever the time differences between the first, second and third position may be, they will still attain the status of first, second and third. Similarly with the results of a UK general election, we tend not to pay much attention to the number of votes cast, but we do know soon enough who forms the government, the opposition and who takes the third party position, regardless of the differences in the number of votes between them. The main point here is that, with ordinal data, there is no information of the distances between points on a scale – we simply know the order of those points, just as with the order of runners in a race or political parties in a general election – and furthermore that we cannot assume the distances between those points to be equal.

Ordinal measures may thus indicate the position of an individual in relation to others in that group, but because the data indicates order only and cannot assume equidistance, certain arithmetic decisions would be meaningless. For example, we cannot add first and second place to make third place! Furthermore, because we cannot know the size of the gaps between each person in the race, we can say nothing about how much faster one was than the others.

Ordinal data is most often found in psychological research in areas such as attitude measurement, where a participant indicates his or her position on an issue on a scale of, say, one to five (where one would indicate strongly disagree, five indicates strongly agree, and the numbers between indicating points between these two extremes). It may be tempting for researchers to manipulate these data (ones, twos, threes and so on) by adding, subtracting or averaging, but it should really be remembered that these are still numerical codes assigned to categories, rather than actual numbers, and therefore that such manipulation should be avoided.

In terms of scale data, a useful example can be found in psychological experiments on reaction time. As reaction time (and time in general) is measured on an equidistant scale, we can say that the interval between 310ms and 313ms is the same as that between 303ms and 306ms. This is due to the duration of the 3ms difference in each case always being the same. This is in contrast to ordinal data, where the length of the gap between the third and the sixth persons past the post may be very different from the gap between the tenth and thirteenth persons past the post (even though there is the same ‘distance’ of three persons in each case).

Reaction time experiments also offer us an example of a continuous level of measurement, as their results are recorded along a continuous scale. Similarly, measurements of height and weight are also recorded along a continuous scale of measurement. In practice this is clearly visible when there are numbers to the right of the decimal point, such as with a reaction time of 320.25 seconds, or a participant’s weight being measured at 82.43 kilograms, or their height being recorded as 1.78 metres.

Discrete variables, on the other hand, will have no such fractional values or numbers to the right of the decimal point. Simple examples of discrete variables could include classification of family size according to the number of children in a family – this would be considered discrete since it is impossible to physically have one and a half or two and a quarter children. Similarly, data recorded on athletes’ performance in the aforementioned race would also be discrete, as although there may be runners in first second and third position (i.e. positions 1, 2 and 3), there will be nobody recorded as being in position 1.5, 2.5 or 3.768.

One last point to make before we move on to consider actual research studies which illustrate the aforementioned aspects of variables concerns the relationship between the tw...

Table of contents

• Cover
• Title page
• Copyright
• Contents
• List of illustrations
• Preface
• Acknowledgements
• chapter 1. Variables and participants
• chapter 2. Descriptive statistics
• chapter 3. Prelude to testing
• chapter 4. Inferential statistics
• And finally ...
• Appendix
• Glossary
• References
• Answers to self-tests
• Index